scholarly journals Low-Complexity Adaptive Saturated Control of a Class of Nonlinear Systems with Its Application

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Gang Zhang ◽  
Deqiang Cheng ◽  
Qiqi Kou
Keyword(s):  
Nonlinear Systems ◽  
Dead Zone ◽  
External Disturbance ◽  
Original System ◽  
Low Complexity ◽  
Control Law ◽  
Zone Model ◽  
Time Varying ◽  
Saturated Control ◽  
Output Constraint

This paper investigates a low-complexity saturated control law for a class of nonlinear systems with consideration of the time-varying output constraint, control constraint, and external disturbance. First, a dead-zone model is employed to transform the control saturation nonlinearity into a linear one with respect to the real input signal. Then, the original system with time-varying output constraint is transformed into a constraint-free one, based on which a novel adaptive saturated control law is devised along the filtered error manifold. By employing minimum learning parameter technique and virtual error concept, only two adaptive parameters are needed to update online, which reduces the computational burdens dramatically. Finally, the applications to Duffing-Holmes chaotic system are organized to validate the effectiveness of the proposed control law.

Output tracking and disturbance rejection for 1-D anti-stable wave equation

2019 ◽  
Vol 25 ◽  
pp. 69 ◽  
Author(s):  
Hua-Cheng Zhou
Keyword(s):  
Wave Equation ◽  
Disturbance Rejection ◽  
External Disturbance ◽  
Reference Signal ◽  
Original System ◽  
Delay Systems ◽  
Transport Systems ◽  
Control Law ◽  
Proportional Control ◽  
Output Tracking

In this paper, we solve the output tracking and disturbance rejection problem for a system described by a one-dimensional anti-stable wave equation, with reference and disturbance signals that belong to W1,∞[0, ∞) and L∞[0, ∞), respectively. Generally, these signals cannot be generated from an exosystem. We explore an approach based on proportional control. It is shown that a proportional gain controller can achieve exponentially the output tracking while rejecting disturbance. Our method consists of three steps: first, we convert the original system without disturbance into two transport equations with an ordinary differential equation by using Riemann variables, then we propose a proportional control law by making use of the properties of transport systems and time delay systems. Second, based on our recent result on disturbance estimator, we apply the estimation/cancellion strategy to cancel to the external disturbance and to track the reference asymptotically. Third, we design a controller using a state observer. Since disturbance does not appear in the observer explicitly (the disturbance is exactly compensated), the controlled output signal is exponentially tracking the reference signal. As a byproduct, we obtain a new output feedback stabilizing control law by which the resulting closed-loop system is exponentially stable using only two displacement output signals.

scholarly journals Asymptotic Stabilization by State Feedback for a Class of Stochastic Nonlinear Systems with Time-Varying Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hui Wang ◽  
Wuquan Li ◽  
Xiuhong Wang
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Original System ◽  
Feedback Stabilization ◽  
Stochastic Nonlinear Systems ◽  
Time Varying ◽  
Globally Asymptotically Stable ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Control Coefficients

This paper investigates the problem of state-feedback stabilization for a class of upper-triangular stochastic nonlinear systems with time-varying control coefficients. By introducing effective coordinates, the original system is transformed into an equivalent one with tunable gain. After that, by using the low gain homogeneous domination technique and choosing the low gain parameter skillfully, the closed-loop system can be proved to be globally asymptotically stable in probability. The efficiency of the state-feedback controller is demonstrated by a simulation example.

scholarly journals Nonsingular Global Fixed-Time Stabilization for Nonlinear Systems

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Wei Hu ◽  
Zhangyong Zhou ◽  
Junjun Tang
Keyword(s):  
Nonlinear Systems ◽  
Control Method ◽  
Original System ◽  
Fixed Time ◽  
Time Varying ◽  
Feedback Systems ◽  
Convergence Problem ◽  
Adding A Power Integrator ◽  
Coordinate Mapping ◽  
Novel Concept

Since existing results about fixed-time stabilization are only applied to strict feedback systems, this paper investigates the nonsingular fixed-time stabilization of more general high-order nonlinear systems. Based on a novel concept named coordinate mapping of time domain, a control method is first proposed to transform the nonsingular fixed-time convergence problem into the finite-time convergence problem of a transformed time-varying system. By extending the existing, adding a power integrator technique into the considered time-varying system, a periodic controller is constructed to stabilize the original system in fixed time. The results of simulations verify the effectiveness of the proposed method.

Robust Adaptive Control of Mildly Nonlinear Systems With Time Varying Input/Output Delays

2012 ◽  
Author(s):  
James P. Nelson ◽  
Mark J. Balas ◽  
Richard S. Erwin
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Adaptive Controller ◽  
Robust Adaptive Control ◽  
Control Law ◽  
Time Varying ◽  
Robust Adaptive ◽  
Input Delays ◽  
Persistent Disturbances ◽  
Adaptive Control Law

Many systems must operate in the presence of delays both internal to the system and in its inputs and outputs. In this paper we present a robustness result for mildly nonlinear systems. We use this result to show that, for small unknown time varying input delays, a simple adaptive controller can produce output regulation to a neighborhood with radius dependent upon the size of an upper bound on the delay. This regulation occurs in the presence of persistent disturbances and the convergence is exponential. We conclude with an example to illustrate the behavior of this adaptive control law.

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