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Model-based Control of Large-scale Baggage Handling Systems
Leveraging the Theory of Linear Positive Systems for Robust Scalable Control Design
Large-scale baggage handling systems, or large-scale logistic networks, for that matter, pose interesting challenges to model-based control design. These challenges concern computational complexity, scalability, and robustness of the proposed solutions. This thesis tackles these issues in a collection of papers organized in two overlapping parts. The first part concerns modeling and Model Predictive Control (MPC) design of large-scale baggage handling systems (BHSs), where a modeling framework for BHSs is proposed that is subsequently used to develop an MPC scheme for control of large-scale BHSs. The MPC controller optimizes for the timely arrival of pieces of baggage at their destination within the BHS network under capacity constraints while minimizing the overall cost of transporting pieces of baggage. Several formulations for the resulting constrained optimization problem are proposed, and they are compared with each other in terms of closed-loop performance and computational complexity. It is shown, via simulation studies, that the proposed solutions can outperform a heuristics-based approach commonly used for control of BHSs while scaling well to larger BHS network instances.
In its second part, the thesis focuses on robustness of control design in the face of a partially known disturbance input (i.e., input baggage demand), and especially on developing a scalable tube-based MPC scheme. For this purpose, considering the BHS model essentially as a linear positive system, a linear-programming-based approach is proposed for the joint calculation of a robustly positively invariant subset and a constrained state feedback controller that minimizes the disturbance-driven L∞ norm of the output over this set. A tube-based MPC control scheme is finally developed by coupling the state feedback controller with a nominal MPC controller, guaranteeing recursive feasibility and asymptotic stability. It is shown via simulation studies that the proposed tube-based approach is effective against unpredictable disturbances. In addition, since the design of both the nominal MPC controller and the state feedback controller involves only linear programs, the proposed tube-based approach scales well to BHS networks of larger size.
Linear positive systems are of interest in several branches of engineering, logistics, biochemistry, and economics. As a spin-off topic and inspired by the applications of the theory of linear positive systems to modeling and control design of systems in the mentioned domains, the third part of the thesis focuses on the reachability analysis of discrete-time linear positive systems. More specifically, we revisit the problem of characterizing the subset of the state space that is reachable from the origin for discrete-time linear positive systems. This problem is of interest in topics such as optimal control of linear positive systems and realization theory of linear positive systems. It is established in this thesis that the reachable subset can be either a polyhedral or a nonpolyhedral cone. For the single-input case, a characterization is provided of when the infinite-time and the finite-time reachable subsets are polyhedral. Finally, for the case of polyhedral reachable subsets, a method, based on solving a set of linear equations, is provided to verify whether a target set can be reached from the origin using positive inputs. ...
In its second part, the thesis focuses on robustness of control design in the face of a partially known disturbance input (i.e., input baggage demand), and especially on developing a scalable tube-based MPC scheme. For this purpose, considering the BHS model essentially as a linear positive system, a linear-programming-based approach is proposed for the joint calculation of a robustly positively invariant subset and a constrained state feedback controller that minimizes the disturbance-driven L∞ norm of the output over this set. A tube-based MPC control scheme is finally developed by coupling the state feedback controller with a nominal MPC controller, guaranteeing recursive feasibility and asymptotic stability. It is shown via simulation studies that the proposed tube-based approach is effective against unpredictable disturbances. In addition, since the design of both the nominal MPC controller and the state feedback controller involves only linear programs, the proposed tube-based approach scales well to BHS networks of larger size.
Linear positive systems are of interest in several branches of engineering, logistics, biochemistry, and economics. As a spin-off topic and inspired by the applications of the theory of linear positive systems to modeling and control design of systems in the mentioned domains, the third part of the thesis focuses on the reachability analysis of discrete-time linear positive systems. More specifically, we revisit the problem of characterizing the subset of the state space that is reachable from the origin for discrete-time linear positive systems. This problem is of interest in topics such as optimal control of linear positive systems and realization theory of linear positive systems. It is established in this thesis that the reachable subset can be either a polyhedral or a nonpolyhedral cone. For the single-input case, a characterization is provided of when the infinite-time and the finite-time reachable subsets are polyhedral. Finally, for the case of polyhedral reachable subsets, a method, based on solving a set of linear equations, is provided to verify whether a target set can be reached from the origin using positive inputs. ...
Large-scale baggage handling systems, or large-scale logistic networks, for that matter, pose interesting challenges to model-based control design. These challenges concern computational complexity, scalability, and robustness of the proposed solutions. This thesis tackles these issues in a collection of papers organized in two overlapping parts. The first part concerns modeling and Model Predictive Control (MPC) design of large-scale baggage handling systems (BHSs), where a modeling framework for BHSs is proposed that is subsequently used to develop an MPC scheme for control of large-scale BHSs. The MPC controller optimizes for the timely arrival of pieces of baggage at their destination within the BHS network under capacity constraints while minimizing the overall cost of transporting pieces of baggage. Several formulations for the resulting constrained optimization problem are proposed, and they are compared with each other in terms of closed-loop performance and computational complexity. It is shown, via simulation studies, that the proposed solutions can outperform a heuristics-based approach commonly used for control of BHSs while scaling well to larger BHS network instances.
In its second part, the thesis focuses on robustness of control design in the face of a partially known disturbance input (i.e., input baggage demand), and especially on developing a scalable tube-based MPC scheme. For this purpose, considering the BHS model essentially as a linear positive system, a linear-programming-based approach is proposed for the joint calculation of a robustly positively invariant subset and a constrained state feedback controller that minimizes the disturbance-driven L∞ norm of the output over this set. A tube-based MPC control scheme is finally developed by coupling the state feedback controller with a nominal MPC controller, guaranteeing recursive feasibility and asymptotic stability. It is shown via simulation studies that the proposed tube-based approach is effective against unpredictable disturbances. In addition, since the design of both the nominal MPC controller and the state feedback controller involves only linear programs, the proposed tube-based approach scales well to BHS networks of larger size.
Linear positive systems are of interest in several branches of engineering, logistics, biochemistry, and economics. As a spin-off topic and inspired by the applications of the theory of linear positive systems to modeling and control design of systems in the mentioned domains, the third part of the thesis focuses on the reachability analysis of discrete-time linear positive systems. More specifically, we revisit the problem of characterizing the subset of the state space that is reachable from the origin for discrete-time linear positive systems. This problem is of interest in topics such as optimal control of linear positive systems and realization theory of linear positive systems. It is established in this thesis that the reachable subset can be either a polyhedral or a nonpolyhedral cone. For the single-input case, a characterization is provided of when the infinite-time and the finite-time reachable subsets are polyhedral. Finally, for the case of polyhedral reachable subsets, a method, based on solving a set of linear equations, is provided to verify whether a target set can be reached from the origin using positive inputs.
In its second part, the thesis focuses on robustness of control design in the face of a partially known disturbance input (i.e., input baggage demand), and especially on developing a scalable tube-based MPC scheme. For this purpose, considering the BHS model essentially as a linear positive system, a linear-programming-based approach is proposed for the joint calculation of a robustly positively invariant subset and a constrained state feedback controller that minimizes the disturbance-driven L∞ norm of the output over this set. A tube-based MPC control scheme is finally developed by coupling the state feedback controller with a nominal MPC controller, guaranteeing recursive feasibility and asymptotic stability. It is shown via simulation studies that the proposed tube-based approach is effective against unpredictable disturbances. In addition, since the design of both the nominal MPC controller and the state feedback controller involves only linear programs, the proposed tube-based approach scales well to BHS networks of larger size.
Linear positive systems are of interest in several branches of engineering, logistics, biochemistry, and economics. As a spin-off topic and inspired by the applications of the theory of linear positive systems to modeling and control design of systems in the mentioned domains, the third part of the thesis focuses on the reachability analysis of discrete-time linear positive systems. More specifically, we revisit the problem of characterizing the subset of the state space that is reachable from the origin for discrete-time linear positive systems. This problem is of interest in topics such as optimal control of linear positive systems and realization theory of linear positive systems. It is established in this thesis that the reachable subset can be either a polyhedral or a nonpolyhedral cone. For the single-input case, a characterization is provided of when the infinite-time and the finite-time reachable subsets are polyhedral. Finally, for the case of polyhedral reachable subsets, a method, based on solving a set of linear equations, is provided to verify whether a target set can be reached from the origin using positive inputs.
Positive systems with positive inputs and positive outputs are used in several branches of engineering, biochemistry, and economics. Both control theory and system theory require the concept of reachability of a time-invariant discrete-time linear positive system. The subset of the state set that is reachable from the origin is therefore of interest. The reachable subset is in general a cone in the positive vector space of the positive real numbers. It is established in this paper that the reachable subset can be either a polyhedral or a nonpolyhedral cone. For a single-input case, a characterization is provided of when the infinite-time and the finite-time reachable subsets are polyhedral. An example is provided for which the reachable subset is nonpolyhedral. Finally, for the case of polyhedral reachable subset(s), a method is provided to verify if a target set can be reached from the origin using positive inputs.
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Positive systems with positive inputs and positive outputs are used in several branches of engineering, biochemistry, and economics. Both control theory and system theory require the concept of reachability of a time-invariant discrete-time linear positive system. The subset of the state set that is reachable from the origin is therefore of interest. The reachable subset is in general a cone in the positive vector space of the positive real numbers. It is established in this paper that the reachable subset can be either a polyhedral or a nonpolyhedral cone. For a single-input case, a characterization is provided of when the infinite-time and the finite-time reachable subsets are polyhedral. An example is provided for which the reachable subset is nonpolyhedral. Finally, for the case of polyhedral reachable subset(s), a method is provided to verify if a target set can be reached from the origin using positive inputs.