Jer-Guang Hsieh

Feedback control of a class of nonlinear singularly perturbed systems with time delay

The feedback control of two classes of nonlinear time-delay singularly perturbed systems with fast actuators is considered. First, by means of the integral manifold method, the asymptotic stability of a class of nonlinear time-delay singularly perturbed systems can be guaranteed and the phase trajectories of the closed-loop systems are steered along the integral manifold to the origin. Second, a continuous state feedback controller is constructed such that the trajectories of a class of uncertain nonlinear time-delay singularly perturbed feedback-controlled systems are uniformly ultimately bounded. We require no a priori information on the uncertain element, except that its restraint set is assumed to be known and compact.

GLOBAL EXPONENTIAL STABILIZATION FOR A CLASS OF UNCERTAIN NONLINEAR SYSTEMS WITH TIME-VARYING DELAY ARGUMENTS AND INPUT DEADZONE NONLINEARITIES

Abstract In this paper, the global exponential stabilization for a class of uncertain nonlinear systems with time-varying delay arguments and input deadzone nonlinearities is considered. A composite feedback control is proposed such that the feedback-controlled system is globally exponentially stable if a simple sufficient condition is met. Furthermore, for slightly more restricted systems, we show that the global exponential stability can always be achieved with any pre-specified convergence rate. A numerical example is provided to illustrate the use of our main results.

Global stabilization of non-linear singularly perturbed systems with fast actuators: exact design manifold approach

In the integral manifold approach, the dynamical behaviour of a non-linear singularly perturbed system is captured geometrically by the rapid approach of the fast system states to the design manifold and remaining on the manifold thereafter. A globally stabilizing composite feedback control, i.e. the sum of a slow control and a fast control, is proposed for a general class of non-linear singularly perturbed systems with fast actuators such that the design manifold becomes an exact slow integral manifold and the trajectories of the closed-loop systems, starting from any initial states, are steered along the integral manifold to the origin, i.e. the original non-linear singularly perturbed system is globally asymptotically stabilized.

ADAPTIVE TRACKING CONTROL OF A CLASS OF NONLINEAR SYSTEMS USING CMAC NETWORK

Abstract In this paper, an adaptive control based on a Cerebellar Model Articulation Controller (CMAC) network is derived to solve the output tracking problem for a class of nonlinear systems with unknown structured nonlinearities. Without requiring a priori knowledge of the system parameter values, the proposed adaptive control consists of the conventional sliding control and a feedforward compensation with the CMAC network. The sliding control is used as a classical tracking controller for the nominal system and the CMAC network is used to compensate the parametrization errors. It is shown by the Lyapunov approach that the outputs of the closed-loop system asymptotically track the desired output trajectories. The effectiveness of the proposed control scheme is verified with an application to a two degree-of-freedom (DOF) robotic manipulator.

Stabilization of nonlinear singularly perturbed systems using multilayered neural networks

Abstract Multilayered neural networks are used to construct a nonlinear learning feedback controller for a class of nonlinear time-invariant singularly perturbed systems with fast actuators. The parameters of the networks are updated on-line by using the gradient descent method with a dead-zone function. The feedback-controlled system is proved to be stable by the Lyapunov approach such that the chosen design manifold becomes an exact integral manifold and the trajectories, starting from the bounded initial states, are steered along the integral manifold to a bounded set centered at the origin, whose size can be arbitrarily chosen for all sufficiently small singular perturbation parameter ϵ;. The simulation results are included to complement the theoretical discussions.

Deterministic control of uncertain feedback systems with time-delay and series nonlinearities

A delay-independent sufficient condition is derived that guarantees the global asymptotic stability of uncertain time-delay systems containing a class of series nonlinearities, under the linear state feedback. Such a linear state feedback is constructed via a suitable choice of parameters to solve an algebraic Riccati equation

Robust LQG optimal controller synthesis against noise spectral uncertainties and nonlinear time-varying unmodeled dynamics

Abstract In this paper, we consider the problem of robust controller synthesis against noise spectral uncertainties and nonlinear time-varying (NLTV) unmodeled dynamics in the discrete LQG (linear-quadratic Gaussian) optimal systems. We derive a necessary and sufficient condition for robust stabilization in multivariable stochastic discrete-time systems with NLTV unmodeled dynamics. Meanwhile, an algorithm based on the robust stabilization criterion is presented for synthesizing a robust controller not only to minimize the least favorable cost functional J but also to satisfy the robust stabilization criterion by specifying an appropriate weighting scalar in the cost functional.

Robust controller synthesis in non–linear multivariable systems: using dither as auxiliary

A dither is a high frequency signal introduced into a non-linear system in order to improve its performance. It is shown that the stability of a dithered system can be predicted rigorously by establishing the stability of its corresponding smoothed system when the dither has a sufficiently large amplitude as well as high–enough frequency, and the transfer function of the ‘linearized’ feedback system has a high-frequency attenuation property. A generally parametrized controller, advanced by Youla et al., and a dither as its auxiliary are simultaneously introduced to augment the stability of the non–linear feedback system, where the controlled plant are not necessarily stable. The main feature of this study is that the technique of robustness optimization is used to find a lower bound on the dither amplitude for stabilization of the non–linear feedback system. Furthermore, there arc no stable, square, and minimum-phase constraints on the controlled plant.

A NOTE ON THE STABILITY OF UNCERTAIN TIME-LAG SYSTEMS

Abstract In this note, new criteria for the global asymptotic stability and the global exponential stability of a class of uncertain time-lag systems with time-varying delays are proposed. A numerical example is given to illustrate our main results.

Using linear feedback laws to augment the quadratic estimates of the stability region of a non-linear system

The effect of linear feedback laws on the quadratic estimates of the stability regions of a class of non-linear systems is investigated. These linear feedback laws include state feedback laws, combined control laws and estimators, and dynamic output feedback laws via the factorization method. Some sufficient conditions are provided for these feedback laws to augment the quadratic estimates of the stability regions of non-linear systems.