Finite-Time Control for High-Order Random Nonlinear Systems With Unknown Control Coefficients

Random differential equations (RDEs) involving colored noise hold more practical significance than stochastic differential equations (SDEs) driven by white noise. The research on random nonlinear systems is becoming more and more popular. This paper considers the problem of finite-time control for high-order random nonlinear systems with general growth conditions and unknown control coefficients. Based on the backstepping and domination idea, the technique of adding a power integrator is adopted to recursively design an adaptive controller that renders the closed-loop system finite-time stable in probability. This paper serves as a pioneering attempt at finite-time control design of random nonlinear systems. The theoretical results are corroborated by a numerical example. Note to Practitioners —This article was motivated to realize the finite-time stability of high-order random nonlinear systems, even though there are unknown control coefficients in the system. The practical significance of this paper is mainly twofold. Firstly, since random noise is ubiquitous in all kinds of engineering environments, the research on random nonlinear systems driven by colored noise is of great importance. Secondly, the asymptotic stability is infeasible in the practical implementation, so the achievement of finite-time control makes the method proposed in this paper applicable.