Discrete Time Optimal Control Problems on Large Intervals
In this paper we study the structure of approximate solutions of an autonomous nonconcave discrete-time optimal control system with a compact metric space of states. In the first part of the paper we discuss our recent results for systems described by a bounded upper semicontinuous objective function which determines an optimality criterion. These optimal control systems are discrete-time analogs of Lagrange problems in the calculus of variations. It is known that approximate solutions are determined mainly by the objective function, and are essentially independent of the choice of time interval and data, except in regions close to the endpoints of the time interval. Our goal is to study the structure of approximate solutions in regions close to the endpoints of the time intervals. The second part of the paper contains new results on the structure of solutions of optimal control systems which are discrete-time analogs of Bolza problems in the calculus of variations. These systems are described by a pair of objective functions which determines an optimality criterion.
KeywordsGood program Optimal control problem Overtaking optimal program Turnpike property
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