Existence and stability analysis for nonlinear optimal control problems with $1$-mean equicontinuous controls
Hongyong Deng Wei Wei
Journal of Industrial & Management Optimization 2015, 11(4): 1409-1422 doi: 10.3934/jimo.2015.11.1409
In this paper, the existence and stability of solutions of nonlinear optimal control problems with $1$-mean equicontinuous controls are discussed. In particular, a new existence theorem is obtained without convexity assumption. We investigate the stability of the optimal control problem with respect to the right-hand side functions, which is important in computational methods for optimal control problems when the function is approximated by a new function. Due to lack of uniqueness of solutions for an optimal control problem, the stability results for a class of optimal control problems with the measurable admissible control set is given based on the theory of set-valued mappings and the definition of essential solutions for optimal control problems. We show that the optimal control problems, whose solutions are all essential, form a dense residual set, and so every optimal control problem can be closely approximated arbitrarily by an essential optimal control problem.
keywords: Optimal control stability essential solution. existence set-valued mapping

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