On Robust Adaptive Control For Nonlinear Systems With Time-varying Output Constraint

There are varieties of uncertainties during the process of the system modeling,such as model errors,measurable noise and so on,which are usually called unmodeled dynamics.Its existence affects the dynamic performance of the system seriously,and even destroys the stability of the system.So eliminating or suppressing the influence of unmodeled dynamics is an important factor to ensure the stability of the closed-loop system.On the other hand,it is often necessary to restrict the input or output of the system in order to realize the effective control of the system.Once the system violates this constraint during operation,then the stability of the system is likely to be undermined.At present,the research on unconstrained systems has been gradually improved,but these methods are difficult to apply to the constrained system.Therefore,it is very important to study the stability of the system with unmodeled dynamics and constrains.Three adaptive control schemes based on the asymmetric barrier Lyapunov function(ABLF)and nonlinear mapping(NM)are proposed for nonlinear system with unmodeled dynamics and time-varying constraint.The main contents of this paper are summarized as follows:Firstly,an adaptive dynamic surface output feedback control scheme is proposed for a class of nonlinear systems with time-varying output constraints and unmodeled dynamics and input saturation.The unknown nonlinear continuous functions are approximated by radial basis function neural networks(RBFNNs).The system is reconstructed by using K-filters and the unmeasurable states are estimated by constructing states observor.The unmodeled dynamics are coped by introducing dynamic signal.ABLF is employed to cope with time-varying output constraint and the adaptive controller designed by ABLF carries out time-varying output constraint.The actual control law can be separated by constructing auxiliary signal.By theoretical analysis,the closed-loop control system is proved to be semi-globally uniformly ultimately bounded,while the output constraint is never violated.Finally,a numerical simulation example is given to further verify the effectiveness of the proposed approach.Secondly,an adaptive neural network control scheme is proposed for strict feedback nonlinear system with unmodeled dynamics and input nonlinearity and time-varying output constraint.Based on the assumption that the unmodeled dynamics is exponentially input state practically stable(ISpS),unmodeled dynamics are handled by standard dynamic signal;the adaptive controller designed by ABLF carries out time-varying output constraint.By theoretical analysis,the closed-loop control system is proved to be semi-globally uniformly ultimately bounded,while the output constraint is never violated.Finally,two numerical simulation examples are given to further verify the effectiveness of the proposed approach.Thirdly,a decentralized adaptive neural network control scheme is proposed for a class of nonlinear interconnected large scale systems with state and input unmodeled dynamics and input nonlinearity.The unknown nonlinear continuous functions are approximated by RBFNNs;state and input unmodeled dynamics are dealt by introducing dynamic signal and normalization signal;the strict feedback system with time-varying output constraint is transformed into a novel strict feedback system without constraint by introducing one to one nonlinear mapping.By theoretical analysis,the closed-loop control system is proved to be semi-globally uniformly ultimately bounded,while the output constraint is never violated.Finally,two numerical simulation examples further illustrate the effectiveness of the proposed approach.