Regularity Properties of Optimal Controls with Application to Discrete Approximation

U. Felgenhauer
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U. Felgenhauer: Brandenburgische Technische Universität

Journal of Optimization Theory and Applications, 1999, vol. 102, issue 1, No 7, 97-110

Abstract: Abstract This paper is directed to the analysis of regularity properties of optimal solutions for a nonlinear control problem with convex control constraints. Since the problem formulation is given typically in L ∞-terms, we introduce first the essential limit set as a tool for the local investigation of L ∞-functions. Under second-order conditions of the coercivity type on the solution, a structural result is obtained characterizing the local behavior of the optimal control by means of Lipschitz continuous functions. Further, the consequences for certain discrete approximations are discussed; for uniquely solvable problems, we show the Lipschitz continuity of the optimal control.

Keywords: Optimal control theory; discretization methods; second-order condition; solution regularity; Lipschitz continuity result (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021842412255

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