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OPTIMAL CONTROL WITH MINIMAX COST.
STATE UNIV OF NEW YORK STONY BROOK COLL OF ENGINEERING
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The subject of this dissertation is the optimal control of systems whose performance is measured by a minimax functional over the state trajectory. The systems are assumed characterized by a set of n first order state equations. Three independent approaches are presented, each of which examines the minimax control problem from an essentially different viewpoint. Utilizing the cost-constraint duality commonly found in optimization problems of this type, the first approach demonstrates the equivalency between the minimax solution and the solution of an optimal constraint problem in bounded state space. In the second approach, a differential minimax cost is developed, allowing the minimax problem to be formulated as a coordinate minimization in the cost-augmented state space x sub zero,x. This formulation leads to the consideration of a certain set of sub-optimal problems, the solutions of which are shown to converge to the required minimax control. The modifications necessary for the application of standard variational techniques to the reformulated problem are also discussed. The final portion of this investigation is concerned with the strong relationships shown to exist between interval and finite set minimax control problem yielding an alternative procedure for the determination of minimax trajectories. Author
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