关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Stability and stabilization of infinite dimensional systems with applications

A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system

This paper presents an adaptive output-feedback neural network (NN) control scheme for a class of stochastic nonlinear time-varying delay systems with unknown control directions. To make the controller design feasible, the unknown control coefficients are grouped together and the original system is transformed into a new system using a linear state transformation technique. Then, the Nussbaum function technique is incorporated into the backstepping recursive design technique to solve the problem of unknown control directions. Furthermore, under the assumption that the time-varying delays exist in the system output, only one NN is employed to compensate for all unknown nonlinear terms depending on the delayed output. Moreover, by estimating the maximum of NN parameters instead of the parameters themselves, the NN parameters to be estimated are greatly decreased and the online learning time is also dramatically decreased. It is shown that all the signals of the closed-loop system are bounded in probability. The effectiveness of the proposed scheme is demonstrated by the simulation results.

Output-Feedback Adaptive Neural Control for Stochastic Nonlinear Time-Varying Delay Systems With Unknown Control Directions

Output feedback stabilization of stochastic feedforward systems with unknown control coefficients and unknown output function

This paper is concerned with the adaptive output-feedback stabilisation for a class of hybrid partial differential equation (PDE)–ordinary differential equation (ODE) systems with uncertain input disturbances. Remarkably, in this paper, only two boundary measurements of the considered system are available for feedback. Moreover, the unknown parameters involved in the system are allowed to belong to an unknown interval. These two aspects make the considered system essentially different from those in the closely related literature. Inspired by the existing results, an observer is first introduced to estimate the unmeasured states of the original system. Then, by adaptive technique and backstepping method, an adaptive output-feedback controller is successfully constructed, which guarantees that the entire closed-loop system is asymptotically stable, and moreover, the parameter estimates converge to their own real values ultimately. Besides, by the semigroup approach, the well-posedness of the entire ...

Adaptive output-feedback stabilisation for hybrid PDE–ODE systems with uncertain input disturbances

This paper concerns the global regulation for a class of stochastic high-order nonlinear systems which admit more general system form than the existing works. For details, except for the serious sy...

Global Regulation for A Class of Stochastic High-order Nonlinear Systems with Multiple Unknown Control Directions*

Semiglobal Stabilization via Output-feedback for a Class of Uncertain Nonlinear Systems

The adaptive stabilisation is investigated for a class of coupled partial differential equation–ordinary differential equation systems with parametric uncertainties. The presence of the uncertainties makes the systems under investigation essentially different from those in the existing literature, and moreover it results in the incapability of the existing methods. Motivated by the related works, an infinite-dimensional backstepping transformation is first introduced to transform the original system into a pivotal target system, which makes the control design and performance analysis much convenient. Then, by utilising Lyapunov method and some adaptive techniques, an adaptive stabilising controller is successfully constructed, which guarantees that all the closed-loop system states are bounded while the original system states converge to zero. A simulation example is provided to validate the proposed method.

Adaptive stabilisation for uncertain coupled PDE–ODE systems

Adaptive stabilisation is investigated for ordinary differential equation systems via distributed effect of uncertain diffusion-dominated actuator dynamics. The presence of the unknowns/uncertainties and the distributed effect makes the system under investigation more general and representative than those of the related literature, and moreover yields the ineffectiveness of the existing methods on this topic. By constructing an invertible spatial and time-varying state transformation, the original closed-loop system is first changed into a target system, from which the design of parameter updating law and the analysis of the closed-loop system performance become more convenient. Then, by Lyapunov method and adaptive compensation technique, an adaptive stabilising controller is successfully constructed, which guarantees that the original system states converge to zero while other closed-loop system states are bounded. A simulation example is provided to validate the proposed method.

Yungang Liu

Papers

Adaptive output-feedback stabilisation for hybrid PDE–ODE systems with uncertain input disturbances

Global Regulation for A Class of Stochastic High-order Nonlinear Systems with Multiple Unknown Control Directions*

Semiglobal Stabilization via Output-feedback for a Class of Uncertain Nonlinear Systems

Adaptive stabilisation for uncertain coupled PDE–ODE systems

Adaptive stabilisation of ODE systems via distributed effect of uncertain diffusion-dominated actuator dynamics