Let a quasilinear control system having the state space\(\bar X \subseteq R^n \) be governed by the vector differential equation
wherex(0) =x 0 andU is the family of all bounded measurable functions from [0,T] intoU, a compact and convex subset ofR m.LetG:U ⇑R be a bounded measurable nonlinear function, such thatG(U) is compact and convex.G −1 can be convex onG(U) or concave. The main results of the paper establish the existence of a controlu ∈U which minimizes the cost functional
whereL(·) is convex. A practical example of application for chemical reactions is worked out in detail.
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Socha, L., andSkrzypek, J.,Application of Open-Loop Control to the Determination of the Optimal Temperature Profile in a Chemical Reactor, Proceedings of 8th IFIP Conference on Optimization Techniques, Würzburg, Germany, 1977.
Boyarsky, A.,On the Existence of Optimal Controls for Nonlinear Systems, Journal of Optimization Theory and Applications, Vol. 20, No. 2, 1976.
Friedland, S.,Global Principle for Free-Endpoint Problems in Optimal Control and Differential Games, Journal of Optimization Theory and Applications, Vol. 24, No. 2, 1978.
Communicated by G. Leitmann
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Socha, L. Some remarks on the existence of optimal controls for quasilinear systems. J Optim Theory Appl 33, 393–399 (1981). https://doi.org/10.1007/BF00935251
- Optimal control
- nonlinear systems
- existence theorems