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The instability of optimal control problems to time delay. (English) Zbl 1081.49020
Time delay optimal control problems are considered. The delay enters in both the state and the control. It is shown that the limit problem obtained by putting the delay equal to zero is not the correct variational limit of the given optimization problem. By a relaxation procedure, the proper variational limit is identified and corresponding well-posedness results are obtained about the convergence of the optimal performance and the optimal control laws.
MSC:
49K40Sensitivity, stability, well-posedness of optimal solutions
49K25Optimal control problems with equations with ret.arguments (nec.) (MSC2000)
34K35Functional-differential equations connected with control problems
93C23Systems governed by functional-differential equations