Second-order necessary optimality conditions for an optimal control problem with nonlinear state equations. (English) Zbl 1485.49009
Second-order necessary optimality conditions are derived for an optimal control problem (OCP) with nonconvex cost function, nonlinear state equation and mixed constraints using tools from functional analysis. An example is given showing that if the second-order necessary condition is not satisfied, then the admissible couple is not a solution even it satisfies first-order necessary conditions.
Reviewer: Bülent Karasözen (Ankara)
MSC:
| 49J15 | Existence theories for optimal control problems involving ordinary differential equations |
| 49J21 | Existence theories for optimal control problems involving relations other than differential equations |
| 49K21 | Optimality conditions for problems involving relations other than differential equations |
| 90C90 | Applications of mathematical programming |
| 93C05 | Linear systems in control theory |
Keywords:
first-order optimality condition; second-order optimality condition; optimal control problem; nonlinear state equation; mixed constraintReferences:
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