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 devoted to the practical tracking control with prescribed transient performance for a class of uncertain Euler-Lagrange (EL) equations. Remarkably, the system allows serious nonparametric uncertainties since all the system matrices are unknown and do not necessarily have known bounds. Moreover, the reference trajectory to be followed is more general since it does not necessarily have known bound or require to be twice-continuously differentiable but those of literature must do. For this, a funnel-based control scheme is proposed to overcome the serious uncertainties, and in turn to achieve certain prescribed closed-loop performance. Specifically, a funnel to which the tracking error belongs is first skillfully constructed with the aid of a time-varying function about a prescribed tracking accuracy parameter. Based on the funnel, a time-varying controller is designed which guarantees that all the closed-loop system signals are bounded while the tracking error evolves in the funnel set, that is, the system output tracks the reference trajectory with the prescribed convergence rate before the prescribed time. Finally, two application examples are used to validate the effectiveness of the theoretical results.

Practical tracking control with prescribed transient performance for Euler-Lagrange equation

This paper considers the global adaptive stabilisation for a class of uncertain stochastic nonlinear systems. Comparing with the existing relevant literature, the systems under investigation allow more serious unknowns/uncertainties. More importantly, by remarkably reducing the dimension of dynamic compensator for system unknowns (from n to 2) and considerably diminishing the overparametrisation in the existing literature, this paper proposes an improved design scheme for adaptive state-feedback controllers. It is turned out that, with the designed controller in loop, all the closed-loop system states are globally bounded and the original system states converge to the origin, both in the sense of probability one. A simulation example is also given to demonstrate the effectiveness of the theoretical results.

Further results on global adaptive stabilisation for a class of uncertain stochastic nonlinear systems

The paper is concerned with the global adaptive stabilisation via output feedback for a class of uncertain planar nonlinear systems. Remarkably, the unknowns in the systems are rather serious: the control coefficients are unknown constants which do not belong to any known interval, and the growth of the systems heavily depends on the unmeasured states and has the rate of unknown polynomial of output. First, a delicate state transformation is introduced to collect the unknown control coefficients, and subsequently, a suitable state observer is successfully designed with two different dynamic gains. Then, an adaptive output feedback controller is proposed by flexibly combining the universal control idea and the backstepping technique. Meanwhile, an appropriate estimation law is constructed to overcome the negative effect caused by the unknown control coefficients. It is shown that, with the appropriate choice of the design parameters, all the states of the resulting closed-loop system are globally bounded, ...

Adaptive output feedback stabilisation for planar nonlinear systems with unknown control coefficients

Output-feedback Control for a Class of Uncertain Nonlinear Systems with Linearly Unmeasured States Dependent Growth

In this paper, the global adaptive regulation is considered for a class of uncertain stochastic high-order nonlinear systems with serious nonlinearities and unknowns. For details, the considered systems admit the general forms which include the strict-feedback systems as the special case, and allow the more complicated nonlinearities. Moreover, the system model suffers from both the unknown parameterized nonlinear growth conditions and the unknown time-varying control gain with unknown control direction (i.e. the sign of the control gain). By introducing two new design parameters and skillfully combining the adaptive design methods with the Nussbaum-type function based technique, a desired adaptive regulation control scheme is successfully presented, by which the obtained smooth controller can effectively guarantee that all the closed-loop system states are bounded almost surely, and especially the original system states converge to the origin with probability one. Finally, to demonstrate the feasibility of the control scheme, a numerical example is given.

Yungang Liu

Papers

Practical tracking control with prescribed transient performance for Euler-Lagrange equation

Further results on global adaptive stabilisation for a class of uncertain stochastic nonlinear systems

Adaptive output feedback stabilisation for planar nonlinear systems with unknown control coefficients

Output-feedback Control for a Class of Uncertain Nonlinear Systems with Linearly Unmeasured States Dependent Growth

Global adaptive regulation of stochastic high-order nonlinear systems with unknown control direction