Adaptive event‐triggered control for nonlinear systems with time‐varying parameter uncertainties

This article is concerned with the trajectory tracking control problem for the nonlinear systems in the sense of the predefined settling time and accuracy. In contrast with the existing works, we focus on the cases where the system dynamics, its bounding functions, the unmatched disturbances, and the time‐varying parameters are totally unknown; the derivatives of the desired trajectory are not required to be available. They significantly challenge the identification and/or approximation‐based control solutions. To overcome this obstacle, a novel robust prescribed performance control approach via state feedback is put forward in this article. It not only ensures the natural satisfaction of the specific initial condition but also realizes a full‐time performance specification for trajectory tracking. Furthermore, for the case of unmeasured state variables, an output‐feedback control approach is further derived by adopting an input‐driven filter and conducting trivial changes on the design procedure. Moreover, both approaches exhibit significant simplicity, without the needs for parameter identification, function approximation, disturbance estimation, derivative calculation, or command filtering. Three simulation studies are conducted to clarify and verify the above theoretical findings.

Practical prescribed‐time tracking control of unknown nonlinear systems: A low‐complexity approach

Xie,

Zhang,

Jing

et al. 2024

Dynamic Event‐Triggered Output Feedback Control for a Class of Uncertain Nonlinear Systems

Liu,

Xing,

Zhang

2024

In this article, the dynamic event‐triggered output feedback control problem for a class of uncertain nonlinear systems is studied. Since system states are not available for controller design, a state observer is designed to estimate them. On the basis of the estimated states, a dynamic event‐triggered control scheme is proposed. Compared with existing event‐triggered schemes, a dynamic auxiliary variable is added in the event conditions. By properly designing the dynamics of the auxiliary variable, it is proved that the tracking/stabilization error is able to converge to zero without the presence of Zeno behavior. The effectiveness of the control scheme is verified by simulation results.

Time/Event‐Triggered Exponential Stabilization for Stochastic Systems: Enhancing Nonlinearity Tolerance

Li,

Liu

2024

This article seeks the enhancement of nonlinearity tolerance in time/event‐triggered stabilization for stochastic systems. In the related results, the controller functions are required to obey global Lipschitz condition for the suppression of sampling/execution error, and the drift and/or diffusion coefficients of the stochastic systems are restricted to polynomial or, even, linear growth. These limitations deserve overcoming for enlarged applications. To this end, a distinct framework of time/event‐triggered controls is established for stochastic systems, targeted at exponential stabilization. Specifically, inclusive Lyapunov‐type feasibility conditions are proposed by capturing the effect of sampling/execution error and distinguishing the role of system nonlinearities. Particularly, different from the related results, the evolution of sampling/execution error is subtly exploited via Lyapunov functions to reveal the dynamic interaction between the sampling/execution errors and system state. Then, time‐triggered exponential stabilization via sampled‐data controller is achieved not only in the moment sense but also in the almost sure sense. Accordingly, Lyapunov function based analysis is performed for the composite dynamics of system state and sampling error, confronted with the coupling of discontinuous and stochastic features. To further reduce execution, periodic event‐triggered control is exploited to achieve exponential stabilization for stochastic nonlinear systems, by virtue of the relation with the dynamic evolution under sampled‐data control. Through typical examples, we demonstrate the potential of our framework in handling the cases with the controller functions violating global Lipschitz condition and with the system nonlinearities beyond polynomial growth.