Distributed model predictive control of large-scale systems

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1 Distributed model predictive control of large-scale systems James B Rawlings 1, Aswin N Venkat 1 and Stephen J Wright 2 1 Department of Chemical and Biological Engineering 2 Department of Computer Sciences University of Wisconsin Madison Assessment and Future Directions of Nonlinear Model Predictive Control Zollernblick, Freudenstadt-Lauterbad, Germany August 2, 2005 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 1 / 39

2 Outline 1 Introduction 2 The Geometry of Decentralization, Communication and Cooperation 3 Results for Distributed MPC Models Communication Based MPC Cooperation Based MPC MPC with Partial Cooperation 4 Conclusions Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 2 / 39

3 Introduction Most large-scale systems consist of networks of interconnected/interacting subsystems Chemical plants, water distribution networks, power grids etc Traditional approach: Decentralized control Wealth of literature from the early 190 s on improved decentralized control (Sandell-Jr et al [198], Siljak [1991], Lunze [1992]) Well-known that poor performance may result if the interconnections are not negligible Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 3 / 39

4 Introduction Steady increase in available computational power has provided the opportunity for centralized control Most practitioners view centralized control of large, networked systems as impractical and unrealistic Centralized control law grows exponentially with system size Difficult to tailor a centralized controller to meet operational objectives A divide and conquer strategy is essential for control of large, networked systems (Ho [2005]) Centralized control: A benchmark control framework for comparing and assessing other control formulations Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 4 / 39

5 Introduction Linear MPC Mid-Late 90 s: Linear MPC became a dominant advanced control technology (Morari and Lee [199], Young et al [2001], Qin and Badgwell [2003]) Properties of centralized linear MPCs well established (Sznaier and Damborg [1990], Rawlings and Muske [1993], Mayne et al [2000], Bemporad et al [2002]) Efficient large-scale solution strategies available (Antwerp and Braatz [2000], Bartlett et al [2002]) Current focus Possibility of horizontal integration of subsystems MPCs to improve overall system performance Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 5 / 39

6 Introduction Integrating subsystem-based MPCs Notion of Nash equilibrium and Pareto optimality in multi-agent games (Li and Başar [198], Cohen [1998], Başar and Olsder [1999]) Distributed optimization algorithms (Bertsekas and Tsitsiklis [1989]) Potential benefits and requirements of cross-integration within the MPC framework (Kulhavý et al [2001], Lu [2003]) Available discrete time distributed MPC formulations in the literature (Camponogara et al [2002], Jia and Krogh [2002], Keviczky et al [2004]) Nominal properties (feasibility, optimality, closed-loop stability) have not all been established for any single distributed MPC framework Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop / 39

7 Nomenclature: Consider Two Interacting Units Objective functions and Φ 1 (x 1, x 2 ), Φ 2 (x 1, x 2 ) decision variables for units x 1, x 2 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop / 39

8 Nomenclature: Consider Two Interacting Units Objective functions and Φ 1 (x 1, x 2 ), Φ 2 (x 1, x 2 ) decision variables for units x 1, x 2 Decentralized Control min x 1 Φ1 (x 1 ) min x 2 Φ2 (x 2 ) Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop / 39

9 Nomenclature: Consider Two Interacting Units Objective functions and Φ 1 (x 1, x 2 ), Φ 2 (x 1, x 2 ) decision variables for units x 1, x 2 Decentralized Control Communication-based Control (Nash equilibrium) min x 1 Φ1 (x 1 ) min x 2 Φ2 (x 2 ) min x 1 Φ 1 (x 1, x 2 ) min x 2 Φ 2 (x 1, x 2 ) Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop / 39

10 Nomenclature: Consider Two Interacting Units Objective functions and Φ 1 (x 1, x 2 ), Φ 2 (x 1, x 2 ) decision variables for units x 1, x 2 Decentralized Control Communication-based Control (Nash equilibrium) min x 1 Φ1 (x 1 ) min x 2 Φ2 (x 2 ) min x 1 Φ 1 (x 1, x 2 ) min x 2 Φ 2 (x 1, x 2 ) Cooperation-based Control Φ = w 1 Φ 1 + w 2 Φ 2 (Pareto optimal) min x 1 Φ(x 1, x 2 ) min x 2 Φ(x 1, x 2 ) Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop / 39

11 Nomenclature: Consider Two Interacting Units Objective functions and Φ 1 (x 1, x 2 ), Φ 2 (x 1, x 2 ) decision variables for units x 1, x 2 Decentralized Control Communication-based Control (Nash equilibrium) min x 1 Φ1 (x 1 ) min x 2 Φ2 (x 2 ) min x 1 Φ 1 (x 1, x 2 ) min x 2 Φ 2 (x 1, x 2 ) Cooperation-based Control Φ = w 1 Φ 1 + w 2 Φ 2 (Pareto optimal) Centralized Control (Pareto optimal) min x 1 Φ(x 1, x 2 ) min x 2 Φ(x 1, x 2 ) min Φ(x 1, x 2 ) x 1,x 2 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop / 39

12 Noninteracting systems x b Φ 2 (x) 0 n, d, p a -1 Φ 1 (x) x 1 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 8 / 39

13 Weakly interacting systems 05 Φ 2 (x) 0 b -05 p n, d x 2-1 a Φ 1 (x) x 1 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 9 / 39

14 Moderately interacting systems 2 15 Φ 1 (x) x b Φ 2 (x) p a d n x 1 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 10 / 39

15 Strongly interacting (conflicting) systems Φ 2 (x) p Φ 1 (x) a x 2 0 b d x 1 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 11 / 39

16 Strongly interacting (conflicting) systems x 2 10 n Φ 2 (x) 0 Φ 1 (x) x 1 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 12 / 39

17 Modeling for distributed MPC Decentralized, interaction models Decentralized Model x ii(k + 1) = A iix ii(k) + B iiu i(k) u i (local subsystem inputs) (A ii, B ii, C ii ) y i (k) Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 13 / 39

18 Modeling for distributed MPC Decentralized, interaction models Decentralized Model x ii(k + 1) = A iix ii(k) + B iiu i(k) u i (local subsystem inputs) (A ii, B ii, C ii ) + + y i (k) = j C ij x ij (k) Interaction Model x ij(k + 1) = A ijx ij(k) + B iju j(k) u j i (external subsystem inputs) (A ij, B ij, C ij ) Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 13 / 39

19 Modeling for distributed MPC The composite plant model 2 4 x 11 x 1M x M1 x MM 3 5 (k + 1) = 2 4 A 11 A1M A M1 AMM x 11 x 1M x M1 x MM 3 5 (k) B 11 B1M B M1 BMM u 1 u M 3 5 (k) Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 14 / 39

20 Modeling for distributed MPC The composite plant model 2 4 y 1 y M 3 5 (k) = 2 4 C 11 C 1M CM1 CMM x 11 x 1M x M1 x MM 3 5 (k) Centralized model A minimal realization of the composite plant model Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 14 / 39

21 Distributed MPC Assumptions and formulations Assumptions All MPC cost functions are positive definite, quadratic Each subsystem represented by a linear, state-space model All interaction models are stable Local input inequality constraints (eg, input bounds) Formulations for distributed MPC Communication Based MPC Cooperation Based MPC Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 15 / 39

22 Communication-based MPC 1 Exchange of state and input trajectory information between MPCs Subsystems MPC optimizations solved until state and input trajectories converge First move in each converged input trajectory injected into the plant u 1 MPC 1 Prediction Prediction horizon State trajectory Setpoint trajectory MPC 2 Prediction MPC 1 MPC 2 Prediction horizon Controlled input trajectory Process-process interactions Process Process 1 2 u 2 y 1 y 2 1 Similar schemes proposed by Jia and Krogh [2001], Camponogara et al [2002] Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 1 / 39

23 Communication-based MPC 1 Exchange of state and input trajectory information between MPCs Subsystems MPC optimizations solved until state and input trajectories converge First move in each converged input trajectory injected into the plant u 1 MPC 1 Prediction Prediction horizon State trajectory Setpoint trajectory MPC 2 Prediction MPC 1 MPC 2 Prediction horizon Controlled input trajectory Process-process interactions Process Process 1 2 u 2 y 1 y 2 1 Similar schemes proposed by Jia and Krogh [2001], Camponogara et al [2002] Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 1 / 39

24 Communication-based MPC Distillation column of Ogunnaike and Ray [1994] Outputs T 21, T ; Inputs L, V Two SISO MPCs Intentionally choose bad pairing: MPC-1 : T 21 V MPC-2 : T L Can communication-based MPC fix this kind of bad design choice? -025 T21-05 V setpoint cent-mpc comm-mpc Time (sec) cent-mpc comm-mpc Time (sec) Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 1 / 39

25 Communication-based MPC An unreliable plantwide control strategy Lack of provable convergence properties Suboptimal, even at convergence of the state and input trajectories Cannot fix bad design choices (eg, bad pairing choices) Can lead to closed-loop instability in some cases Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 18 / 39

26 Cooperation-based MPC Tasks involved Model interconnections between subsystems Exchange state and input trajectories among interconnected subsystems Replace local objectives by a suitable global objective eg, Φ = i w i Φ i w i 0, M w i = 1 i=1 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 19 / 39

27 Cooperation-based MPC Intermediate termination Implementation issues for large-scale systems Optimal (centralized) performance at convergence Unrealistic for large-scale systems Computational time for convergence >> sampling interval Intermediate termination may be necessary Cooperation-based MPC terminated at an intermediate iterate 1 Feasible? 2 Stable? Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 20 / 39

28 Feasible cooperation-based MPC (FC-MPC) Tasks involved Model interconnections between subsystems Exchange input trajectories among interconnected subsystems Replace local objectives by a suitable global objective eg, Φ = i w i Φ i w i 0, M w i = 1 i=1 Eliminate the state variables using the model equality constraints Each MPC solves an optimization problem in the local input variables Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 21 / 39

29 Geometry of FC-MPC Φ 1 Φ 2 u 2 u 1 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 22 / 39

30 Geometry of FC-MPC Pareto optimal surface Φ 1 Φ 2 u 2 p 0 u 1 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 22 / 39

31 Geometry of FC-MPC Φ Pareto optimal surface Φ 1 Φ 2 u 2 p 0 u 1 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 22 / 39

32 Geometry of FC-MPC Φ Pareto optimal surface Φ 1 Φ 2 u 2 p 0 FC MPC 1 (u 1 ) u 1 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 22 / 39

33 Geometry of FC-MPC Pareto optimal surface FC MPC 2 (u 2 ) Φ Φ 1 Φ 2 u 2 p 0 FC MPC 1 (u 1 ) u 1 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 22 / 39

34 Geometry of FC-MPC Pareto optimal surface FC MPC 2 (u 2 ) Φ (0) Φ 2 Φ 1 u 2 p 0 FC MPC 1 (u 1 ) u 1 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 22 / 39

35 Geometry of FC-MPC Pareto optimal surface FC MPC 2 (u 2 ) Φ (0) Φ 2 Φ 1 u 2 p 1 0 FC MPC 1 (u 1 ) u 1 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 22 / 39

36 Feasible cooperation-based MPC (FC-MPC) Properties 1 All iterates are plantwide feasible 2 The sequence of cost functions is a non-increasing function of the iteration number Also bounded below, hence convergent 3 The sequence of iterates converges to an optimal limit point (centralized MPC solution) Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 23 / 39

37 Closed-loop properties of FC-MPC Distributed MPC control law First input move in the last calculated input trajectory of each subsystem s FC-MPC injected into the plant Properties Nominal closed-loop stability under intermediate termination Disturbance scenarios that destabilize FC-MPC also destabilize centralized MPC Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 24 / 39

38 Performance of FC-MPC Distillation column of Ogunnaike and Ray [1994] Outputs T 21, T ; Inputs L, V Two SISO MPCs Intentionally choose bad pairing: MPC-1 : T 21 V MPC-2 : T L Communication-based MPC cannot fix this kind of bad design choice -025 T21-05 V setpoint cent-mpc comm-mpc Time (sec) cent-mpc comm-mpc Time (sec) Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 25 / 39

39 Performance of FC-MPC Distillation column of Ogunnaike and Ray [1994] Outputs T 21, T ; Inputs L, V Two SISO MPCs Intentionally choose bad pairing: MPC-1 : T 21 V MPC-2 : T L Communication-based MPC cannot fix this kind of bad design choice FC-MPC can fix this kind of bad design choice -025 T21-05 V setpoint cent-mpc comm-mpc FC-MPC (1 iterate) Time (sec) cent-mpc comm-mpc FC-MPC (1 iterate) Time (sec) Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 25 / 39

40 Integrated styrene polymerization plants, cm0, Tf0 Fm0, ci0, Tf0 Finit0 Fc0, Tc0, cs, Tf0 Fs0 Plant 1, cs2, Tf2 Fs2, cm2, Tf2 Fm2, ci2, Tf2 Finit2 Fc2, Tc2 Frecy, Cmr, Tr End use grade fraction: (1 β), cm1, T1 Fm1 Plant 2, cm3, T2 Fm3 Two MPCs, one for each plant L V B D Cp, Cmbot, Cinitbot Plant 1: Manipulate F init0 to control T 1 Produces grade A (lower grade) of polymer Plant 2: Two units polymerization reactor and separator MPC manipulates F init2, F recy and V to control T 2, C mr and C p Produces grade B (higher grade) of polymer Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 2 / 39

41 Integrated styrene polymerization plants Modeling and control of a styrene polymerization reactor well studied (Hidalgo and Brosilow [1990], Russo and Bequette [1998]) Transport of material between plants causes significant time delays Time delays and recycle dynamics known to complicate control (Luyben [1993], Samyudia and Kadiman [2002], Monroy-Loperena et al [2004]) Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 2 / 39

42 Integrated styrene polymerization plants Performance of different MPC frameworks T setpoint Centralized MPC Decentralized MPC Time (hrs) T setpoint Centralized MPC Decentralized MPC Time (hrs) Finit Centralized MPC Decentralized MPC Time (hrs) Finit Centralized MPC Decentralized MPC Time (hrs) Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 28 / 39

43 Integrated styrene polymerization plants Performance of different MPC frameworks T setpoint Centralized MPC Decentralized MPC FC-MPC (1 iterate) Time (hrs) T setpoint Centralized MPC Decentralized MPC FC-MPC (1 iterate) Time (hrs) Finit Centralized MPC Decentralized MPC FC-MPC (1 iterate) Time (hrs) Finit Centralized MPC Decentralized MPC FC-MPC (1 iterate) Time (hrs) Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 28 / 39

44 Integrated styrene polymerization plants Controller performance measure Λ cost (k) = 1 k k M L [x i (j), u i (j)] j=0 i=1 Performance comparison Λ cost Performance loss (wrt centralized MPC) Centralized-MPC Decentralized-MPC % FC-MPC (1 iterate) % FC-MPC (5 iterates) % Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 29 / 39

45 MPC with partial cooperation An industrially motivated scenario u1 u2 pfc MPC 1 Plant y1 Weak interaction Strong interaction y2 Operational objective Use u 1 to track y 1, u 2 to track y 2 Decentralized control gives poor control performance Centralized control uses both u 1 and u 2 pfc MPC 2 Design MPCs to explicitly handle operational objectives Performance may not be Pareto optimal Modular multivariable controller (MMC) approach (Meadowcroft et al [1992]) Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 30 / 39

46 MPC with partial cooperation An industrially motivated scenario u1 u2 pfc MPC 1 Plant y1 Weak interaction Strong interaction y2 Operational objective Use u 1 to track y 1, u 2 to track y 2 Decentralized control gives poor control performance Centralized control uses both u 1 and u 2 pfc MPC 2 pfc MPC 1 min u 1 Φ 1 pfc MPC 2 min u 2 Φ = w 1 Φ 1 + w 2 Φ 2 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 30 / 39

47 Geometry of pfc-mpc Φ 2 (x) b d n x Φ(x) p p Φ 1 (x) x 1 a Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 31 / 39

48 MPC with partial cooperation Weight for output y 2 = 50 weight for output y y setpoint cent-mpc pfc-mpc Time y setpoint cent-mpc pfc-mpc Time u cent-mpc pfc-mpc Time u cent-mpc pfc-mpc Time Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 32 / 39

49 Conclusions The explicit model and prediction horizon of MPC provide a wealth of opportunities for integrating unit level MPCs Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 33 / 39

50 Conclusions The explicit model and prediction horizon of MPC provide a wealth of opportunities for integrating unit level MPCs In this talk we used communication and cooperation to achieve distributed control that approaches the performance of centralized optimal control while maintaining the unit control structure Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 33 / 39

51 Conclusions The explicit model and prediction horizon of MPC provide a wealth of opportunities for integrating unit level MPCs In this talk we used communication and cooperation to achieve distributed control that approaches the performance of centralized optimal control while maintaining the unit control structure Intermediate termination of the cooperation control law retains nominal closed-loop stability and robustness to disturbances Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 33 / 39

52 Conclusions The explicit model and prediction horizon of MPC provide a wealth of opportunities for integrating unit level MPCs In this talk we used communication and cooperation to achieve distributed control that approaches the performance of centralized optimal control while maintaining the unit control structure Intermediate termination of the cooperation control law retains nominal closed-loop stability and robustness to disturbances Structured cooperation (modular control) is also transparently implemented, but its general closed-loop properties remain unclear Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 33 / 39

53 Future research Develop identification methods for minimal modeling of the unit interactions Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 34 / 39

54 Future research Develop identification methods for minimal modeling of the unit interactions Develop structured optimization methods to compute the distributed control law Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 34 / 39

55 Future research Develop identification methods for minimal modeling of the unit interactions Develop structured optimization methods to compute the distributed control law Extend these ideas to nonlinear models Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 34 / 39

56 Future research Develop identification methods for minimal modeling of the unit interactions Develop structured optimization methods to compute the distributed control law Extend these ideas to nonlinear models Test and implement the approach on industrial applications Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 34 / 39

57 Acknowledgments Support from the US National Science Foundation through grant CTS Collaboration with and support from Aspentech, Eastman, ExxonMobil and Shell Global Solutions Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 35 / 39

58 Further Reading I J Antwerp and R Braatz Model predictive control of large scale processes J Proc Control, 10:1 8, 2000 T Başar and G J Olsder Dynamic Noncooperative Game Theory SIAM, Philadelphia, 1999 R Bartlett, L Biegler, J Backstrom, and V Gopal Quadratic programming algorithms for large-scale model predictive control J Proc Cont, 12():5 95, 2002 A Bemporad, M Morari, V Dua, and E Pistikopoulos The explicit linear quadratic regulator for constrained systems Automatica, 38(1):3 20, 2002 D P Bertsekas and J N Tsitsiklis Parallel and Distributed Computation Prentice-Hall, Inc, Englewood Cliffs, New Jersey, 1989 E Camponogara, D Jia, B H Krogh, and S Talukdar Distributed model predictive control IEEE Ctl Sys Mag, pages 44 52, February 2002 J E Cohen Cooperation and self interest: Pareto-inefficiency of Nash equilibria in finite random games Proc Natl Acad Sci USA, 95: , 1998 P M Hidalgo and C B Brosilow Nonlinear model predictive control of styrene polymerization at unstable operating points Comput Chem Eng, 14(4/5): , 1990 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 3 / 39

59 Further Reading II Y-C Ho On Centralized Optimal Control IEEE Trans Auto Cont, 50(4):53 538, 2005 D Jia and B H Krogh Distributed model predictive control In Proceedings of the American Control Conference, Arlington, Virginia, June 2001 D Jia and B H Krogh Min-max feedback model predictive control for distributed control with communication In Proceedings of the American Control Conference, Anchorage,Alaska, May 2002 T Keviczky, F Borelli, and G J Balas A study on decentralized receding horizon control for decoupled systems In Proceedings of the American Control Conference, Boston, Massachusetts, July 2004 R Kulhavý, J Lu, and T Samad Emerging technologies for enterprise optimization in the process industries In J B Rawlings, B A Ogunnaike, and J W Eaton, editors, Chemical Process Control VI: Sixth International Conference on Chemical Process Control, pages , Tucson, Arizona, January 2001 AIChE Symposium Series, Volume 98, Number 32 S Li and T Başar Distributed algorithms for the computation of noncooperative equilibria Automatica, 23(4): , 198 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 3 / 39

60 Further Reading III J Lu Challenging control problems and emerging technologies in enterprise optimization Control Eng Prac, 11(8):84 858, August 2003 J Lunze Feedback Control of Large Scale Systems Prentice-Hall, London, UK, 1992 W L Luyben Dynamics and control of recycle systems 1 simple open-loop and closed-loop systems Ind Eng Chem Res, 32:4 45, 1993 D Q Mayne, J B Rawlings, C V Rao, and P O M Scokaert Constrained model predictive control: Stability and optimality Automatica, 3():89 814, 2000 T Meadowcroft, G Stephanopoulos, and C Brosilow The Modular Multivariable Controller: 1: Steady-state properties AIChE J, 38(8): , 1992 R Monroy-Loperena, R Solar, and J Alvarez-Ramirez Balanced control scheme for reactor/separator processes with material recycle Ind Eng Chem Res, 43: , 2004 M Morari and J H Lee Model predictive control: past, present and future In Proceedings of joint th international symposium on process systems engineering (PSE 9) and 30th European symposium on computer aided process systems engineering (ESCAPE ), Trondheim, Norway, 199 B A Ogunnaike and W H Ray Process Dynamics, Modeling, and Control Oxford University Press, New York, 1994 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 38 / 39

61 Further Reading IV S J Qin and T A Badgwell A survey of industrial model predictive control technology Control Eng Prac, 11():33 4, 2003 J B Rawlings and K R Muske Stability of constrained receding horizon control IEEE Trans Auto Cont, 38(10): , October 1993 L P Russo and B W Bequette Operability of chemical reactors: multiplicity behavior of a jacketed styrene polymerization reactor Chem Eng Sci, 53(1):2 45, 1998 Y Samyudia and K Kadiman Control design for recycled, multi unit processes J Proc Control, 13:1 14, 2002 N R Sandell-Jr, P Varaiya, M Athans, and M Safonov Survey of decentralized control methods for larger scale systems IEEE Trans Auto Cont, 23(2): , 198 D Siljak Decentralized Control of Complex Systems Academic Press, London, 1991 M Sznaier and M J Damborg Heuristically enhanced feedback control of constrained discrete-time linear systems Automatica, 2(3): , 1990 R E Young, R D Bartusiak, and R W Fontaine Evolution of an industrial nonlinear model predictive controller In J B Rawlings, B A Ogunnaike, and J W Eaton, editors, Chemical Process Control VI: Sixth International Conference on Chemical Process Control, pages , Tucson, Arizona, January 2001 AIChE Symposium Series, Volume 98, Number 32 Rawlings, Venkat and Wright (Wisconsin) Distributed, Large-scale MPC 2005 NMPC Workshop 39 / 39

Coordinating multiple optimization-based controllers: new opportunities and challenges

Coordinating multiple optimization-based controllers: new opportunities and challenges James B. Rawlings and Brett T. Stewart Department of Chemical and Biological Engineering University of Wisconsin Madison