An optimal control problem for systems described by partial differential equations of hyperbolic type with delay. (English) Zbl 0586.49009
An optimal control problem of the Goursat type with delay is investigated. With a given aim functional, a necessary condition of optimality is formulated and proved in the form of a maximum principle. The proof is based on the reduction of a problem with delay to a problem without delay.
MSC:
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 35R10 | Partial functional-differential equations |
| 93C20 | Control/observation systems governed by partial differential equations |
| 35B37 | PDE in connection with control problems (MSC2000) |
References:
| [1] | Egorov, A. I.,Optimal Processes in Systems with Distributed Parameters and Some Problems of Invariance Theory, Izvestiya Akademii Nauk SSSR, Seriya Matematika, Vol. 29, No. 6, 1965. · Zbl 0151.13305 |
| [2] | Guinn, T.,Reduction of Delayed Optimal Control Problems to Nondelayed Problems, Journal of Optimization Theory and Applications, Vol. 18, No. 3, 1976. · Zbl 0304.49017 |
| [3] | Butkovski, A. G.,Theory of Optimal Control of Systems with Distributed Parameters, Fizmatgiz, Moscow, USSR, 1965. |
| [4] | Tricomi, F.,Lectures on Equations in Partial Derivatives, IIL, Moscow, USSR, 1957. |
| [5] | Tcutcunava, M. T.,On a Boundary-Value Problem for Systems of Hyperbolic Equations, Perm Polytechnical Institute, Interuniversity Collection of Scientific Works, USSR, 1979. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
