Determination of a controllable set for a controlled dynamic system

Abstract

The controllable set of a controlled ordinary differential dynamic system to a given set is defined. Under certain reasonable conditions, the controllable set is characterised by a level set of the unique viscosity solution to some Hamilton-JacobiBellman equation. The result is used to determine the asymptotic stable set of nonlinear autonomous differential equations.

Determination of a controllable set for a class of non‐linear stochastic control systems

“…Some relevant results about the uniform s-controllability can be found in Reference [9]. In this paper, the following assumption is given as one of the sufficient conditions of the main results.…”