Discontinuous Control of Nonlinear Systems with convex input constraint via Locally Semiconcave Control Lyapunov Functions

Abstract

Recently, locally semiconcave control Lyapunov functions (LS-CLFs) play important roles in nonlinear control theory. Many LS-CLF based stabilizing controllers are proposed. In this paper, we consider the locally asymptotic stabilization problem of the input affine nonlinear systems with convex input constraints. To design a stabilizing state feedback under the input constraints, we employ the LS-CLF and convex optimization theory. Due to nonsmoothness of LS-CLF, the proposed state feedback is discontinuous on the state space. Therefore, we consider sample and hold solutions and guarantee the asymptotic stability of the closed loop system in the sense of sample stability. The effectiveness of the proposed method is confirmed by the numerical example.