Rui Yan

On Repetitive Learning Control for Periodic Tracking Tasks

In this note, a repetitive learning control (RLC) approach is proposed to deal with periodic tracking tasks for nonlinear dynamical systems with nonparametric uncertainties. We address two fundamental issues associated with the learning control methodology: The existence of the solution, and learning convergence property. Applying the existence theorem of the neutral differential difference equation, and using Lyapunov-Krasovskii functional, the existence of the solution and learning convergence can be proven rigorously. A further extension of the RLC to cascade systems is also explored

Adaptive and Learning Control for SI Engine Model With Uncertainties

Air-fuel ratio control is a challenging control problem for port-fuel-injected and throttle-body-fuel-injected spark ignition (SI) engines, since the dynamics of air manifold and fuel injection of the SI engines are highly nonlinear and often with unmodeled uncertainties and disturbance. This paper presents nonlinear control approaches for multi-input multi-output engine models, by developing adaptive control and learning control design methods. Theoretical proofs are established that ensure that proposed controllers are able to give asymptotical tracking performance. As a comparison, the method applying global linearizing controller can give accurate tracking for the engine model without uncertainty and disturbance, but it fails to keep tracking performance when uncertainty is incorporated into the system. Adaptive control and learning control approaches are capable of dealing with both constant uncertainty and time-varying periodic uncertainty. Simulation results illustrate the efficacy of the proposed controllers.

Iterative learning control design without a priori knowledge of control directions

In this work, we explore the possibility of designing a suitable iterative learning control system without a priori knowledge of the control directions. By incorporating a Nussbaum-type function, a new learning control mechanism is constructed with both differential and difference updating laws. The new learning control mechanism can warrant a L/sup 2/-norm convergence of the tracking error sequence in the iteration domain. The new learning control can be applied to systems without the identical initial resetting condition (i.i.c.), and in the presence of time varying parametric uncertainties associated with non-global Lipschitz continue.

Nonlinear robust adaptive SVC controller design for power systems

In this paper, a nonlinear static var compensator (SVC) controller is proposed to improve power system voltage stability. A third order nonlinear dynamical description for the SVC system is developed and used in the controller design. Adaptive and robust control techniques are employed to deal with both constant and time varying uncertainties in a power system with SVCs. The effectiveness of the controller on voltage stability enhancement is demonstrated by a three-bus power system. The simulation results show that the time toward voltage collapse can be avoided which would otherwise happen without the controller. This validates the effectiveness of the proposed nonlinear robust adaptive controller in voltage stability enhancement.

Synchronization of chaotic systems via learning control

In this paper, a learning control approach is applied to the synchronization of two uncertain chaotic systems, which contain both, time varying and time invariant parametric uncertainties. The new learning approach also deals with unknown time varying parameters having distinct periods in the master and slave systems. Using the Lyapunov-Krasovskii functional and incorporating periodic parametric learning mechanism, the global stability and asymptotic synchronization between the master and the slave systems are obtained. Simulations on representative classes of chaotic systems show the effectiveness of the method.

Fixed point theorem-based iterative learning control for LTV systems with input singularity

In this paper, we address a challenging and open problem: how to design a suitable iterative learning control (ILC) system in the presence of input singularity, which is incurred by the singularities of the system direct feed-through term. Considering two typical types of input singularities, we first revise the ILC operators accordingly by adding a forgetting factor and incorporating a time-varying learning gain, in the sequel guarantee ILC operators to be contractible. Next, using the Banach fixed-point theorem, we demonstrate that the output sequence can either enter and remains ultimately in a designated neighborhood of the target trajectory, or is bounded by a class K function. Finally, an illustrative example is presented.

An Algorithm for Melnikov Functions and Application to a Chaotic Rotor

In this work we study a dynamical system with a complicated nonlinearity, which describes oscillation of a turbine rotor, and give an algorithm to compute Melnikov functions for analysis of its chaotic behavior. We first derive the rotor model whose nonlinear term brings difficulties to investigating the distribution and qualitative properties of its equilibria. This nonlinear model provides a typical example of a system for which the homoclinic and heteroclinic orbits cannot be analytically determined. In order to apply Melnikovs method to make clear the underlying conditions for chaotic motion, we present a generic algorithm that provides a systematic procedure to compute Melnikov functions numerically. Substantial analysis is done so that the numerical approximation precision at each phase of the computation can be guaranteed. Using the algorithm developed in this paper, it is straightforward to obtain a sufficient condition for chaotic motion under damping and periodic external excitation, whenever the rotor parameters are given.

Direct learning control design for a class of linear time-varying switched systems

In this brief, a direct learning control method for a class of switched systems is proposed. The objective of direct learning is to generate the desired control profile for a newly switched system without any feedback, even if the system may have uncertainties. This is achieved by exploring the inherent relationship between any two systems before and after a switch. The new method is applicable to a class of linear time varying, uncertain, and switched systems, when the trajectory tracking control problem is concerned. A numerical simulation demonstrates the effectiveness of the proposed method.

On Learning Wavelet Control for Affine Nonlinear Systems

Function Approximation has been proven to be an effective approach when dealing with nonlinear dynamics. Among numerous function approximation methods, wavelet network shows unique advantage in terms of its orthonormality and multi-layer resolution properties, which enable the on-line tuning or closed-loop tuning for the wavelet network structure. Using such a constructive wavelet network, an adaptive iterative learning control approach was proposed for finite interval tracking problems [1]. In this work, the adaptive learning control approach with wavelet approximation (denoted by learning wavelet control or LWC) is applied two general classes of plants affine-in-input. One class is with nonlinear unknown input coefficient, and the other class is in cascade form. With the help of Lyapunov method, the learning convergence properties of the adaptive learning control system can be analyzed while the wavelet network undergoes on-line structure adaptation.

ON THE PERIODICITY OF AN IMPLICIT DIFFERENCE EQUATION WITH DISCONTINUITY: ANALYSIS AND SIMULATIONS

In this note we analyze the periodicity of an implicit nonlinear difference equation subject to perturbations and discontinuity. We prove the existence of multiple periodic solutions under certain conditions, and derive the periods which are functions of the sampling period and the period of the perturbation. In this work, we further present a simulation algorithm which enables the computation of the solution for the implicit difference equation in an iterative manner. The Van der Pol circuit is used as an illustrative example.