A Controller Design for a Class of Nonlinear Systems Using the Lyapunov-Bellman Approach

1992 ◽  
Vol 114 (3) ◽  
pp. 390-393 ◽  
Author(s):  
R. T. Yanushevsky
Keyword(s):  
Optimal Control ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Optimal Control Problem ◽  
Lyapunov Functions ◽  
Bellman Equation ◽  
Controller Design ◽  
Variable Structure ◽  
System A

The method of synthesis for a wide class of nonlinear systems affine in control is considered. The proposed approach is based on the solution of a special optimal control problem. The integrand of the optimized functional is chosen in such a way that the Bellman equation has a desired solution. The nonlinear system design is reduced to the examination of the integrand of the optimized functional. To extend the domain of asymptotic stability of the nonlinear system, a sequence of the Lyapunov functions is used. The whole system becomes a system with variable structure.

Variable structure based robust backstepping controller design for nonlinear systems

2010 ◽  
Vol 63 (1-2) ◽  
pp. 253-262 ◽  
Author(s):  
Chao-Chung Peng ◽  
Albert Wen-Jeng Hsue ◽  
Chieh-Li Chen
Keyword(s):  
Nonlinear Systems ◽  
Controller Design ◽  
Variable Structure ◽  
Backstepping Controller

scholarly journals Robust Output Feedback Passivity-Based Variable Structure Controller Design for Nonlinear Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Jeang-Lin Chang ◽  
Tsui-Chou Wu
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Controller Design ◽  
Sliding Mode ◽  
Damping Ratio ◽  
Variable Structure ◽  
Sliding Surface ◽  
Estimation Errors ◽  
System States ◽  
Approach Zero

This paper examines the use of an output feedback variable structure controller with a nonlinear sliding surface for a class of SISO nonlinear systems in the presence of matched disturbances. With only the measurable system output, the discontinuous observer reconstructs the system states and ensures that the estimation errors exponentially approach zero. Using the estimation states, the proposed nonlinear sliding surface with variable damping ratio can simultaneously achieve low overshoot and short settling time. Then the passivity-based controller including a discontinuous term can guarantee that the closed-loop system asymptotically converges to the sliding surface. Compared with other sliding mode controllers, the proposed passivity-based control scheme has better transient performance and effectively reduces the control gain. Finally, simulation results demonstrate the validity of the proposed method.

Extended Finite Time Inverse Optimal Control of Nonlinear Systems

2011 ◽  
Vol 403-408 ◽  
pp. 1499-1502
Author(s):  
Xin Jun Ren ◽  
Yan Jun Shen
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Finite Time ◽  
Lyapunov Functions ◽  
Control Law ◽  
Inverse Optimal Control ◽  
Closed Loop System ◽  
Affine Nonlinear Systems ◽  
Definition Of ◽  
The Cost

In this paper, we use the definition of control Lyapunov functions to study finite time inverse optimal control for affine nonlinear systems. Based on control Lyapunov functions, a finite time universal control formula is presented, which can ensure the closed-loop system is finite time stable. From this, less conservative conditions for the finite time inverse optimal control are derived. We design a finite time inverse optimal control law, which minimizes the cost functional. A numerical example verifies the validity of the proposed method.

Stabilization of Nonlinear Systems Using Linear Observers

1974 ◽  
Vol 96 (1) ◽  
pp. 55-60 ◽  
Author(s):  
R. E. Strane ◽  
W. G. Vogt
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Nonlinear Equations ◽  
Linear Approximation ◽  
Asymptotically Stable ◽  
State Variables ◽  
Finite Region ◽  
Linear Portion ◽  
Linear Observer

In this paper, it is shown that a linear observer can always be designed to stabilize a nonlinear system which contains a Lur’e type nonlinearity in the sector [0, k], where k is finite, if both the output of the nonlinearity and a completely observable output of the linear portion are available as inputs to the observer. In case a completely observable output is not available from the linear portion, stabilization is shown to be possible if the original linear approximation of the system is asymptotically stable or those state variables corresponding to the unstable eigenvalues are available. It is also established that a linear observer can be used to guarantee that a finite region of asymptotic stability exists for a plant described by a more general set of nonlinear equations, and in some cases the domain of asymptotic stability can be made as large as desired.

scholarly journals On an Optimal Control Problem for a Linear System With Variable Structure

2016 ◽  
Author(s):  
Р.О. Масталиев
Keyword(s):  
Optimal Control ◽  
Linear System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Variable Structure

В задаче оптимального управления с переменной линейной структурой, описываемой линейным разностным и интегро-дифференциальным уравнениями типа Вольтерра, получено необходимое и достаточное условие оптимальности в форме принципа максимума Понтрягина. В случае выпуклости функционала критерия качества получено достаточное условие оптимальности.

scholarly journals A unified framework of rapid exponential stability and optimal feedback control for nonlinear systems

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983320
Author(s):  
Yan Li ◽  
Yuanchun Li
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Exponential Stability ◽  
Real Time ◽  
Lyapunov Functions ◽  
Bellman Equation ◽  
Optimal Feedback Control ◽  
Optimal Feedback ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman

A novel framework of rapid exponential stability and optimal feedback control is investigated and analyzed for a class of nonlinear systems through a variant of continuous Lyapunov functions and Hamilton–Jacobi–Bellman equation. Rapid exponential stability means that the trajectories of nonlinear systems converge to equilibrium states in accelerated time. The sufficient conditions of rapid exponential stability are developed using continuous Lyapunov functions for nonlinear systems. Furthermore, according to a variant of continuous Lyapunov functions, a rapid exponential stability is guaranteed which satisfies some canonical conditions and Hamilton–Jacobi–Bellman equation for controlled nonlinear systems. It is can be seen that the solution of Hamilton–Jacobi–Bellman equation is a continuous Lyapunov function, and, therefore, rapid exponential stability and optimality are guaranteed for nonlinear systems. Last, the main result of this article is investigated via a nonlinear model of a spacecraft with one axis of symmetry through simulations and is used to check rapid exponential stability. Moreover, for the disturbance problem of initial point, a rapid exponential stable controller can reject the large-scale disturbances for controlled nonlinear systems. In addition, the proposed optimal feedback controller is applied to the tracking trajectories of 2-degree-of-freedom manipulator, and the numerical results have illustrated high efficiency and robustness in real time. The simulation results demonstrate the use of the rapid exponential stability and optimal feedback approach for real-time nonlinear systems.

Sign in / Sign up

Export Citation Format

Share Document