Design And Analysis Of Robust Predictive Controllers For Asymmetric Nonlinear Systems

The asymmetric systems exhibit different dynamic response processes under the action of the input in opposite directions,especially near the equilibrium point,the dynamic characteristics of asymmetries are more obvious.At present,most studies are limited to the linear description of asymmetric systems.In the case of a few asymmetrical systems which are nonlinear descriptions,the linearization approximation method is generally used,and then the control is carried out,however,when the nonlinear degree of the system is relatively high,the linearized system model may be mismatched with the original system model,which leads to unsatisfactory control results.Therefore,controllers are designed for asymmetrical nonlinear systems with constraints and external disturbances to stabilize the closed-loop system in the paper.The work of this paper can be summarized into three parts:Firstly,the robust control problem for a class of constrained asymmetric nonlinear systems is studied.First,robust controllers based on Lyapunov function are designed for both positive and negative systems respectively,and the stability regions are estimated,the control action at each moment is calculated by using the robust controllers with the positive and negative directions,then the system selects the controller according to the matching of the positive and negative control,so that the closed-loop system can achieve the global asymptotic stability,finally,a simulation example is given to verify the effectiveness of the proposed scheme.Secondly,the robust control problem for a class of asymmetric nonlinear systems with constraints and external disturbances is studied.First,robust controllers based on Lyapunov function are designed for both positive and negative systems respectively,and the stability regions are estimated,the control action at each time is calculated by using the robust controllers with the positive and negative directions,then the system selects the controller according to the matching of the positive and negative control,so that the closed-loop system can achieve the global asymptotic stability,finally,a simulation example is given to verify the effectiveness of the proposed scheme.Thirdly,the finite time robust predictive control problem for a class of constrained asymmetric nonlinear systems is studied.Considering the relationship between the initial state and the stability regions of the system,two controllers are designed based on the Lyapunov function to make the closed-loop system stable in finite time under any initial state.The details are as follows: first,robust controllers based on Lyapunov function are designed for both positive and negative systems respectively,and the stability regions are estimated.When the initial stateof the system is in the stability regions,the system is stabilized in finite time by using robust controllers.When the initial state of the system is outside the stability regions,predictive controllesrs based on Lyapunov function are designed for both positive and negative systems,which are used to pull the state into the stability regions in finite time,and then the robust controllers are used to make the system stable in finite time in the stability regions,finally,a simulation example is given to verify the effectiveness of the scheme.