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

Adaptive Output-feedback Stabilization for a Class of Uncertain Nonlinear Systems

This article is concerned with the adaptive stabilising control design for the ordinary differential equation systems with uncertain diffusion-dominated actuator dynamics. This problem is highly difficult to solve and worthy of investigation, mainly due to the unknown diffusion coefficient which does not belong to any known finite interval and essentially different from the existing literature. By introducing an infinite-dimensional backstepping transformation, the pivotal target system is thus obtained, which makes the control design and stability analysis become more convenient. Then, based on the idea of certainty equivalence principle and recently developed adaptive technique, 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 presented to illustrate the effectiveness of the proposed method.

Adaptive control of the ODE systems with uncertain diffusion-dominated actuator dynamics

This paper is concerned with the global practical tracking via adaptive output feedback for a class of uncertain nonlinear systems. The system under investigation possesses function control coefficients, the polynomial-of-output growth rate and serious unknowns in the system nonlinearities and the reference signal, and hence is essentially different from those in the closely related literature. To solve the problem, a high-gain observer is introduced to reconstruct the unmeasured system states. The involved high gain is the multiplication of two dynamic gains: one is to compensate the polynomial-of-output in the system growth rate, and the other one is to overcome the serious unknowns in the system and reference signal and the extra system nonlinearities in function control coefficients. Based on the high-gain observer, an adaptive output-feedback controller is successfully designed to guarantee that, for any initial condition of the system, all signals of the closed-loop system are bounded, and t...

Further results on global practical tracking via adaptive output feedback for uncertain nonlinear systems

This paper addresses the global adaptive stabilisation via switching and learning strategies for a class of uncertain nonlinear systems. Remarkably, the systems in question simultaneously have unknown control directions, unknown input disturbance and unknown growth rate, which makes the problem in question challenging to solve and essentially different from those in the existing literature. To solve the problem, an adaptive scheme via switching and learning is proposed by skilfully integrating the techniques of backstepping design, adaptive learning and adaptive switching. One key point in the design scheme is the introduction of the learning mechanism, in order to compensate the unknown input disturbance, and the other one is the design of the switching mechanism, through tuning the design parameters online to deal with the unknown control directions, unknown bound and period of input disturbance and unknown growth rate. The designed controller guarantees that all the signals of the resulting clo...

Global adaptive stabilisation for nonlinear systems with unknown control directions and input disturbance

In this paper, the adaptive disturbance attenuation via output feedback is investigated for a class of nonlinear systems with uncertain control coefficients. Notably, the considered systems depend on unmeasured states with polynomial-of-output growth rate, and hence the systems have severe unknowns. Due to the existence of both the virtual and actual uncertain control coefficients, we first introduce a suitable state transformation, such that the control design becomes convenient. Then, we construct an appropriate and simple state observer with two important gains, and one gain is large enough to handle the constants appeared in the design procedure, and the other is updated on-line to deal with the polynomial-of-output growth rate of the system. After that, an output feedback controller is proposed based on the observer in a step-by-step manner. Finally, it is shown that, by appropriate choice of the design parameters, the states of the closed-loop system are globally bounded, and the disturbance attenua...

Yungang Liu

Papers

Adaptive Output-feedback Stabilization for a Class of Uncertain Nonlinear Systems

Adaptive control of the ODE systems with uncertain diffusion-dominated actuator dynamics

Further results on global practical tracking via adaptive output feedback for uncertain nonlinear systems

Global adaptive stabilisation for nonlinear systems with unknown control directions and input disturbance

Adaptive disturbance attenuation via output feedback for nonlinear systems with polynomial-of-output growth rate