Adaptive robust stabilization of a class of uncertain non-linear systems with mismatched time-varying parameters

2011 ◽  
Vol 226 (2) ◽  
pp. 204-214 ◽  
Author(s):  
M M Arefi ◽  
M R Jahed-Motlagh
Keyword(s):  
Linear Systems ◽  
Closed Loop ◽  
Robust Stabilization ◽  
Lyapunov Theory ◽  
Loop System ◽  
Time Varying ◽  
Closed Loop System ◽  
Mismatched Uncertainties ◽  
Non Linear ◽  
Non Linear Systems

In this paper, an adaptive robust stabilization algorithm is presented for a class of non-linear systems with mismatched uncertainties. In this regard, a new controller based on the Lyapunov theory is proposed in order to overcome the problem of stabilizing non-linear time-varying systems with mismatched uncertainties. This method is such that the stability of the closed-loop system is guaranteed in the absence of the triangularity assumption. The proposed approach leads to asymptotic convergence of the states of the closed-loop system to zero for unknown but bounded uncertainties. Subsequently, this method is modified so that all the signals in the closed-loop system are uniformly ultimately bounded. Eventually, numerical simulations support the effectiveness of the given algorithm.

Stochastic disturbance observer-based adaptive anti-disturbance control for non-linear systems with stochastic non-harmonic multiple disturbances

2017 ◽  
Vol 40 (10) ◽  
pp. 3222-3231 ◽  
Author(s):  
Yanpeng Pan
Keyword(s):  
Linear Systems ◽  
Disturbance Observer ◽  
Closed Loop ◽  
Loop System ◽  
State Feedback Control ◽  
Closed Loop System ◽  
Stochastic Disturbance ◽  
Multiple Disturbances ◽  
Non Linear ◽  
Non Linear Systems

In this paper, the problem of anti-disturbance control is studied for non-linear systems with stochastic multiple disturbances. The multiple disturbances include two types: one is the stochastic harmonic disturbance and the other non-harmonic noise generated by a linear stochastic exogenous system. An adaptive stochastic disturbance observer (ASDO) is constructed to estimate both the two aforementioned disturbances. Combining the disturbance estimation with a conventional state feedback control law, a composite anti-disturbance control scheme is constructed such that the closed-loop system is stochastically stable, and different types of disturbances may be attenuated and rejected. By using the Lyapunov function method and linear matrix inequalities technique, sufficient conditions for the stochastic stability of the closed-loop system are established. Moreover, an adaptive stochastic extended state observer (ASESO) is proposed for the output feedback case. Finally, an application example is provided to demonstrate the effectiveness of the proposed method.

Stabilization of Nonlinear Strict-Feedback Systems With Time-Varying Delayed Integrators

2011 ◽  
Author(s):  
Nikolaos Bekiaris-Liberis ◽  
Miroslav Krstic
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Loop System ◽  
Time Varying ◽  
Feedback Systems ◽  
Closed Loop System ◽  
Feedback Form ◽  
Globally Asymptotically Stable ◽  
Strict Feedback

We consider nonlinear systems in the strict-feedback form with simultaneous time-varying input and state delays, for which we design a predictor-based feedback controller. Our design is based on time-varying, infinite-dimensional backstepping transformations that we introduce, to convert the system to a globally asymptotically stable system. The solutions of the closed-loop system in the transformed variables can be found explicitly, which allows us to establish its global asymptotic stability. Based on the invertibility of the backstepping transformation, we prove global asymptotic stability of the closed-loop system in the original variables. Our design is illustrated by a numerical example.

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