Stabilisation of Nonlinear Systems by Discontinuous Dynamic State Feedback
نویسندگان
چکیده
In this paper, a dynamic state feedback that stabilizes general nonlinear affine in the control systems is proposed. It is deduced from the solution of an Hamilton-Jacobi like equality with two boundary conditions. The asymptotic stability of the closed loop system is proved and some examples are given. An interesting feature of this method is that the so obtained feedback takes the form of a generalised sliding mode control, in the sense that it is a dynamic feedback on one half part of the space and a static feedback on the other half with eventually a discontinuity on the surface dividing the space.
منابع مشابه
Robust Stabilization of Nonlinear Systems by Discontinuous Dynamic State Feedback
In this paper, a discontinuous dynamic state feedback that robustly stabilizes affine in control uncertain nonlinear systems is proposed. The formulation is based on Hamilton-Jacobi-Isaacs partial differential equations with two boundary conditions. The resulting dynamic state feedback is then expressed in terms of the solution of the related PDE’s. An interesting feature is that the internal s...
متن کاملTime-Invariant State Feedback Control Laws for a Special Form of Underactuated Nonlinear Systems Using Linear State Bisection
Linear state bisection is introduced as a new method to find time-invariant state feedback control laws for a special form of underactuated nonlinear systems. The specialty of the systems considered is that every unactuated state should be coupled with at least two directly actuated states. The basic idea is based on bisecting actuated states and using linear combinations with adjustable parame...
متن کاملConvergence of Pseudospectral Methods for a Class of Discontinuous-Control Nonlinear Optimal Control Problems
We consider the optimal control of feedback linearizable dynamic systems subject to mixed state and control constraints. The optimal controller is allowed to be discontinuous including bang-bang control. Although the nonlinear system is assumed to be feedback linearizable, in general, the optimal control does not linearize the dynamics. The continuous optimal control problem is discretized usin...
متن کاملDiscontinuous Feedback Stabilization Using Nonlinear Model Predictive Controllers
We propose a Model Predictive Control (MPC) framework to generate feedback controls for time-varying nonlinear systems with input constraints. One of the main features of this framework is to allow the feedback laws to be discontinuous and thereby enlarge the class of nonlinear systems that can be stabilized by continuous-time MPC. We consider a continuous-time MPC framework and perform a conti...
متن کاملA Lyapunov based nonlinear small-gain theorem for discontinuous discrete-time large-scale systems
We present a nonlinear Lyapunov function based small-gain theorem for analyzing input-to-state stability of discrete-time large-scale systems. Motivated by the fact that many feedback control laws lead to discontinuous closed loop systems, we pose no continuity assumptions on the system dynamics. For characterizing input-to-state stability in this discontinuous setting, we utilize a recently in...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002