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Title: Robust model predictive control : robust control invariant sets and efficient implementation
Author: Liu, Chengyuan
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2017
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Robust model predictive control (RMPC) is widely used in industry. However, the online computational burden of this algorithm restricts its development and application to systems with relatively slow dynamics. We investigate this problem in this thesis with the overall aim of reducing the online computational burden and improving the online efficiency. In RMPC schemes, robust control invariant (RCI) sets are vitally important in dealing with constraints and providing stability. They can be used as terminal (invariant) sets in RMPC schemes to reduce the online computational burden and ensure stability simultaneously. To this end, we present a novel algorithm for the computation of full-complexity polytopic RCI sets, and the corresponding feedback control law, for linear discrete-time systems subject to output and initial state constraints, performance bounds, and bounded additive disturbances. Two types of uncertainty, structured norm-bounded and polytopic uncertainty, are considered. These algorithms are then extended to deal with systems subject to asymmetric initial state and output constraints. Furthermore, the concept of RCI sets can be extended to invariant tubes, which are fundamental elements in tube based RMPC scheme. The online computational burden of tube based RMPC schemes is largely reduced to the same level as model predictive control for nominal systems. However, it is important that the constraint tightening that is needed is not excessive, otherwise the performance of the MPC design may deteriorate, and there may even not exist a feasible control law. Here, the algorithms we proposed for RCI set approximations are extended and applied to the problem of reducing the constraint tightening in tube based RMPC schemes. In order to ameliorate the computational complexity of the online RMPC algorithms, we propose an online-offline RMPC method, where a causal state feedback structure on the controller is considered. In order to improve the efficiency of the online computation, we calculate the state feedback gain offline using a semi-definite program (SDP). Then we propose a novel method to compute the control perturbation component online. The online optimization problem is derived using Farkas' Theorem, and then approximated by a quadratic program (QP) to reduce the online computational burden. A further approximation is made to derive a simplified online optimization problem, which results in a large reduction in the number of variables. Numerical examples are provided that demonstrate the advantages of all our proposed algorithms over current schemes.
Supervisor: Jaimoukha, Imad M. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral