Discontinuous Control of Nonlinear Systems with Convex Input Constraint Via Locally Semiconcave Control Lyapunov Functions
نویسندگان
چکیده
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.
منابع مشابه
Strong Implication-Form ISS-Lyapunov Functions for Discontinuous Discrete-Time Systems
Input-to-State Stability (ISS) and the ISSLyapunov function have proved to be useful tools for the analysis and design of nonlinear systems in a variety of contexts. Motivated by the fact that many feedback control laws, such as model predictive control or event-based control, lead to discontinuous discrete-time dynamics, we investigate ISS-Lyapunov functions for such systems. ISS-Lyapunov func...
متن کاملA Linear Matrix Inequality (LMI) Approach to Robust Model Predictive Control (RMPC) Design in Nonlinear Uncertain Systems Subjected to Control Input Constraint
In this paper, a robust model predictive control (MPC) algorithm is addressed for nonlinear uncertain systems in presence of the control input constraint. For achieving this goal, firstly, the additive and polytopic uncertainties are formulated in the nonlinear uncertain systems. Then, the control policy can be demonstrated as a state feedback control law in order to minimize a given cost funct...
متن کاملExistence of Lipschitz and Semiconcave Control-Lyapunov Functions
Given a locally Lipschitz control system which is globally asymptotically controllable to the origin, we construct a control-Lyapunov function for the system which is Lipschitz on bounded sets and we deduce the existence of another one which is semiconcave (and so locally Lipschitz) outside the origin. The proof relies on value functions and nonsmooth calculus.
متن کاملSemiconcave Control-Lyapunov Functions and Stabilizing Feedbacks
We study the general problem of stabilization of globally asymptotically controllable systems. We construct discontinuous feedback laws, and particularly we make it possible to choose these continuous outside a small set (closed with measure zero) of discontinuity in the case of control systems which are affine in the control; moreover this set of singularities is shown to be repulsive for the ...
متن کاملStability analysis and feedback control of T-S fuzzy hyperbolic delay model for a class of nonlinear systems with time-varying delay
In this paper, a new T-S fuzzy hyperbolic delay model for a class of nonlinear systems with time-varying delay, is presented to address the problems of stability analysis and feedback control. Fuzzy controller is designed based on the parallel distributed compensation (PDC), and with a new Lyapunov function, delay dependent asymptotic stability conditions of the closed-loop system are derived v...
متن کامل