An LQ R weight selection approach to the discrete generalized H 2 control problem
|
|
- Matthew Hopkins
- 6 years ago
- Views:
Transcription
1 INT. J. CONTROL, 1998, VOL. 71, NO. 1, 93± 11 An LQ R weight selection approach to the discrete generalized H 2 control problem D. A. WILSON², M. A. NEKOUI² and G. D. HALIKIAS² It is known that a generalized H 2 (GH 2 ) controller for a continuous-time system takes the form of a conventional Kalman lter together with a state feedback control law, and that the feedback gains can be determined using convex programming. In this paper the discrete-time version of the GH 2 control problem and the related convex programmes involving weight selection in a full information LQR problem are considered. 1. Introduction In a generalized H 2 (GH 2 ) control problem, the conventional H 2 norm is replaced by an operator norm (Wilson 1989, 1991, Rotea 1993, Wilson and Rubio 1995), and a stabilizing controller is sought such that the closed loop gain from time-domain input disturbances in L 2 to time-domain regulated outputs in L is either minimized or kept below a certain bound. A complete solution to the continuous-time GH 2 control problem was presented by Rotea (1993), where it was shown that the solution consists of a conventional Kalman lter together with a state feedback control law in which the gains depend on the Kalman lter. It was also shown that in the case of output feedback the GH 2 synthesis problem could be reduced to a full information/state-feedback problem involving an auxiliary system. The procedure for extending these results to the discrete-time case was given by Kaminer et al. (1993). Wilson and Rubio (1995) showed that in the case where the GH 2 norm is de ned from L 2,2 to L, (the d max problem), the solution consists of a Kalman lter with estimated feedback where the feedback gains could be determined from a weighted LQR problem. The possibility of using a convex programme for LQR weight selection for a GH 2 problem was noted by Rotea (1993), with reference to the work of Boyd and Barratt (1991). Although weight selection was not used by Rotea (1993), the convex programme associated with this method is less than or equal to n + m 2-1, where the system is of order n with m 2 control inputs which, for high-order multi-input systems, o ers a potential reduction in computational burden. The purpose of this paper is to consider the use of weight for the discrete-time GH 2 problem. Following Rotea (1993), the computations are carried out on an auxiliary system, the derivation of which is provided in section 2 for discrete-time systems. The LQR weight selection method is presented in section 3, and section 4 contains a numerical example. Received 8 August Revised 12 March ² Department of Electronic and Electrical Engineering, University of Leeds, Leeds LS2 9JT, UK. d.a.wilson@elec-eng.leeds.ac.uk /98$12. Ñ 1998 Taylor & Francis Ltd.
2 êêê þ 94 D. A. Wilson et al. 2. Discrete-time representation and the auxiliary system This section shows how an auxiliary system with the structure of a state feedback sysem can be derived from the more general output feedback representation. Consider the discrete state space system x(k + 1) = Ax(k) + B 1 w(k) + B 2 u(k) y 1 (k) = C 1 x(k) + D 1 u(k) y 2 (k) = C 2 x(k) + D 2 w(k) where x(k) Î R n, w(k) Î R m 1, u(k) Î R m 2, y 1 (k) Î R p 1 and y 2 (k) Î R p 2 are the states, disturbances, control inputs, errors and measurements, respectively. Throughout this paper we assume, without loss of generality, that C T 1 D 1 = and B T 1 D 2 =. In addition, the pairs (A,B 2 ) and (A,C 2 ) are assumed to be stabilizable and detectable, respectively. In what follows, attention is restricted to linear controllers, and we begin by determining that the Youla-parametrized (Francis 1987) closed-loop transfer function matrix between y 1 and w is given by T y1w (z) = T 11 (z) + T 12 (z)q(z) T 21 (z) (2) where T 11 (z), T 12 (z), T 21 (z) and Q(z) belong to H 2. Using the standard notation for a real rational matrix transfer function we have (Francis 1987, Gu et al. 1989) T (z) = C(zI - A) - 1 B + D = z A B T 11 = C A c - B 2 F B 1 A f B f C c - D 1 F T 12 = A c B 2 C c D 1 T 21 = A f B f C 2 D 2 with A c = A + B 2 F, A f = A + HC 2, B f = B 1 + HD 2 and C c = C 1 + D 1 F, and with F and H any matrices stabilizing A. It is also assumed that A f is devoid of eigenvalues at the origin. The H 2 norm of the system de ned in equation (2) can be found by calculating the cost matrix S(Q) = 1 T 2p j$ y1 w(z) T * y 1 w (z) dz c z (with T * y 1 w = T T y 1 w (z - 1 ) and c the unit circle). Then, the H 2 norm is de ned by i T y1 wi 2 2 = trace (S (Q)) úúú ïïü ïïý D (1) (3) (4) (5) (6)
3 Note that, in contrast to the continuous-time case, T y1 w (z) need not be strictly proper to obtain a nite H 2 norm. Consequently, Q(z) may have a constant term. The discrete-time H 2 control problem involves determining inf trace (S(Q)) QÎ H 2 In the discrete-time version of the GH 2 setting, obtained from its continuous-time counterpart de ned by Rotea (1993) and Wilson and Rubio (1995), w Î z 2,2, y 1 Î z,r with r = 2 or depending on the spatial norm used on the controlled sequence {y 1 (k)} where w Î z 2,2 «i wi 2,2 = å y 1 Î z,2 «i y 1 i,2 = sup - <k< w T (k)w(k) ( - ) y 1 Î z, «i y 1i, = sup - <k< The performance measure is then 1 /2 < (y T 1 (k)y 1 (k)) 1/2 < max y 1,i 1 i p 1 (k) < { (7) f r (S(Q)) = max(s (Q)) r = 2 d max (S (Q)) r = where max and d max denote maximum eigenvalue and maximum diagonal entry, respectively, of a non-negative de nite matrix. The GH 2 norm is then given by i T y1 wi = Ï ê f ê ê ê ê ê ê ê ê ê ê ê ê ê ê ê êê r (S (Q)) (8) The discrete-time GH 2 control problem involves determining inf f QÎ r (S(Q)) H 2 It is well known that the H 2 norm is both left and right unitary invariant, that is, equation (2) can be pre- and post-multiplied by a unitary matrix without altering the norm. The GH 2 norm in equation (8), however, is only right unitary invariant. This property will be used in this section to obtain a simpli ed expression for the cost matrix, and hence to derive an auxiliary system with full state accessibility. The rst step is to choose H as where Y satis es the Riccati equation and Discrete-time version of the H 2 control problem 95 H =- AYC T 2 Z 2 AYA T - Y - AYC T 2 (D 2 D T 2 + C 2 YC T 2 ) - 1 C 2 YA T + B 1 B T 1 = Z = (D 2 D T 2 + C 2 YC T 2 ) - 1 /2 Then, based on the results from Gu et al. (1989), the following factorization can be derived: T 21 = Z - 1 ZT 21 = Z - 1 T 21ci (9)
4 êêê 96 D. A. Wilson et al. where T 21ci = A + HC 2 B 1 + HD 2 ZC 2 ZD 2 is co-inner. Using equation (9), equation (2) can be written as T y1 w = T 11 + T 12 QZ - 1 T 21ci = T 11 + T 12 Q n T 21ci (1) where Q n = QZ - 1. Using the right unitary invariance property of the GH 2 norm, equation (1) can be post-multiplied by the unitary matrix [T * 21ci.. T 21ci^ ] without altering the norm [T 11 + T 12 Q n T 21ci][T * 21ci.. T 21ci^ ] = [T 11 T * 21ci + T 12 Q n.. T 11 T 21ci^ ] (11) The complementary part of T 21ci is chosen such that T 21ci... T 21ci^ is square and unitary, in the following way (Gu et al. 1989) where T 21ci^ = A f B f C^ D^ C^ =- D^ B T f A - T f Y + D^ (D 2 - C 2 Y Y + A - 1 f B f ) T = D^ (I + B T f A - T f Y + A - 1 f B f )D^ T = I (Y + being the pseudo-inverse of Y ). Using similarity transformations, the T 11 T * 21ci term on the right-hand side of equation (11) can be written as T 11 T * 21ci = A c AYC T 2 A - T F A - T f C T 2 C c C 1 Y = A c AYC2 T Z C c úúú Z + A- f T A - f T C2 T Z C 1 Y 7 (T 11 T * 21ci) + + (T 11 T * 21ci) - (12) where, in equation (12), T 11 T * 21ci has been decomposed into its causal and strictly anti-causal parts. Note that for an impulse response sequence {M(k)} -, the causal part will be de ned by {M(k)} and the strictly anti-causal part by {M(k)} - 1, i.e. the response at time zero is associated with the causal part. Also, again using similarity transformations,
5 å å T 11 T 21ci^ * = A- f T A - T f C 1 Y C^ T Z The transfer function matrix in equation (11) can now be decomposed as follows: N 1 L N 2 ( ) ) ) ) ) ) ) *, (T 11 T 21ci) * ) ) ) ) ) ) ) & ( ) ) ) ) ) ) ) ) ) ) ) - + (T 11T 21ci) * ) ) ) ) )) *, ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )) &. ( ) ) ) ) ) *, - + T 21 Q n T11 T 21ci^ * ) ) ) ) )) & [ ] Denote the operation of taking the discrete inverse Fourier transform by I - 1, then {N(k)} - 7 I - 1 [ (T 11 T * 21ci) - + (T 11 T * 21ci) + + T 21 Q n.. T 11 T * 21ci^ ] = [{N 1 (k)} {L (k)}. {N 2 (k)} - ] The cost matrix is then - 1 S (Q n ) = å N(k)N T (k) = - å N 1 (k)n1 T (k) + - å - N 2 (k)n T 2 (k) + å L (k) L T (k) The rst two summations on the right-hand side can be determined using discrete Lyapunov equations: N 1 (k)n T 1 (k) = C 1 YP 1 YC T 1 - C 1 YC T 2 Z 2 C 2 YC T 1 where P 1 satis es the discrete Lyapunov equation Similarly, - P 1 = A T f P 1 A f + C T 2 Z 2 C 2 N 2 (k)n T 2 (k) = C 1 YP 2 YC T 1 where P 2 satis es the discrete Lyapunov equation P 2 = A T f P 2 A f + C^ T C^ It can then be shown that C 1 Y (P 1 + P 2 ) YC1 T = C 1 YC1 T and hence S(Q n ) = å N(k)N T (k) = - å L (k) L T (k) + C 1 YC1 T - C 1 YC2 T Z 2 C 2 YC1 T The transfer matrix function analysis associated with the causal sequence {L (k)} (T 11 T * 21ci) + + T 12 Q n = A c AYC T 2 Z C c C 1 YC T 2 Z + A c B 2 C c D 1 is Q n (13) This is the sum of two transfer functions, and can be written in terms of the following sets of state-space equations: and Discrete-time version of the H 2 control problem 97 x 1 (k + 1) = (A + B 2 F)x 1 (k) + AYC T 2 Zr(k) z 1 (k) = (C 1 + D 1 F)x 1 (k) + C 1 YC T 2 Zr(k)
6 å å þ 98 D. A. Wilson et al. x 2 (k + 1) = (A + B 2 F)x 2 (k) + B 2 Q n (x )r(k) z 2 (k) = (C 1 + D 1 F)x 2 (k) + D 1 Q n (x )r(k) where x denotes the forward shift operator. Now let x a = x 1 + x 2, y 1a = z 1 + z 2, then the system with impulse response {L (k)} has the state-space realization x a (k + 1) = Ax a (k) + B a r(k) + B 2 u a (k) y 1a (k) = C 1 x a (k) + D 1 u a (k) + C 1 YC2 T Zr(k) y 2a (k) = x a(k) [ r(k) ] where B a = AYC T 2 Z and u a (k) = Fx a (k) + Q n (x )r(k). This is a state-space model of a full information plant and will be referred to as the auxiliary system. For a given F, with A + B 2 F stable, the closed-loop impulse response sequence between {r(k)} and {y 1a (k)} will be denoted by {L (Q n; k)} to display the explicit dependence on Q n (x ). Then, it follows that the cost matrix is given by S(Q n ) = å k= ïïïïïü ïïïïïý (14) L (Q n ; k) L T (Q n ; k) + C 1 YC T 1 - C 1 YC T 2 Z 2 C 2 YC T 1 (15) This new form of the cost matrix explains how the output feedback problem is related to a state feedback problem through the constant term S c 7 C 1 YC T 1 - C 1 YC T 2 Z 2 C 2 YC T 1 This will be used in the next section to develop the weight selection method. 3. Weight selection method The continuous-time version of the weight selection method for the GH 2 problem was considered by Wilson and Rubio (1995) and Nekoui and Wilson (1996). This problem involves determining inf d QÎ max (S(Q)) = inf H 2 QÎ H 2 max s i (Q) 1 i p 1 where s i (Q), i = 1... p 1 are the diagonal entries of S(Q). Using a result from Medanic and Andjelic (1971), this problem is equivalent to determining inf max QÎ H 2 iî X p 1 i=1 is i (Q) p where X = { i : i, å i i=1 i p = 1}. Since å 1 i=1 is i (Q) is convex in Q and concave in i, and the sets H 2 and X are convex, the minimax theorem (Balakrishnan 1981) implies that where K solving inf max QÎ H 2 iî X p 1 i=1 is i (Q) = sup iî X inf QÎ H 2å p 1 i=1 is i (Q) = sup iî X inf trace QÎ H 2 [ K S(Q) ] = diag ( i). Hence, the d max version of the GH 2 control problem consists of
7 K inf iî [- inf trace X QÎ H 2 [ K S(Q) ]] (16) This de nes a weight selection problem which can be solved using convex programming (Boyd and Barratt 1991, pp. 335± 337). To avoid a singular LQR problem, the search will be restricted to over strictly positive weights. Using the auxiliary system, the cost matrix is as de ned in equation (15), and equation (16) can be replaced by inf iî X { } - inf trace QÎ H 2 å K L (Q n : k) L T (Q n; k) + trace (K S c ) [ k= ] = inf - trace (K S iî c ) - inf trace X QÎ H 2 å 1/2 L (Q n : k) L T (Q n ; k)k 1 /2 [ k= ] (17) where L (Q n; k) denotes the closed-loop impulse response sequence of the auxiliary system between r and y 1a de ned in equation (14). The second term in equation (17) corresponds to a conventional H 2 problem for the weighted full information plant given by x a (k + 1) = Ax a (k) + B a r(k) + B 2 u a (k) 1 y 1a (k) = K /2 C 1 x a (k) + K y 2a (k) = x a(k) [ r(k) ] 1 /2 D 1 u a (k) + K 1/2 C 1 YC T 2 Zr(k) The solution to this full information problem is given by (Zhou et al. 1996) u a (k) = Fx a (k) + Gr(k) (Note that, unlike the continuous-time case, the full information solution to the discrete-time case involves feedback of the disturbance. Also, the form of the solution is precisely that required by equation (14).) The feedback matrices F and G depend on K, and are obtained from the weighted full information discrete LQR problem F(K ) =- (D T 1 K D 1 + B T 2 XB 2 ) - 1 B T 2 XA G(K ) =- (D T 1 K D 1 + B T 2 XB 2 ) - 1 B T 2 XB a = F(K ) YC T 2 Z where X (which also depends on K equation Note that C T K Discrete-time version of the H 2 control problem 99 ) is the solution to the discrete algebraic Riccati A T XA - X- A T XB 2 (D T 1 K D 1 + B T 2 XB 2 ) - 1 B T 2 XA + C T 1 K C 1 = D 1 = has been assumed, although this condition can easily be relaxed (Zhou et al. 1996). It follows that Q n (x ) = G(K ) and that Q(x ) = Q n (x )Z = F(K ) YC2 T Z 2. The form of the controller for the d max problem is therefore a standard observer-based controller with Q(x ) contributing additional dynamics: x c (k + 1) = (A + HC 2 )x c (k) + B 2 u(k) - Hy 2 (k) u(k) = F(K )x c (k) + F(K ) YC T 2 Z 2 (y 2 (k) - C 2 x c (k)) } (18)
8 êê Ï êê úú ê êê úú úú êê ú úú êê úú 1 D. A. Wilson et al. Remark 1: The conventional discrete-time H2 control problem, as detailed by Zhou et al. (1996), can be recovered by setting equal to the identity matrix in equation (18). Remark 2: The control in equation (18) can be written in the form u(k) = F(K ) (x c (k) + YC T 2 Z 2 (y 2 (k) - C 2 x c (k))) = F(K )x (k) where x c (k) can be interpreted as the optimal (Kalman lter) estimate of x(k) based on the measurements up to stage (k - 1), and x (k) as the optimal estimate of x(k) based on measurements up to stage k. Remark 3: At the outset, Q(z) could have been restricted to be strictly proper, and in this case the optimal solution would be Q(z) =. The optimal control would then be u(k) = F(K )xc(k), and would not involve the measurement update term. This solution is clearly more appropriate for real-time implementation. In fact one could take the view that the use of the measurement update in equation (18) implies a non-causal controller. It should be noted, however, that the matrix F(K ) will be di erent in the strictly proper case as compared with that for the non-strictly proper case. 4. Example The following example involves a discretized version of the system taken from Rotea (1993) using a sampling time of.1 s. An ellipsoid algorithm (Boyd and Barratt 1991) with an exit tolerance of 1-9 was used. A = C 1 =, B 1 = The optimal cost matrix is given by , B 2 =, D 1 = C 2 = [1-1 ], D 2 = [.1] S = with the corresponding optimal control law u(k) =- 231x c1 (k) x c2 (k) - 191x c3 (k) y 2 (k) Note that the diagonal entries of the optimal cost matrix are all equal, and that the optimal cost is ê.9994 ê ê ê ê ê ê ê ê ê ê ê êê. If the controller is constrained to be strictly proper, the optimal cost matrix becomes
9 ê ú Ï S = with the corresponding optimal control law u(k) = 323x c1 (k) x c2 (k) - 192x c3 (k) Note that for this example the cost has increased only slightly to strictly proper controller is used. 5. Conclusions Discrete-time version of the H 2 control problem 11 ê ê ê ê ê ê ê ê ê ê ê ê êê when a A discrete-time version of the weight selection method for the d max version of the generalized H 2 control problem has been presented. The form of the solution is similar to that in continuous-time, and, as in the conventional H 2 problem, one has the choice of using either a proper controller, or a strictly proper controller, which in general will incur some loss in performance. It is not clear at present whether the max version of the GH 2 problem can be solved using some form of weight selection. The technique of Kaminer et al. (1993) therefore remains the only option for solving this version of the problem. References Balakrishnan, A. V., 1981, Applied Functional Analysis (2nd edn) (New York: Springer- Verlag). Boyd, S. P., and Barratt, C. H., 1991, L inear Controller Design: L imits of Performance (Englewood Cli s, NJ: Prentice-Hall). Francis, B. A., 1987, A Course in H Control Theory (New York: Springer-Verlag). Gu, D. W., Tsai, M. C., O Young, S. D., and Postlethwaite, I., 1989, State-space formulae for discrete-time optimisation. International Journal of Control, 49, 1683± Kaminer, I., Khargonekar, P. P., and Rotea, M. A., 1993, Mixed H 2 /H control for discrete-time systems via convex optimization. Automatica, 29, 57± 7. Medanic, J., and Andjelic, M., On a class of di erential games without saddle point solutions. Journal of Optimization Theory and Applications, 8, 413± 43. Nekoui, M. A., and Wilson, D. A., 1996, LQR weight selection in generalized H 2 control for continuous and discrete systems using convex programming. Proceedings 13th IFAC World Congress, C, San Francisco, CA, pp. 121± 126. Rotea, M. A., 1993, The generalized H 2 control problem. Automatica, 29, 373± 385. Wilson, D. A., 1989, Convolution and Hankel operator norms for linear systems. IEEE Transactions on Automatic Control, 34, 94± 97. Wilson, D. A., 1991, Extended optimality properties of the linear quadratic regulator and stationary Kalman lter. IEEE Transactions on Automatic Control, 36, 583± 585. Wilson, D. A., and Rubio, J. E., 1995, Computation of generalized H 2 optimal controllers. International Journal of Control, 61, 99± 112. Zhou, K., Doyle, J. C., and Glover, K., 1996, Robust and Optimal Control (Englewood Ci s: Prentice-Hall).
Structured State Space Realizations for SLS Distributed Controllers
Structured State Space Realizations for SLS Distributed Controllers James Anderson and Nikolai Matni Abstract In recent work the system level synthesis (SLS) paradigm has been shown to provide a truly
More informationFurther results on Robust MPC using Linear Matrix Inequalities
Further results on Robust MPC using Linear Matrix Inequalities M. Lazar, W.P.M.H. Heemels, D. Muñoz de la Peña, T. Alamo Eindhoven Univ. of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands,
More informationDynamic Model Predictive Control
Dynamic Model Predictive Control Karl Mårtensson, Andreas Wernrud, Department of Automatic Control, Faculty of Engineering, Lund University, Box 118, SE 221 Lund, Sweden. E-mail: {karl, andreas}@control.lth.se
More informationDiscrete-Time H Gaussian Filter
Proceedings of the 17th World Congress The International Federation of Automatic Control Discrete-Time H Gaussian Filter Ali Tahmasebi and Xiang Chen Department of Electrical and Computer Engineering,
More informationLinear Quadratic Gausssian Control Design with Loop Transfer Recovery
Linear Quadratic Gausssian Control Design with Loop Transfer Recovery Leonid Freidovich Department of Mathematics Michigan State University MI 48824, USA e-mail:leonid@math.msu.edu http://www.math.msu.edu/
More informationAppendix A Solving Linear Matrix Inequality (LMI) Problems
Appendix A Solving Linear Matrix Inequality (LMI) Problems In this section, we present a brief introduction about linear matrix inequalities which have been used extensively to solve the FDI problems described
More informationClosed-Loop Structure of Discrete Time H Controller
Closed-Loop Structure of Discrete Time H Controller Waree Kongprawechnon 1,Shun Ushida 2, Hidenori Kimura 2 Abstract This paper is concerned with the investigation of the closed-loop structure of a discrete
More informationStability of neutral delay-diœerential systems with nonlinear perturbations
International Journal of Systems Science, 000, volume 1, number 8, pages 961± 96 Stability of neutral delay-diœerential systems with nonlinear perturbations JU H. PARK{ SANGCHUL WON{ In this paper, the
More informationH 1 optimisation. Is hoped that the practical advantages of receding horizon control might be combined with the robustness advantages of H 1 control.
A game theoretic approach to moving horizon control Sanjay Lall and Keith Glover Abstract A control law is constructed for a linear time varying system by solving a two player zero sum dierential game
More information4F3 - Predictive Control
4F3 Predictive Control - Lecture 2 p 1/23 4F3 - Predictive Control Lecture 2 - Unconstrained Predictive Control Jan Maciejowski jmm@engcamacuk 4F3 Predictive Control - Lecture 2 p 2/23 References Predictive
More informationStatic Output Feedback Stabilisation with H Performance for a Class of Plants
Static Output Feedback Stabilisation with H Performance for a Class of Plants E. Prempain and I. Postlethwaite Control and Instrumentation Research, Department of Engineering, University of Leicester,
More informationOptimal discrete-time H /γ 0 filtering and control under unknown covariances
International Journal of Control ISSN: 0020-7179 (Print) 1366-5820 (Online) Journal homepage: http://www.tandfonline.com/loi/tcon20 Optimal discrete-time H filtering and control under unknown covariances
More information6.241 Dynamic Systems and Control
6.241 Dynamic Systems and Control Lecture 24: H2 Synthesis Emilio Frazzoli Aeronautics and Astronautics Massachusetts Institute of Technology May 4, 2011 E. Frazzoli (MIT) Lecture 24: H 2 Synthesis May
More informationand the nite horizon cost index with the nite terminal weighting matrix F > : N?1 X J(z r ; u; w) = [z(n)? z r (N)] T F [z(n)? z r (N)] + t= [kz? z r
Intervalwise Receding Horizon H 1 -Tracking Control for Discrete Linear Periodic Systems Ki Baek Kim, Jae-Won Lee, Young Il. Lee, and Wook Hyun Kwon School of Electrical Engineering Seoul National University,
More informationA Simple Derivation of Right Interactor for Tall Transfer Function Matrices and its Application to Inner-Outer Factorization Continuous-Time Case
A Simple Derivation of Right Interactor for Tall Transfer Function Matrices and its Application to Inner-Outer Factorization Continuous-Time Case ATARU KASE Osaka Institute of Technology Department of
More informationThe norms can also be characterized in terms of Riccati inequalities.
9 Analysis of stability and H norms Consider the causal, linear, time-invariant system ẋ(t = Ax(t + Bu(t y(t = Cx(t Denote the transfer function G(s := C (si A 1 B. Theorem 85 The following statements
More informationMulti-Model Adaptive Regulation for a Family of Systems Containing Different Zero Structures
Preprints of the 19th World Congress The International Federation of Automatic Control Multi-Model Adaptive Regulation for a Family of Systems Containing Different Zero Structures Eric Peterson Harry G.
More informationIMPROVED MPC DESIGN BASED ON SATURATING CONTROL LAWS
IMPROVED MPC DESIGN BASED ON SATURATING CONTROL LAWS D. Limon, J.M. Gomes da Silva Jr., T. Alamo and E.F. Camacho Dpto. de Ingenieria de Sistemas y Automática. Universidad de Sevilla Camino de los Descubrimientos
More informationDigital Signal Processing, Homework 1, Spring 2013, Prof. C.D. Chung
Digital Signal Processing, Homework, Spring 203, Prof. C.D. Chung. (0.5%) Page 99, Problem 2.2 (a) The impulse response h [n] of an LTI system is known to be zero, except in the interval N 0 n N. The input
More informationOptimization based robust control
Optimization based robust control Didier Henrion 1,2 Draft of March 27, 2014 Prepared for possible inclusion into The Encyclopedia of Systems and Control edited by John Baillieul and Tariq Samad and published
More informationA Convex Characterization of Distributed Control Problems in Spatially Invariant Systems with Communication Constraints
A Convex Characterization of Distributed Control Problems in Spatially Invariant Systems with Communication Constraints Bassam Bamieh Petros G. Voulgaris Revised Dec, 23 Abstract In this paper we consider
More informationLifted approach to ILC/Repetitive Control
Lifted approach to ILC/Repetitive Control Okko H. Bosgra Maarten Steinbuch TUD Delft Centre for Systems and Control TU/e Control System Technology Dutch Institute of Systems and Control DISC winter semester
More informationLOW ORDER H CONTROLLER DESIGN: AN LMI APPROACH
LOW ORDER H CONROLLER DESIGN: AN LMI APPROACH Guisheng Zhai, Shinichi Murao, Naoki Koyama, Masaharu Yoshida Faculty of Systems Engineering, Wakayama University, Wakayama 640-8510, Japan Email: zhai@sys.wakayama-u.ac.jp
More informationHere represents the impulse (or delta) function. is an diagonal matrix of intensities, and is an diagonal matrix of intensities.
19 KALMAN FILTER 19.1 Introduction In the previous section, we derived the linear quadratic regulator as an optimal solution for the fullstate feedback control problem. The inherent assumption was that
More informationIterative Learning Control Analysis and Design I
Iterative Learning Control Analysis and Design I Electronics and Computer Science University of Southampton Southampton, SO17 1BJ, UK etar@ecs.soton.ac.uk http://www.ecs.soton.ac.uk/ Contents Basics Representations
More informationParametrization of All Strictly Causal Stabilizing Controllers of Multidimensional Systems single-input single-output case
Parametrization of All Strictly Causal Stabilizing Controllers of Multidimensional Systems single-input single-output case K. Mori Abstract We give a parametrization of all strictly causal stabilizing
More informationDenis ARZELIER arzelier
COURSE ON LMI OPTIMIZATION WITH APPLICATIONS IN CONTROL PART II.2 LMIs IN SYSTEMS CONTROL STATE-SPACE METHODS PERFORMANCE ANALYSIS and SYNTHESIS Denis ARZELIER www.laas.fr/ arzelier arzelier@laas.fr 15
More information8 A First Glimpse on Design with LMIs
8 A First Glimpse on Design with LMIs 8.1 Conceptual Design Problem Given a linear time invariant system design a linear time invariant controller or filter so as to guarantee some closed loop indices
More informationOn Discrete-Time H Problem with a Strictly Proper Controller
On Discrete-Time H Problem with a Strictly Proper Controller Leonid Mirkin Faculty of Mechanical Engineering Technion IIT Haifa 3000, Israel E-mail: mersglm@txtechnionacil May 8, 1996 Abstract In this
More informationH 2 and H 1 cost estimates for time-invariant uncertain
INT. J. CONTROL, 00, VOL. 75, NO. 9, ±79 Extended H and H systems norm characterizations and controller parametrizations for discrete-time M. C. DE OLIVEIRAy*, J. C. GEROMELy and J. BERNUSSOUz This paper
More informationLinear Quadratic Zero-Sum Two-Person Differential Games Pierre Bernhard June 15, 2013
Linear Quadratic Zero-Sum Two-Person Differential Games Pierre Bernhard June 15, 2013 Abstract As in optimal control theory, linear quadratic (LQ) differential games (DG) can be solved, even in high dimension,
More informationRobust control in multidimensional systems
Robust control in multidimensional systems Sanne ter Horst 1 North-West University SANUM 2016 Stellenbosch University Joint work with J.A. Ball 1 This work is based on the research supported in part by
More informationDESIGN OF ROBUST CONTROL SYSTEM FOR THE PMS MOTOR
Journal of ELECTRICAL ENGINEERING, VOL 58, NO 6, 2007, 326 333 DESIGN OF ROBUST CONTROL SYSTEM FOR THE PMS MOTOR Ahmed Azaiz Youcef Ramdani Abdelkader Meroufel The field orientation control (FOC) consists
More informationThe Solvability Conditions for the Inverse Eigenvalue Problem of Hermitian and Generalized Skew-Hamiltonian Matrices and Its Approximation
The Solvability Conditions for the Inverse Eigenvalue Problem of Hermitian and Generalized Skew-Hamiltonian Matrices and Its Approximation Zheng-jian Bai Abstract In this paper, we first consider the inverse
More informationRobust control for a multi-stage evaporation plant in the presence of uncertainties
Preprint 11th IFAC Symposium on Dynamics and Control of Process Systems including Biosystems June 6-8 16. NTNU Trondheim Norway Robust control for a multi-stage evaporation plant in the presence of uncertainties
More informationRank-one LMIs and Lyapunov's Inequality. Gjerrit Meinsma 4. Abstract. We describe a new proof of the well-known Lyapunov's matrix inequality about
Rank-one LMIs and Lyapunov's Inequality Didier Henrion 1;; Gjerrit Meinsma Abstract We describe a new proof of the well-known Lyapunov's matrix inequality about the location of the eigenvalues of a matrix
More informationLinear Quadratic Zero-Sum Two-Person Differential Games
Linear Quadratic Zero-Sum Two-Person Differential Games Pierre Bernhard To cite this version: Pierre Bernhard. Linear Quadratic Zero-Sum Two-Person Differential Games. Encyclopaedia of Systems and Control,
More informationOn the Dual of a Mixed H 2 /l 1 Optimisation Problem
International Journal of Automation and Computing 1 (2006) 91-98 On the Dual of a Mixed H 2 /l 1 Optimisation Problem Jun Wu, Jian Chu National Key Laboratory of Industrial Control Technology Institute
More informationRobust Output Feedback Controller Design via Genetic Algorithms and LMIs: The Mixed H 2 /H Problem
Robust Output Feedback Controller Design via Genetic Algorithms and LMIs: The Mixed H 2 /H Problem Gustavo J. Pereira and Humberto X. de Araújo Abstract This paper deals with the mixed H 2/H control problem
More informationEL2520 Control Theory and Practice
EL2520 Control Theory and Practice Lecture 8: Linear quadratic control Mikael Johansson School of Electrical Engineering KTH, Stockholm, Sweden Linear quadratic control Allows to compute the controller
More informationTHIS paper deals with robust control in the setup associated
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL 50, NO 10, OCTOBER 2005 1501 Control-Oriented Model Validation and Errors Quantification in the `1 Setup V F Sokolov Abstract A priori information required for
More informationChapter 3. LQ, LQG and Control System Design. Dutch Institute of Systems and Control
Chapter 3 LQ, LQG and Control System H 2 Design Overview LQ optimization state feedback LQG optimization output feedback H 2 optimization non-stochastic version of LQG Application to feedback system design
More informationChapter 7 Interconnected Systems and Feedback: Well-Posedness, Stability, and Performance 7. Introduction Feedback control is a powerful approach to o
Lectures on Dynamic Systems and Control Mohammed Dahleh Munther A. Dahleh George Verghese Department of Electrical Engineering and Computer Science Massachuasetts Institute of Technology c Chapter 7 Interconnected
More informationRobust control of uncertain structures
PERGAMON Computers and Structures 67 (1998) 165±174 Robust control of uncertain structures Paolo Venini Department of Structural Mechanics, University of Pavia, Via Ferrata 1, I-27100 Pavia, Italy Abstract
More informationIn the previous chapters we have presented synthesis methods for optimal H 2 and
Chapter 8 Robust performance problems In the previous chapters we have presented synthesis methods for optimal H 2 and H1 control problems, and studied the robust stabilization problem with respect to
More informationVIBRATION CONTROL OF CIVIL ENGINEERING STRUCTURES VIA LINEAR PROGRAMMING
4 th World Conference on Structural Control and Monitoring 4WCSCM-65 VIBRATION CONTROL OF CIVIL ENGINEERING STRUCTURES VIA LINEAR PROGRAMMING P. Rentzos, G.D. Halikias and K.S. Virdi School of Engineering
More informationFEL3210 Multivariable Feedback Control
FEL3210 Multivariable Feedback Control Lecture 8: Youla parametrization, LMIs, Model Reduction and Summary [Ch. 11-12] Elling W. Jacobsen, Automatic Control Lab, KTH Lecture 8: Youla, LMIs, Model Reduction
More informationAchievable performance of multivariable systems with unstable zeros and poles
Achievable performance of multivariable systems with unstable zeros and poles K. Havre Λ and S. Skogestad y Chemical Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway.
More informationLMI based output-feedback controllers: γ-optimal versus linear quadratic.
Proceedings of the 17th World Congress he International Federation of Automatic Control Seoul Korea July 6-11 28 LMI based output-feedback controllers: γ-optimal versus linear quadratic. Dmitry V. Balandin
More informationNull controllable region of LTI discrete-time systems with input saturation
Automatica 38 (2002) 2009 2013 www.elsevier.com/locate/automatica Technical Communique Null controllable region of LTI discrete-time systems with input saturation Tingshu Hu a;, Daniel E. Miller b,liqiu
More informationDecentralized LQG Control of Systems with a Broadcast Architecture
Decentralized LQG Control of Systems with a Broadcast Architecture Laurent Lessard 1,2 IEEE Conference on Decision and Control, pp. 6241 6246, 212 Abstract In this paper, we consider dynamical subsystems
More informationEEE582 Homework Problems
EEE582 Homework Problems HW. Write a state-space realization of the linearized model for the cruise control system around speeds v = 4 (Section.3, http://tsakalis.faculty.asu.edu/notes/models.pdf). Use
More informationNonlinear H control and the Hamilton-Jacobi-Isaacs equation
Proceedings of the 7th World Congress The International Federation of Automatic Control Seoul, Korea, July 6-, 8 Nonlinear H control and the Hamilton-Jacobi-Isaacs equation Henrique C. Ferreira Paulo H.
More information6. Linear Quadratic Regulator Control
EE635 - Control System Theory 6. Linear Quadratic Regulator Control Jitkomut Songsiri algebraic Riccati Equation (ARE) infinite-time LQR (continuous) Hamiltonian matrix gain margin of LQR 6-1 Algebraic
More informationA Partial Order Approach to Decentralized Control
Proceedings of the 47th IEEE Conference on Decision and Control Cancun, Mexico, Dec. 9-11, 2008 A Partial Order Approach to Decentralized Control Parikshit Shah and Pablo A. Parrilo Department of Electrical
More informationEE363 homework 7 solutions
EE363 Prof. S. Boyd EE363 homework 7 solutions 1. Gain margin for a linear quadratic regulator. Let K be the optimal state feedback gain for the LQR problem with system ẋ = Ax + Bu, state cost matrix Q,
More informationThe model reduction algorithm proposed is based on an iterative two-step LMI scheme. The convergence of the algorithm is not analyzed but examples sho
Model Reduction from an H 1 /LMI perspective A. Helmersson Department of Electrical Engineering Linkoping University S-581 8 Linkoping, Sweden tel: +6 1 816 fax: +6 1 86 email: andersh@isy.liu.se September
More informationThe Q-parametrization (Youla) Lecture 13: Synthesis by Convex Optimization. Lecture 13: Synthesis by Convex Optimization. Example: Spring-mass System
The Q-parametrization (Youla) Lecture 3: Synthesis by Convex Optimization controlled variables z Plant distubances w Example: Spring-mass system measurements y Controller control inputs u Idea for lecture
More informationAuxiliary signal design for failure detection in uncertain systems
Auxiliary signal design for failure detection in uncertain systems R. Nikoukhah, S. L. Campbell and F. Delebecque Abstract An auxiliary signal is an input signal that enhances the identifiability of a
More informationNoncausal Optimal Tracking of Linear Switched Systems
Noncausal Optimal Tracking of Linear Switched Systems Gou Nakura Osaka University, Department of Engineering 2-1, Yamadaoka, Suita, Osaka, 565-0871, Japan nakura@watt.mech.eng.osaka-u.ac.jp Abstract. In
More informationJune Engineering Department, Stanford University. System Analysis and Synthesis. Linear Matrix Inequalities. Stephen Boyd (E.
Stephen Boyd (E. Feron :::) System Analysis and Synthesis Control Linear Matrix Inequalities via Engineering Department, Stanford University Electrical June 1993 ACC, 1 linear matrix inequalities (LMIs)
More informationA New Algorithm for Solving Cross Coupled Algebraic Riccati Equations of Singularly Perturbed Nash Games
A New Algorithm for Solving Cross Coupled Algebraic Riccati Equations of Singularly Perturbed Nash Games Hiroaki Mukaidani Hua Xu and Koichi Mizukami Faculty of Information Sciences Hiroshima City University
More informationContents lecture 5. Automatic Control III. Summary of lecture 4 (II/II) Summary of lecture 4 (I/II) u y F r. Lecture 5 H 2 and H loop shaping
Contents lecture 5 Automatic Control III Lecture 5 H 2 and H loop shaping Thomas Schön Division of Systems and Control Department of Information Technology Uppsala University. Email: thomas.schon@it.uu.se,
More informationOn Optimal Performance for Linear Time-Varying Systems
On Optimal Performance for Linear Time-Varying Systems Seddik M. Djouadi and Charalambos D. Charalambous Abstract In this paper we consider the optimal disturbance attenuation problem and robustness for
More informationTrack-Following Control Design and Implementation for Hard Disk Drives with Missing Samples
Track-Following Control Design and Implementation for Hard Disk Drives with Missing Samples Jianbin Nie Edgar Sheh Roberto Horowitz Department of Mechanical Engineering, University of California, Berkeley,
More informationROBUST CONSTRAINED REGULATORS FOR UNCERTAIN LINEAR SYSTEMS
ROBUST CONSTRAINED REGULATORS FOR UNCERTAIN LINEAR SYSTEMS Jean-Claude HENNET Eugênio B. CASTELAN Abstract The purpose of this paper is to combine several control requirements in the same regulator design
More informationDecentralized and distributed control
Decentralized and distributed control Centralized control for constrained discrete-time systems M. Farina 1 G. Ferrari Trecate 2 1 Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB) Politecnico
More informationOn Spectral Factorization and Riccati Equations for Time-Varying Systems in Discrete Time
On Spectral Factorization and Riccati Equations for Time-Varying Systems in Discrete Time Alle-Jan van der Veen and Michel Verhaegen Delft University of Technology Department of Electrical Engineering
More informationCONVERGENCE PROOF FOR RECURSIVE SOLUTION OF LINEAR-QUADRATIC NASH GAMES FOR QUASI-SINGULARLY PERTURBED SYSTEMS. S. Koskie, D. Skataric and B.
To appear in Dynamics of Continuous, Discrete and Impulsive Systems http:monotone.uwaterloo.ca/ journal CONVERGENCE PROOF FOR RECURSIVE SOLUTION OF LINEAR-QUADRATIC NASH GAMES FOR QUASI-SINGULARLY PERTURBED
More informationOn the Stabilization of Neutrally Stable Linear Discrete Time Systems
TWCCC Texas Wisconsin California Control Consortium Technical report number 2017 01 On the Stabilization of Neutrally Stable Linear Discrete Time Systems Travis J. Arnold and James B. Rawlings Department
More informationOPTIMAL H CONTROL FOR LINEAR PERIODICALLY TIME-VARYING SYSTEMS IN HARD DISK DRIVES
OPIMAL H CONROL FOR LINEAR PERIODICALLY IME-VARYING SYSEMS IN HARD DISK DRIVES Jianbin Nie Computer Mechanics Laboratory Department of Mechanical Engineering University of California, Berkeley Berkeley,
More informationFINITE HORIZON ROBUST MODEL PREDICTIVE CONTROL USING LINEAR MATRIX INEQUALITIES. Danlei Chu, Tongwen Chen, Horacio J. Marquez
FINITE HORIZON ROBUST MODEL PREDICTIVE CONTROL USING LINEAR MATRIX INEQUALITIES Danlei Chu Tongwen Chen Horacio J Marquez Department of Electrical and Computer Engineering University of Alberta Edmonton
More informationOptimal control and estimation
Automatic Control 2 Optimal control and estimation Prof. Alberto Bemporad University of Trento Academic year 2010-2011 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 2010-2011
More informationState and Parameter Estimation Based on Filtered Transformation for a Class of Second-Order Systems
State and Parameter Estimation Based on Filtered Transformation for a Class of Second-Order Systems Mehdi Tavan, Kamel Sabahi, and Saeid Hoseinzadeh Abstract This paper addresses the problem of state and
More informationAn Optimization-based Approach to Decentralized Assignability
2016 American Control Conference (ACC) Boston Marriott Copley Place July 6-8, 2016 Boston, MA, USA An Optimization-based Approach to Decentralized Assignability Alborz Alavian and Michael Rotkowitz Abstract
More informationInternational Journal of PharmTech Research CODEN (USA): IJPRIF, ISSN: Vol.8, No.7, pp , 2015
International Journal of PharmTech Research CODEN (USA): IJPRIF, ISSN: 0974-4304 Vol.8, No.7, pp 99-, 05 Lotka-Volterra Two-Species Mutualistic Biology Models and Their Ecological Monitoring Sundarapandian
More informationOn Solving Large Algebraic. Riccati Matrix Equations
International Mathematical Forum, 5, 2010, no. 33, 1637-1644 On Solving Large Algebraic Riccati Matrix Equations Amer Kaabi Department of Basic Science Khoramshahr Marine Science and Technology University
More informationOn Positive Real Lemma for Non-minimal Realization Systems
Proceedings of the 17th World Congress The International Federation of Automatic Control On Positive Real Lemma for Non-minimal Realization Systems Sadaaki Kunimatsu Kim Sang-Hoon Takao Fujii Mitsuaki
More informationFRTN10 Multivariable Control, Lecture 13. Course outline. The Q-parametrization (Youla) Example: Spring-mass System
FRTN Multivariable Control, Lecture 3 Anders Robertsson Automatic Control LTH, Lund University Course outline The Q-parametrization (Youla) L-L5 Purpose, models and loop-shaping by hand L6-L8 Limitations
More informationMathematical Relationships Between Representations of Structure in Linear Interconnected Dynamical Systems
American Control Conference on O'Farrell Street, San Francisco, CA, USA June 9 - July, Mathematical Relationships Between Representations of Structure in Linear Interconnected Dynamical Systems E. Yeung,
More informationContents. 1 State-Space Linear Systems 5. 2 Linearization Causality, Time Invariance, and Linearity 31
Contents Preamble xiii Linear Systems I Basic Concepts 1 I System Representation 3 1 State-Space Linear Systems 5 1.1 State-Space Linear Systems 5 1.2 Block Diagrams 7 1.3 Exercises 11 2 Linearization
More informationSUCCESSIVE POLE SHIFTING USING SAMPLED-DATA LQ REGULATORS. Sigeru Omatu
SUCCESSIVE POLE SHIFING USING SAMPLED-DAA LQ REGULAORS oru Fujinaka Sigeru Omatu Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Sakai, 599-8531 Japan Abstract: Design of sampled-data
More informationA Method to Teach the Parameterization of All Stabilizing Controllers
Preprints of the 8th FAC World Congress Milano (taly) August 8 - September, A Method to Teach the Parameterization of All Stabilizing Controllers Vladimír Kučera* *Czech Technical University in Prague,
More informationA NECESSARY AND SUFFICIENT CONDITION FOR STATIC OUTPUT FEEDBACK STABILIZABILITY OF LINEAR DISCRETE-TIME SYSTEMS 1
KYBERNETIKA VOLUME 39 (2003), NUMBER 4, PAGES 447-459 A NECESSARY AND SUFFICIENT CONDITION FOR STATIC OUTPUT FEEDBACK STABILIZABILITY OF LINEAR DISCRETE-TIME SYSTEMS 1 DANICA ROSINOVÁ, VOJTECH VESELÝ AND
More informationOPTIMAL CONTROL AND ESTIMATION
OPTIMAL CONTROL AND ESTIMATION Robert F. Stengel Department of Mechanical and Aerospace Engineering Princeton University, Princeton, New Jersey DOVER PUBLICATIONS, INC. New York CONTENTS 1. INTRODUCTION
More informationA NUMERICAL METHOD TO SOLVE A QUADRATIC CONSTRAINED MAXIMIZATION
A NUMERICAL METHOD TO SOLVE A QUADRATIC CONSTRAINED MAXIMIZATION ALIREZA ESNA ASHARI, RAMINE NIKOUKHAH, AND STEPHEN L. CAMPBELL Abstract. The problem of maximizing a quadratic function subject to an ellipsoidal
More informationOptimal Sensor and Actuator Location for Descriptor Systems using Generalized Gramians and Balanced Realizations
Optimal Sensor and Actuator Location for Descriptor Systems using Generalized Gramians and Balanced Realizations B. MARX D. KOENIG D. GEORGES Laboratoire d Automatique de Grenoble (UMR CNRS-INPG-UJF B.P.
More informationRobust Observer for Uncertain T S model of a Synchronous Machine
Recent Advances in Circuits Communications Signal Processing Robust Observer for Uncertain T S model of a Synchronous Machine OUAALINE Najat ELALAMI Noureddine Laboratory of Automation Computer Engineering
More informationPosition Control Using Acceleration- Based Identification and Feedback With Unknown Measurement Bias
Position Control Using Acceleration- Based Identification and Feedback With Unknown Measurement Bias Jaganath Chandrasekar e-mail: jchandra@umich.edu Dennis S. Bernstein e-mail: dsbaero@umich.edu Department
More informationH-INFINITY CONTROLLER DESIGN FOR A DC MOTOR MODEL WITH UNCERTAIN PARAMETERS
Engineering MECHANICS, Vol. 18, 211, No. 5/6, p. 271 279 271 H-INFINITY CONTROLLER DESIGN FOR A DC MOTOR MODEL WITH UNCERTAIN PARAMETERS Lukáš Březina*, Tomáš Březina** The proposed article deals with
More informationResearch Article An Equivalent LMI Representation of Bounded Real Lemma for Continuous-Time Systems
Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 28, Article ID 67295, 8 pages doi:1.1155/28/67295 Research Article An Equivalent LMI Representation of Bounded Real Lemma
More informationCONSTRAINED MODEL PREDICTIVE CONTROL ON CONVEX POLYHEDRON STOCHASTIC LINEAR PARAMETER VARYING SYSTEMS. Received October 2012; revised February 2013
International Journal of Innovative Computing, Information and Control ICIC International c 2013 ISSN 1349-4198 Volume 9, Number 10, October 2013 pp 4193 4204 CONSTRAINED MODEL PREDICTIVE CONTROL ON CONVEX
More informationRobustness of Discrete Periodically Time-Varying Control under LTI Unstructured Perturbations
1370 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 45, NO. 7, JULY 000 Robustness of Discrete Periodically Time-Varying Control under LTI Unstructured Perturbations Jingxin Zhang and Cishen Zhang Abstract
More informationGuaranteed H 2 Performance in Distributed Event-based State Estimation
Guaranteed H 2 Performance in Distributed Event-based State Estimation Michael Muehlebach Institute for Dynamic Systems and Control ETH Zurich Email: michaemu@ethz.ch Sebastian Trimpe Autonomous Motion
More informationGraph and Controller Design for Disturbance Attenuation in Consensus Networks
203 3th International Conference on Control, Automation and Systems (ICCAS 203) Oct. 20-23, 203 in Kimdaejung Convention Center, Gwangju, Korea Graph and Controller Design for Disturbance Attenuation in
More informationON CHATTERING-FREE DISCRETE-TIME SLIDING MODE CONTROL DESIGN. Seung-Hi Lee
ON CHATTERING-FREE DISCRETE-TIME SLIDING MODE CONTROL DESIGN Seung-Hi Lee Samsung Advanced Institute of Technology, Suwon, KOREA shl@saitsamsungcokr Abstract: A sliding mode control method is presented
More informationState-Feedback Optimal Controllers for Deterministic Nonlinear Systems
State-Feedback Optimal Controllers for Deterministic Nonlinear Systems Chang-Hee Won*, Abstract A full-state feedback optimal control problem is solved for a general deterministic nonlinear system. The
More informationSubspace-based Identification
of Infinite-dimensional Multivariable Systems from Frequency-response Data Department of Electrical and Electronics Engineering Anadolu University, Eskişehir, Turkey October 12, 2008 Outline 1 2 3 4 Noise-free
More informationR. Balan. Splaiul Independentei 313, Bucharest, ROMANIA D. Aur
An On-line Robust Stabilizer R. Balan University "Politehnica" of Bucharest, Department of Automatic Control and Computers, Splaiul Independentei 313, 77206 Bucharest, ROMANIA radu@karla.indinf.pub.ro
More informationBalancing of Lossless and Passive Systems
Balancing of Lossless and Passive Systems Arjan van der Schaft Abstract Different balancing techniques are applied to lossless nonlinear systems, with open-loop balancing applied to their scattering representation.
More information