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Optimal Control of Discrete Time Linear Hybrid Systems


A. Bemporad, F. Borrelli, M. Morari

vol. AUT01-20

In~cite{BBM00acc} we proposed a procedure for synthesizing piecewise affine optimal controllers for discrete-time linear hybrid systems. The procedure consisted of finding the state-feedback solution to finite-time optimal control problems with performance criteria based on linear norms via multiparametric programming. We have successfully applied this type of optimal controllers to a range of problems including traction control. The use of linear norms could have two main practical disadvantages: (i) a satisfactory performance could be achieved only with a long time-horizon with a consequent increase of the complexity of the controller law, (ii) the tuning of the controller may not be a smooth function of the weighting matrices, i.e., a slight change to the weighting matrices could lead to a completely different closed-loop performance. This work is a step towards the solution of optimal control problems for linear hybrid systems with performance criteria based on quadratic norms. For discrete time constrained hybrid systems we prove that the solution to constrained finite time optimal control problems is a time varying piecewise affine feedback control law. We give insight into the structure of the optimal control law and of the value function for optimal control problems with performance criteria based on quadratic and linear norms. We briefly describe how the optimal control law can be efficiently computed by means of multiparametric programming, for linear and convex performance criteria. The infinite horizon controller can be approximated by a stabilizing controller obtained from a receding horizon optimal controller over a finite horizon.


Type of Publication:

(04)Technical Report

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% Autogenerated BibTeX entry
@TechReport { BemBor:2001:IFA_980,
    author={A. Bemporad and F. Borrelli and M. Morari},
    title={{Optimal Control of Discrete Time Linear Hybrid Systems}},
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