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Robust maximum principle for multi-model LQ-problem

This paper presents the version of the robust maximum principle in the context of multi-model control formulated as the minimax Bolza problem. The cost function contains a terminal term as well as an integral one. A fixed horizon and terminal set are considered. The necessary conditions of the optimality are derived for the class of uncertain systems given by an ordinary differential equation with parameters from a given finite set. This problem consists in the control design providing a good behaviour for a given class of multi-model system. It is shown that the design of the minimax optimal controller is reduced to a finite-dimensional optimization problem given at the corresponding simplex set containing the weight parameters to be found. The robust optimal control may be interpreted as a mixture (with the optimal weights) of the controls which are optimal for each fixed parameter value. The proof is based on the recent results obtained for minimax Mayer problem (Boltyanski and Poznyak 1999a). The minimax linear quadratic control problem is considered in detail and the illustrative examples dealing with finite as well as infinite horizons conclude this paper.