Abstract
Relaxed variational techniques are applied to a minimum sensitivity control problem. Sensitivity of a trajectory is minimized to perturbations in initial conditions. Rather than using the optimal control that does indeed exist and that satisfies the final conditions exactly, a suboptimal control is used that transfers the system from the given initial state to an arbitrary small neighborhood of the given final state, and that results in a considerably better performance than the optimal solution. The suboptimal control is constructed using the optimal controls of the relaxed problem.
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Communicated by G. Leitmann
This paper is based upon the Ph.D. dissertation by the author at Purdue University, Lafayette, Indiana. The author wishes to thank Professor Violet B. Haas, School of Electrical Engineering, Purdue University, for introducing him to relaxed variational problems and for many very helpful suggestions through the course of this work.
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Steinberg, A.M. Application of relaxed solutions to minimum sensitivity optimal control. J Optim Theory Appl 10, 178–186 (1972). https://doi.org/10.1007/BF00934732
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DOI: https://doi.org/10.1007/BF00934732