Abstract
Largescale baggage handling systems, or largescale logistic networks, for that matter, pose interesting challenges to modelbased 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 largescale baggage handling systems (BHSs), where a modeling framework for BHSs is proposed that is subsequently used to develop an MPC scheme for control of largescale 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 closedloop performance and computational complexity. It is shown, via simulation studies, that the proposed solutions can outperform a heuristicsbased 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 tubebased MPC scheme. For this purpose, considering the BHS model essentially as a linear positive system, a linearprogrammingbased approach is proposed for the joint calculation of a robustly positively invariant subset and a constrained state feedback controller that minimizes the disturbancedriven L∞ norm of the output over this set. A tubebased 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 tubebased 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 tubebased 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 spinoff 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 discretetime linear positive systems. More specifically, we revisit the problem of characterizing the subset of the state space that is reachable from the origin for discretetime 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 singleinput case, a characterization is provided of when the infinitetime and the finitetime 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 tubebased MPC scheme. For this purpose, considering the BHS model essentially as a linear positive system, a linearprogrammingbased approach is proposed for the joint calculation of a robustly positively invariant subset and a constrained state feedback controller that minimizes the disturbancedriven L∞ norm of the output over this set. A tubebased 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 tubebased 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 tubebased 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 spinoff 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 discretetime linear positive systems. More specifically, we revisit the problem of characterizing the subset of the state space that is reachable from the origin for discretetime 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 singleinput case, a characterization is provided of when the infinitetime and the finitetime 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.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Thesis sponsors  
Award date  24 Jun 2022 
Print ISBNs  9789055843114 
Electronic ISBNs  9789055843114 
DOIs  
Publication status  Published  2022 
Bibliographical note
TRAIL Thesis Series no. T2022/8, the Netherlands TRAIL Research SchoolKeywords
 Baggage Handling Systems
 Polyhedral Cones
 Reachable Subsets
 Linear positive systems
 Baggage Handling Systems, Model Predictive Control