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Model Predictive Control (MPC) for constrained nonlinear systems


S. De Oliveira

vol. AUT96-33

This thesis addresses the development of stabilizing model predictive control algorithms for nonlinear systems subject to input and state constraints and in the presence of parametric and/or structural uncertainty, disturbances and measurement noise. Our basic model predictive control (MPC) scheme consists of a finite horizon MPC technique with the introduction of an additional state constraint which we have denoted {em contractive constraint}. This is a Lyapunov-based approach in which a Lyapunov function chosen a priori is decreased, not continuously, but discretely; it is allowed to increase at other times (between prediction horizons). We will show in this work that the implementation of this additional constraint into the on-line optimization makes it possible to prove rather strong stability properties of the closed-loop system. In the nominal case and in the absence of disturbances, it is possible to show that the presence of the contractive constraint renders the closed-loop system exponentially stable. We will also examine how the stability properties weaken as structural and/or parametric model/plant mismatch, disturbances and measurement noise are considered. Another important aspect considered in this work is the computational efficiency and implementability of the algorithms proposed. The MPC schemes previously proposed in the literature which are able to guarantee stability of the closed-loop system involve the solution of a nonlinear programming problem at each time step in order to find the optimal (or, at least, feasible) control sequence. Nonlinear programming is the general case in which both the objective and constraint functions may be nonlinear, and is the most difficult of the smooth optimization problems. Due to the difficulties inherent to solving nonlinear programming problems and since MPC requires the optimal (or feasible) solution to be computed on-line, it is important that an alternative implementation be found which guarantees that the problem can be solved in a finite number of steps. It is well-known that both linear and quadratic programming (QP) problems satisfy this requirement.


Type of Publication:

(04)Technical Report

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% Autogenerated BibTeX entry
@TechReport { Xxx:1996:IFA_1517,
    author={S. De Oliveira},
    title={{Model Predictive Control (MPC) for constrained nonlinear
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