Towards a robust multi-level control approach for baggage handling systems

Transcription

1 Delft University of Technology Delft Center for Systems an Control Technical report 3-37 Towars a robust multi-level control approach for baggage hanling systems Y. Zeinaly, B. De Schutter, an H. Hellenoorn If you want to cite this report, please use the following reference instea: Y. Zeinaly, B. De Schutter, an H. Hellenoorn, Towars a robust multi-level control approach for baggage hanling systems, Proceeings of the 5n IEEE Conference on Decision an Control, Florence, Italy, pp. 8 87, Dec. 3. Delft Center for Systems an Control Delft University of Technology Meelweg, 68 CD Delft The Netherlans phone: (secretary) fax: URL: This report can also be ownloae viahttp://pub.eschutter.info/abs/3_37.html

2 Towars a Robust Multi-level Control Approach for Baggage Hanling Systems Yashar Zeinaly, Bart De Schutter, Senior Memeber, IEEE, an Hans Hellenoorn Abstract This paper revisits the routing problem in baggage hanling systems. We propose a two-level control approach base on a moel preictive controller at the top level an a constraine feebac controller at the bottom level that minimizes the L gain of the close-loop system. The moel preictive control problem is recast as a linear programming problem an the constraine feebac controller esign problem is formulate as minimization of a linear objective function subject to linear matrix inequalities. The effectiveness of the propose metho is illustrate by a case stuy. I. INTRODUCTION There has been a growing interest, in the last ecae, in automate moern baggage hanling systems for large airports. Such baggage hanling systems have enable big airports to achieve high throughput of passengers an cargo. The efficiency an reliability of baggage hanling systems have improve over time by implementing more avance control strategies. However, in orer to meet the increasing eman for air travel an cargo shipment, we nee more intelligent an reliable control methos than the currently available state-of-the-art methos. Moern baggage hanling systems are compose of the following main components: i) loaing stations, where the baggage eman originates. The pieces of baggage arrive at the loaing stations either from a chec-in es or from a transfer flight, ii) unloaing stations that are the final estination of the luggage an from where the pieces of baggage are boare on to the planes, iii) a networ of tracs that connect loaing stations to unloaing stations through junctions, iv) high-spee estination coe vehicles (DCV) that transport the pieces of baggage on the networ form the loaing stations to the unloaing stations, v) switch controllers at the junctions that etermine the route of DCVs. A complete escription of the baggage hanling system, the state-of-the-art control approaches, an the highlevel control problems can be foun in [] an []. In this paper, builing on the wor of [3], we evelop a new approach for ynamic routing of DCVs within the networ such that the pieces of baggage arrive at their estination within a given time winow with minimum energy consumption. We also improve the robustness of our approach against variations in the baggage eman. The propose control structure is compose of a controller base on moel preictive control (MPC) at the top level Research supporte by the European Union Seventh Framewor Programme [FP7/7-3] uner grant agreement no HYCON Networ of Excellence, Y. Zeinaly, B. De Schutter, an H. Hellenoorn are with Delft Center for Systems an Control, Delft University of Technology, 68 CD Delft, The Netherlans. y.zeinaly@tuelft.nl an a controller base on L gain optimization at the bottom level. The MPC controller computes the nominal control input base on nominal preiction of the baggage eman such that the pieces of baggage arrive at their estination within a specifie time winow with minimal energy consumption. The L base controller then minimizes the eviation of system trajectories from the nominal behavior ue to unpreicte variations in the nominal preicte baggage eman. Fig. epicts a schematic overview of the propose twolevel control approach. ˆ + + u historical ata u system K L optimization moel optimization queue length/flow constraints y y time winows Fig.. Schematic overview of the propose two-level control approach, where u an y are the nominal input generate by the MPC controller an the resulting output trajectory, respectively, ˆ is the preicte baggage eman, an is the unpreicte eviation of baggage eman aroun ˆ The rest of the paper is organize as follows. In Section II, we present the ynamical moel of the baggage hanling system use for our control purposes. Section III an Section IV escribe the MPC approach an the L optimization control approach, respectively. In Section V, we explain how to combine these two controller approaches into a two-level control structure. In Section VI, we present a case stuy illustrating the performance of our propose control scheme an finally Section VII conclues the paper. II. DYNAMICAL MODEL The baggage hanling system networ can be seen as a irecte graph G=(V,A), where V = O I D is the set of noes compose of origin noes O (i.e., loaing stations), intermeiate noes I (i.e., junctions), an estination noes

3 D (i.e., unloaing stations), an A is the set of arcs compose of lins (i.e., tracs) connecting the noes. The queue lengths are associate with the noes an the control variables are efine at each noe as the flows of DCVs from that noe to its neighbor noes. In a similar manner to the moel in [4], the flows are inexe by their estination, enabling us to istinguish between baggage with ifferent estinations. This is important as the baggage must en up in the right estination. Accoringly, at each noe v V there is a partial queue of DCVs associate with each estination D. The following assumptions are mae in the erivation of the moel: A Each noe in the networ belongs to at least one irecte path from an origin noe (i.e., a loaing station) to a estination noe (i.e., an unloaing station). A A DCV is present at the loaing station whenever a piece of baggage arrives. A3 The movement of pieces of baggage on the networ is approximate by a continuous flow of baggage. A4 At each noe v, with exception of estination noes, the DCVs stac up in vertical queues accoring to their estination. The queue lengths at estination noes are consiere to be zero. This is because we assume either estination noes have unlimite capacity or there is no restriction on the outflow of estination noes so the baggage are immeiately taen to the planes upon arrival. A5 The DCV travel time on each lin is an integer multiple of the sampling time T s. Assumption A guarantees that there are no reunant noes in the networ. By Assumption A, the pieces of baggage are immeiately ispatche from the loaing stations as they arrive. Therefore, we o not nee to istinguish between baggage flows an DCV flows within the system. Otherwise, we woul nee to tae into account the movement of empty DCVs from the unloaing stations to the loaing stations. Assumption A3 is necessary for tractability of the control problem. Although the number of DCVs is an integer in reality, for a fairly large number of DCVs, the movement of DCVs can be approximate by continuous flows. This is not very restrictive as the compute flows can then be realize as well as possible by a lower-level control loop that etermines the optimal switching pattern for the switch controllers at the junctions. The actual time require to travel from a noe to another one epens on the length of the DCV queue at the en of the lin connecting these noes. However, if the queue lengths are sufficiently small compare to the length of the lins, the variation in the travel time is negligible. This is equivalent to having vertical queues at each noe as state in assumption A4. Assumption A5 allows us to arrive at a linear iscrete-time moel of the system. We also mae use of the following notation: The set of sening noes of a noe v V efine as Vv sen = {w V (w,v) A}, is the set of noes that can sen flow to noe v. The set of receiving noes of a noe v V efine as Vv recv = {w V (v,w) A}, is the set of noes that can receive flow from noe v. The set of all noes that are on some irecte path to a estination noe D is V. For each estination noe D an for each origin noe v O V, Q v, () is the baggage inflow (eman) at v with estination uring the time interval [T s,(+ )T s ). For each estination D an each v V an each w Vv recv V, we efine the control variable q v,w, () that is the partial flow of DCVs with estination noe from noe v to noe w uring the time interval [T s,(+)t s ). Accoringly, x v, () enotes the vertical queue length at noe v associate with estination. The set of feasible trajectories of the system is escribe by the following linear constraints in iscrete time: x v, (+ )=x v, ()+T s (Fv, in () Fout v, ()) x v, () q v,w, () (a) (b) (c) where Fv, in () is the total inflow of DCVs to noe v, associate with estination, given by Q v, ()+ q w,v, ( w,v ) if v V O w V sen Fv, in v ()= q w,v, ( w,v ) if v V (D I) () w Vv sen otherwise with w,v T s being the travel time on the lin (w,v), an Fv, out () is the total outflow of DCVs from noe v with estination, given by F v, in() if v V D Fv, out ()= q v,w, () if v V (O I) (3) w Vv recv otherwise Equation (a) escribes the evolution of the queue lengths an (b) constrains queue lengths to non-negative values. Liewise, (c) guarantees non-negativity of the control variables (flows). Let x() be the state vector that inclues all queue lengths x v, () an elaye samples of q v,w, () with elay. Let u() an () be the control input vector that inclues all control variables q v,w, (), an the eman vector compose of all iniviual emans Q v, (), respectively. Then () can be expresse by a constraine iscrete-time linear system as x(+ )=Ax()+B ()+B u() x() u() with properly efine matrices A, B, an B. (4a) (4b) (4c) Assuming a constant spee for DCVs v DCV, w,v is given by w,v = s w,v T sv DCV, where s w,v is the length of lin (w,v).

4 III. MPC PROBLEM FORMULATION The moel presente in Section II is use as internal preiction moel for the MPC approach. At time step, given the current state of the system an an estimate of future baggage eman, this moel is use to compute the trajectories of the system base on which a constraine optimal control problem is solve over a horizon yieling an optimal control sequence. The first element out of the optimal control sequence is then applie to the system accoring to the receing horizon policy an this process is then repeate at the next time step + with new measurements [5]. The objective function must reflect the following performance criteria: i) the pieces of baggage assigne to a certain estination (unloaing station) must reach the estination within a given time winow, ii) the energy consumption of the system shoul be minimize. The time winow represents the time uration in which the en point is reay to receive the luggage. It is unesirable to have the luggage arrive at the estination out of this time winow. Inee, if the pieces of luggage arrive too late, they will miss the flight. Too early arrival of the luggage at the estination point also might inflict a high storage cost on the operator. The energy consumption is associate with manipulating the actuators in the system an wear an tear inflicte on the actuators. There are two contributors to the energy consumption in the system: i) movements of DCVs in the system, which is relate to the magnitue of DCV flows, an ii) variation in the DCV flows. This is particularly important when the DCV flows obtaine here will be realize using switch controllers at each junction of the networ. The variation in the flow then translates to switching frequency. In orer to achieve the aforementione control objectives, we consier a cost function that is a weighte combination of four penalty terms that penalize the DCV queue lengths, DCV flows (control variables), an the variation of DCV flows. The cost associate with the DCV is efine as: The constraine linear moel given in Section II cannot be use to etermine the time instant at which a certain flow of baggage reaches to its estination explicitly. However, we can consier a cost function to inirectly penalize baggage arrival time eviation from a given time winow. The cost function is compose of three penalty terms. The first penalty term penalizes the queue lengths being efine as J tw ()= Cv, tw ()x v,() (5) v V where Cv, tw () as illustrate in Fig. is given as if + v, open v, ()= c tw ( open c tw ( close C tw open + v, ) if open < + v, close ) if + v, > close where open an close are, respectively, the opening an the closing time steps of estination an v, T s is the expecte travel time from noe v to estination uner the current (6) nominal operating conitions. Note that since Cv, tw ()= for open v,, the queue lengths associate with estination are not penalize before the estination is open, taing into account the DCVs travel time from v to. During the time winow of estination, the weight associate with DCV queues increases linearly in time, hence, forcing the DCVs to move towars. The penalty term associate with the DCV flows is efine as: J flow ()= v V C flow w Vv recv V with Cv, flow () as epicte in Fig. 3 being c flow ( open v, ()= if open C flow v, ()q v,w,() (7) + v, ) if + v, open < + v, close c flow ( close + v, ) if + v, > close Note that Cv, flow () is chosen in such a way that DCV flows to estination are allowe uring the time winow of. Higher values Cv, flow () outsie of the time winow prevent early or late DCV flows to the estination. Moreover, in orer to allow late DCVs to reach the estination, the slope of the thir part of Cv, flow () is smaller than the slope of the first part. Now we will introuce the terms in the cost function that reflect the energy consumption in the networ. We penalize all flows in the networ in orer to avoi inefinite circulation of DCVs throughout the networ. Hence, we consier the following penalty term: J e ()= D v V (8) w V recv v V q v,w, () (9) In aition, we use the following penalty term to penalize the total variation of the control signal (i.e., flows), which reflects the wear an tear of the DCVs: J sw ()= D l V w V recv v V q v,w, () q v,w, ( ) () The total cost at time step is therefore given as J()= J tw ()+α D J flow D ()+α J e ()+α 3 J sw () () where α i > is a weight factor inicating the relative importance of the associate term in the objective function. The MPC performance inex over the preiction horizon of N p step is thus given as +N p J(,N p )= i= J(i) () Now we woul lie to highlight the following remars: R The plots of Fig. an Fig. 3 show respectively coefficients of the penalty terms (5) an (7), not the penalty terms themselves. In fact, at the given time step an for a preiction horizon N p the values of these coefficients are nown for,...,+n p. Therefore, these coefficients have fixe values an hence These can be obtaine base on historical ata for perios with similar conitions as the current one.

5 the associate penalty terms (5) an (7) are linear in the control variable. R By introucing some ummy variables accoring to stanar techniques in optimization [6], terms of the form () can be recast as a linear programming problem with linear constraints. Consier u(), x(), an () as introuce in Section II. At every time step we solve the following optimization problem: min u() F()u() subject to: A ineq ()u() b ineq () A eq ()u()=b eq () (3) where the vector F() is efine base on the MPC objective function (), an the vector u() inclues the control inputs u(),...,u(+n p ) an the ummy variables mentione in Remar R. Moreover, A ineq (), an A eq () are etermine base on the constraints, an b ineq (), an b eq () are constant vectors that epen on the current state x() an the eman values (),...,(+ N p ). The optimization problem given by (3) is an LP problem, that can be solve efficiently with currently available solvers, e.g., MATLAB linprog. C tw v, Fig.. open v, close v, The coefficient for the queue length penalty term. where the system matrices, x R n, R n, an u R m are those of (4a) an z R n z is the controlle output vector. Assume that (A,B ) is stabilizable an K is a stabilizing feebac gain. The L gain of the close-loop system is z boune by γ > (i.e., sup γ) if an only if there z exists a P> such that [7], [8] [ A T PA P+ γ C T C A T PB+ γ C ] T D B T PA + γ D T C B T PB+ γ D T D γi (6) where [ ] [ ] A B A+B K B = (7) C D C + D K D or equivalently Q A Q B QA T Q QC T B T γi D T C Q D γi (8) with Q=P >. Consier the problem of etermining a feebac gain K that minimizes the L gain of the close-loop system. It is well-nown [8] that with the transformation Y = KQ, the matrix inequality of (8) can be written as Q AQ+B Y B QA T +Y T B T Q QC T +Y T D T B T γi D T C Q+D Y D γi (9) with Q>. Note that for the close-loop system given by (4) an (5), (6) implies C flow v, Fig. 3. open v, close v, The coefficient for the flow penalty term. IV. FEEDBACK CONTROL PROBLEM FORMULATION A. Problem Setup Consier a iscrete-time linear system x(+ )=Ax()+B ()+B u() with full state feebac z()= C x()+d ()+D u() (4a) (4b) u()=kx() (5) x T (+ )Px(+ ) x T ()Px()+ γ zt ()z() γ T ()() () Now we efine the ellipsoi ε γ :={x x T P γ x }. Assuming x()=, () yiels x T T (T)Px(T) γ T ()()<γ = = for any T N. Assuming 3 =, we get T ()() () x T (T) P x(t)< () γ which shows that x(t) ε γ. Since () hols for all T, ε γ contains the set of states that are reachable by a unit energy input signal when the L gain of the close-loop system is boune by γ. 3 It is always possible to scale such that =.

6 B. Har State Constraints Now we consier the problem of searching for the feebac gain K that minimizes the L gain of the close-loop system subject to polytopic state constraints of the form a T i x(), i=,...,r. (3) To inclue the state constraints of (3), consier the polytope P ={x R n a T i x,i=,...,r} (4) associate with (3). We assume that P has the origin in its interior. To guaranty that (3) hols for all > with x()=, we must have ε γ P or equivalently [8] a T i γqa i, i=,...,r (5) Therefore, the following optimization problem nees to be solve: min γ Q,Y,γ subject to: (9), (5), Q> (6) This problem is not jointly convex in γ an Q an Y. Moreover, it can be shown in a straightforwar manner that the constraints of (8) an (5) o not satisfy the monotonicity property G(Q,Y,γ ) > G(Q,Y,γ ) if γ > γ, where G < represents constraints (9) an (5) combine. Therefore, this problem cannot even be recast as a generalize eigenvalue problem, which is a class of quasiconvex optimization problems [8]. Now we will replace constraint (5) by a more conservative one that is convex in the optimization variables, in the following manner. Note that γq= 4 (γi+ Q)T (γi+ Q) 4 (γi Q)T (γi Q) (7) Obviously, γq< 4 (γi+ Q)T (γi+ Q). Hence, 4 at i (γi+ Q) T (γi+ Q)a i = a T i γqa i < (8) or equivalently expresse using the Schur complement [ ] I (γi+ Q)a i > (9) (γi+ Q) 4 a T i Clearly, this introuces conservatism as the feasibility set of (9) is a subset of the feasibility set of (5). This conservatism can be reuce if one can fin a lower boun for (γi Q) T (γi Q) such that (γi Q) T (γi Q) α I or equivalently γi Q α (in matrix norm sense) for some α >. Then, instea of (9), one obtains [ ] I (γi+ Q)a i a T i (γi+ Q) > (3) 4+aT i α a i Therefore we consier (6) with (5) replace by (9) or by (3). This is an eigenvalue problem [8], which is a convex optimization problem that can be solve with currently available LMI optimization toolboxes, e.g., MATLAB LMI toolbox, YALMIP [9], an CVX [], []. C. Soft State Constraints In the view of the propose two-level control scheme, it maes more sense to replace the har constraints of (5) by soft constraints ue to the following observations: i) the constraints are mainly hanle at the top level by the MPC controller, ii) if the constraints are too restrictive the conservative version of the original constraints as expresse by (9) may become infeasible, which is not esirable. As an alternative to the approach presente in Section IV-B, one can replace har constraints by soft ones by consiering a multi-objective optimization approach that penalizes the L gain of the close-loop system an, inirectly, the constraint violation at the same time. More precisely, we efine the following optimization problem with the objective function that penalizes γ, an the volume of the ellipsoi ε γ, which is proportional to et γq : min c γγ+ log ( et(γq) ) Q,Y,γ subject to: Q> an (9) (3) where c γ > is a weight factor. The magnitue of c γ etermines the trae-off between the L gain an the volume of the ellipsoi that represents the set of reachable states. By minimizing the volume of ε γ, we confine the set of reachable state from the origin. This inirectly minimizes constraint violation since the origin lies in the interior of polytope P. However, this objective function is not convex in the optimization variables γ an Q. To mitigate this problem, instea of penalizing the volume of ε γ, we penalize an upper boun on the length of semi-major axis of ε γ, which is λmax (γq), where λ max (γq) is the largest eigenvalue of γq. It is clear from (7), that λ max ( 4 (γi+ Q) T (γi + Q) ) constitutes an upper boun on λ max (γq). Then we get min c ( γγ+ λ max Q,Y,γ 4 (γi+ Q)T (γi+ Q) ) subject to: Q> an (9) (3) or equivalently min c γγ+ λ Q,Y,γ,λ subject to: (9), Q>, [ λi γi+ Q γi+ Q 4I ] > (33) This is an eigenvalue problem [8] that can be solve efficiently with currently available LMI solvers such as MAT- LAB LMI toolbox. Note that, by inspecting (7), the upper boun on λ max (γq) can be mae tighter if one can fin an α > such that (γi Q) T (γi Q) α I or equivalently, in matrix norm 4 sense, γi Q α. Then the last constraint in (33) will be replace by [ ] (λ + α 4 )I γi+ Q > (34) γi+ Q 4I 4 For matrix norm, we use the efinition A =σ max (A), where σ max (A) is the largest singular value of matrix A.

7 As an example, consier a iscrete-time linear system given by A= , C = I B = ,B = , D =, D = For c γ taing values in the interval[.,], Fig. 4 illustrates the trae-off between minimizing the L gain an the length of the semi-major axis of ε γ. varying slowly with time, one can use a controller sampling time mt s, with m> being an integer number. VI. CASE STUDY Fig. 5. A layout of baggage hanling system with one loaing station an one unloaing station. The length of each lin in the networ is 4 m λmax(γq) γ Fig. 4. Trae-off curve between the optimal γ an the length of the semimajor axis of ε γ. V. INTEGRATION OF MPC AND FEEDBACK CONTROLLERS In this section, we briefly explain how the two control schemes presente in Sections III an IV can be combine. The baggage eman at each origin noe is compose of a base eman, which is assume to be preictable over the preiction horizon N p, an a small aitive perturbation aroun the base eman that cannot be preicte. Base on a future preiction of, the MPC controller computes the optimal DCV flows u an system trajectories z subject to flow an queue length constraints such that the DCVs arrive at their estinations with minimal energy consumption an with minimal eviation from the time winows. To minimize the averse effect of on optimal system trajectories compute by the MPC controller, a feebac gain K minimizing z = z z base on the measurement y() y () is implemente along the MPC controller in the configuration epicte in Fig.. Therefore, the control law applie to the system at time step is u() = u ()+K ( y() y () ) = u ()+Kỹ(). When we impose constraints on the controlle output z()=z ()+ z(), the constraints on z() epen on value of z (). As a result, one nees to upate the feebac gain K whenever the value of z () changes. This can be avoie if soft constraints as in Section IV-C are use. Moreover, the MPC control law u oes not have to be upate at every time instant T s. Particularly, if the base eman is () [DCV/sec] () () () Fig. 6. Base baggage eman,the perturbations on the base eman, an the actual eman at the loaing station. u() [DCV/sec] u 4,5 () u 3,5 () time winow Fig. 7. Optimal flows of DCVs at the unloaing station. One can observe that most of the DCVs arrive at the unloaing station within the specifie time winow. In this section we present a case stuy to illustrate the performance of our propose control approach for the baggage hanling system. For the sae of simplicity, we consier a simple baggage hanling system, the layout of which is epicte in Fig. 5. Here, the focus is to illustrate the effect of the feebac controller on suppressing the averse effects of an unpreicte baggage eman on the behavior of the system. First, assuming that the eman is fully nown, the optimal flows an optimal system trajectories are compute. Next, we consier some unpreictable ranom perturbations on the base eman an evaluate how closely our propose two-level control approach can follow the optimal trajectory.

8 x () mpc only two level optimal Fig. 8. Queue lengths at noe. One can observe that for the two-level control approach, the queue length at noe is only slightly affecte by the isturbance. TABLE I CONTROLLER DESIGN AND SIMULATION PARAMETERS MPC Parameters N p time winow u max[dcv/s] (α,α,α 3) (c flow,c flow,c tw ) [4,7] 4 (,5,) (,.,) Feebac Controller Parameters c γ γmin γ min λmax λ max Close-loop Simulation Parameters T s[s] N sim x (initial conition) eman perturbation v DCV [m/s].4 U (,), = 4..4 For the two-level control approach, we have compute the feebac gain K base the approach of Section IV-C using the MATLAB LMI toolbox. Table I lists the parameters use for the controller esign an the close-loop simulation. In Table I, λmax an γmin enote, respectively, the actual values of λ max (γq) an γ achieve by the close-loop system whereas λmax an γmin enote those values obtaine by solving (33). For the base eman () epicte in Fig. 6, the optimal flows to the estination (noe 5) are illustrate in Fig. 7 an the resulting optimal queue length at the origin noe (noe ) is epicte in Fig. 8. It is clear from Fig. 7 that the optimal flows arrive at the estination within the esire time winow. The perturbation on the base eman () U (,) is epicte in Fig. 6. It is obvious from Fig. 8 that in the presence of unpreictable eman perturbations, the twolevel controller follows the optimal trajectory very closely whereas the MPC base approach eviates from the optimal trajectory. VII. CONCLUSIONS AND FUTURE WORK The routing problem in baggage hanling systems was revisite. A new flow-base moel was erive for our control purposes, which are elivering the pieces of baggage at the unloaing stations within a pre-specifie time winow, an minimizing the energy consumption. We propose a multi-level control approach with an MPC controller at the top level an a constraine feebac controller at the bottom level that minimizes the L gain of the close-loop system. The iea was that base on some prior nowlege on the baggage eman, the MPC controller computes the optimal control inputs an system trajectories such that the pieces of baggage arrive at their estination within a esire time winow an with minimal energy consumption. The feebac controller then woul guarantee minimal eviation from this optimal trajectory in face of unnown perturbations on the baggage eman. We showe that the MPC problem can be formulate as a linear programming problem. We propose two methos to inclue state constraints in esign proceure of the feebac controller that can be recast as LMI constraints. Using a simple case stuy, we showe the effectiveness of the propose two-level control approach. This approach shoul be extenable to large-scale system. However, for large-scale systems, the conservatism introuce by (8) may rener the LMIs in (33) infeasible. Hence, one may nee to fin a tighter lower boun α in (34). For future wor, the scalability of the propose two-level approach to large networ layouts will be investigate. In aition, we will compare the performance of the two-level control approach with the MPC-base approach for larger networ layouts an more elaborate scenarios. As a secon extension to the current wor, we will inclue non-polytopic state constraints as well as control signal constraints in the esign proceure of the feebac controller. REFERENCES [] A. Tarău, B. De Schutter, an H. Hellenoorn, Moel-base control for route choice in automate baggage hanling systems, IEEE Transactions on Systems, Man, an Cybernetics, Part C: Applications an Reviews, vol. 4, no. 3, pp , May. [] Y. Zeinaly, B. De Schutter, an J. 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