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Title: Robust distributed control of constrained linear systems
Author: Trodden, P. A.
ISNI:       0000 0004 2679 1488
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2009
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This thesis presents new algorithms for the distributed control of a group of constrained, linear time-invariant (LTI) dynamic subsystems. Control agents for subsystems, which are dynamically-decoupled but share coupling constraints, exchange plans to achieve constraint satisfaction in the presence of unknown, persistent, but bounded, state disturbances. Based on the tube model predictive control method for robust control of LTI systems, the distributed model predictive control (DMPC) method guarantees robust feasibility and stability. As agents communicate only after optimizing, the resulting algorithm offers low and flexible communication levels; this is the first work to combine robust feasibility and convergence with flexible communications. A cooperative form of the distributed MPC is presented, for problems where application of the standard DMPC results in poor performance owing to 'greedy' behaviour. By a local agent designing plans for other subsystems in the problem, cooperative behaviour is promoted by sacrificing local performance. A key contribution is that robust constraint satisfaction, feasibility and stability guarantees are maintained, yet system-wide performance may improve with only partial cooperation. This thesis includes a formal analysis of cooperation in DMPC. Firstly, under specified assumptions, weaker than those required for robust stability, convergence of the system to a state limit set is shown. By relating game-theoretical concepts to the algorithm at convergence, it is shown the set of limit sets does not enlarge with cooperation; confirmation of an intuitive concept despite the extra conditions imposed for constraint satisfaction. In terms of closed-loop performance, adding cooperation may steer the system to a 'better' outcome. Secondly, cooperation is linked to the coupling structure. It is shown that 'full' cooperation is not always necessary. A new algorithm with adaptive cooperation is proposed, where a local agent searches for paths to other agents in a graph of active couplings; if a path exists to another agent, cooperation with that agent may offer a benefit. Furthermore, it is confirmed that the set of immediately-coupled neighbours, as adopted by previous cooperative DMPC approaches, is not necessarily the optimal cooperating set, and is insufficient to guarantee best distributed performance. A further contribution is a generalization to permit local optimizations in parallel. The proposed approach further tightens each agent's coupling constraints by some margin; sufficient conditions are developed on the size of margin required to guarantee robust constraint satisfaction. Simulations show the method may not be excessively conservative, with closed-loop performance improving over that of the single-update formulation, yet at the expense of increased communication. The algorithms are demonstrated throughout by numerical examples. A multivehicle applications chapter is also included, applying the DMPC to two problems: search, or coverage, of an area by a team of vehicles, and tracking and observation of dynamic targets by sensing vehicles. Simulations demonstrate the practicality of the proposed algorithms, and, furthermore, the benefits of inter-agent cooperation.
Supervisor: Richards, Arthur Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available