Vector-valued measure and the necessary conditions for the optimal control problems of linear systems. (English) Zbl 0564.49014
The vector-valued measure defined by well-posed linear boundary value problems is discussed. The maximum principle of the optimal control problem with non-convex constraint is proved by using the vector-valued measure. Especially, necessary conditions of optimal control of elliptic systems are derived without the convexity of the control domain and the cost function.
MSC:
| 49K27 | Optimality conditions for problems in abstract spaces |
| 28B05 | Vector-valued set functions, measures and integrals |
| 93C05 | Linear systems in control theory |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 35B37 | PDE in connection with control problems (MSC2000) |
| 35J55 | Systems of elliptic equations, boundary value problems (MSC2000) |
| 93C20 | Control/observation systems governed by partial differential equations |
