Nonlinear Control of Convex Input Costrained Nonlinear Systems Based on Locally Semiconcave Control Lyapunov Functions

Abstract

Semiconcave control Lyapunov functions (semiconcave CLFs) play important roles in nonlinear control theory. Many semiconcave CLF based stabilizing controllers were proposed. In this paper, we consider a local asymptotic stabilization problem of input affine nonlinear systems under convex input constraints. To design a stabilizing state feedback under the input constraints, we employ a locally semiconcave CLF and the convex optimization theory. Due to nonsmoothness of the semiconcave CLF, the proposed state feedback is discontinuous on the state space. We consider sample and hold solutions and guarantee the asymptotic stability of the closed loop system in the sense of sample stability.