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 investigates the problem of output-feedback adaptive stabilization control design for non-holonomic chained systems with strong non-linear drifts, including modelled non-linear dynamics, unmodelled dynamics, and those modelled but with unknown parameters. An observer and an estimator are introduced for state and parameter estimates, respectively. By using the integrator backstepping approach and based on the observer and parameter estimator, a constructive design procedure for output-feedback adaptive stabilization control is given. It is shown that, under some conditions, the control design ensures the closed-loop system is globally asymptotically stable when there is no non-linear drift in the first subsystem, and semiglobally asymptotically stable, otherwise. An example is given to show the effectiveness of the theory.

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Output-feedback adaptive stabilization control design for non-holonomic systems with strong non-linear drifts

Output-feedback Adaptive Control for a Class of Nonlinear Systems with Unknown Control Directions

Adaptive Practical Output Tracking Control for High-order Nonlinear Uncertain Systems

The problem of global adaptive stabilisation by state-feedback is investigated for a class of high-order non-linear systems with uncertain control coefficients and zero dynamics. First, some appropriate unknown parameters are introduced to obtain the updating laws when adapting control design. Then, by the flexible way of combining adding a power integrator with adaptive technique and the idea of changing supply functions, the requirement on the uncertain control coefficients is relaxed, and a recursive design procedure is successfully developed to achieve a continuous adaptive stabilising controller. Finally, an example is provided to illustrate the correctness of the theoretical results.

Adaptive stabilisation for a large class of high-order uncertain non-linear systems

This paper is concerned with adaptive stabilization for a class of uncertain high-order nonlinear systems with time delays. To the authors' knowledge, there has been no analogous result. Hence during investigation, the conditions on delay effect and the control design framework should be established for the first time. In this paper, under somewhat necessary restrictions on the system nonlinearities, by the method of adding a power integrator and the related adaptive technique, a procedure is developed to design the continuous adaptive state-feedback controller without overparametrization. Moreover, the uniform stability and convergence of the resulting closed-loop system are rigorously proven, with the aid of a suitable Lyapunov-Krasovskii functional. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical result.

Yungang Liu

Papers

Output-feedback adaptive stabilization control design for non-holonomic systems with strong non-linear drifts

Output-feedback Adaptive Control for a Class of Nonlinear Systems with Unknown Control Directions

Adaptive Practical Output Tracking Control for High-order Nonlinear Uncertain Systems

Adaptive stabilisation for a large class of high-order uncertain non-linear systems

Adaptive Control Design for a Class of Uncertain High-Order Nonlinear Systems with Time Delay