Nonsmooth Optimal Regulation and Discontinuous Stabilization
نویسنده
چکیده
For affine control systems, we study the relationship between an optimal regulation problem on the infinite horizon and stabilizability. We are interested in the case the value function of the optimal regulation problem is not smooth and feedback laws involved in stabilizability may be discontinuous.
منابع مشابه
Linearization and Stabilization of Second-Order Nonholonomic Chained Systems
This paper presents a theoretical framework for linearization and stabilization of second-order nonholonomic chained systems. By giving a new criterion for the problem of nonsmooth nonregular feedback linearization, it is proved that second-order chained systems are nonregular static state feedback linearizable. A discontinuous control law is obtained based on linear system theory and the inver...
متن کاملF. Ceragioli EXTERNAL STABILIZATION OF DISCONTINUOS SYSTEMS AND NONSMOOTH CONTROL LYAPUNOV-LIKE FUNCTIONS
The main result of this note is an external stabilizability theorem for discontinuous systems affine in the control (with solutions intended in the Filippov’s sense). In order to get it we first prove a sufficient condition for external stability which makes use of nonsmooth Lyapunov-like functions.
متن کاملA tutorial on solutions , nonsmooth analysis , and stability
A tutorial on solutions, nonsmooth analysis, and stability Discontinuous dynamical systems arise in a large number of applications. In optimal control problems, open-loop bang-bang controllers switch discontinuously between extreme values of the inputs to generate minimum-time trajectories from the initial to the final states [1]. Thermostats implement on-off controllers to regulate room temper...
متن کاملTime-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time
While non-smooth approaches (including sliding mode control) provide explicit feedback laws that ensure finite-time stabilization but in terminal time that depends on the initial condition, fixed-time optimal control with a terminal constraint ensures regulation in prescribed time but lacks the explicit character in the presence of nonlinearities and uncertainties. In this paper we present an a...
متن کاملFeedback linearization and stabilization of second-order nonholonomic chained systems
This paper presents a theoretical framework for nonregular feedback linearization and stabilization of second-order nonholonomic chained systems. By giving a new criterion for the problem of nonsmooth nonregular feedback linearization, it is proved that second-order chained systems are nonregular static state feedback linearizable. A discontinuous control law is obtained based on linear system ...
متن کامل