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What is viability theory. (Czech) Zbl 0727.34019
The paper is a survey about the mathematical aspects of viability theory. The theory is based on the differential inclusion $$\dot x\in F(x)$$ with the constraints x(t)$$\in K$$, where K is called the viability set. The necessary and sufficient conditions for the existence of viable solutions are described. Various types of the set K are considered. The relationship with the optimal control problem $$\dot x=f(x(t),u(t))$$, u(t)$$\in U(x(t))$$ is mentioned, too.
MSC:
 34A60 Ordinary differential inclusions 49J15 Existence theories for optimal control problems involving ordinary differential equations 49J24 Optimal control problems with differential inclusions (existence) (MSC2000) 34A40 Differential inequalities involving functions of a single real variable