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Constrained Control - Computations, Performance and Robustness


M. Baric

no. 18063

The topic of the thesis is control of discrete-time systems subject to constraints on control inputs and state variables. The first part of the thesis is devoted primarily to computational issues. We start with the problem of finite horizon optimal control of piecewise-affine systems subject to polytopic constraints. For the cost function based on polyhedral norms we discuss two formulations of the solution procedure and propose an algorithm that yields significant improvements in efficiency by exploiting a particular structure of the problem. Improvements of one order of magnitude in efficiency are observed in numerical trials. The following chapter addresses the issue of explicit solution to model predictive control for constrained linear systems. We consider parametrization of the cost and compute receding horizon control law which is a function of the state vector as well as of the parameters in the cost function. With such parametrization the performance of the explicit solution can be adjusted during the controller operation by direct modification of the cost parameters. The corresponding computations are based on the so-called rim parametric linear program. We develop an algorithm for solving such parametric linear programs, using the concept of lexicographic perturbation for resolving degeneracy. Particular structure of the problem makes the computed explicit controller amenable for the off-line stability analysis. Second part of the thesis deals with aspects related to feasibility and performance of control under constraints and in the presence of perturbations.We consider two classes of problems. One is concerned with the so-called “max–min” control problems, where the current value of the perturbations is known to the controller, while their future realization cannot be anticipated. We develop general framework for analyzing such problems. Reachability and computation of controllability sets is put in focus. Cost optimal and time optimal control schemes are discussed for a number of system classes. The final part of the thesis deals with the robust control of constrained linear systems. We investigate specific parametrization for characterization of (robust) control invariant sets. Using the first parametrization we develop a method for synthesis of stabilizing control law and construction of set–induced local control Lyapunov functions and subsequently use this method for the design of stabilizing robust model predictive controller. The final chapter introduces a novel, more general parametrization scheme for construction of robust control invariant sets for constrained linear system subject to additive, bounded perturbations. This novel parametrization enables implicit characterization of robust control invariant sets as a Minkowski sum of compact sets. The method also offers a possibility to construct set–induced local control Lyapunov functions of controlled complexity. We show that the new method is more general compared to the similar, already existing scheme.


Type of Publication:

(03)Ph.D. Thesis

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% Autogenerated BibTeX entry
@PhDThesis { Xxx:2008:IFA_4998,
    author={M. Baric},
    title={{Constrained Control - Computations, Performance and
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