oxiang Gu

Approximation of infinite-dimensional systems

A Fourier series-based method for approximation of stable infinite-dimensional linear time-invariant system models is discussed. The basic idea is to compute the Fourier series coefficients of the associated transfer function T/sub d/(Z) and then take a high-order partial sum. Two results on H/sup infinity / convergence and associated error bounds of the partial sum approximation are established. It is shown that the Fourier coefficients can be replaced by the discrete Fourier transform coefficients while maintaining H/sup infinity / convergence. Thus, a fast Fourier transform algorithm can be used to compute the high-order approximation. This high-order finite-dimensional approximation can then be reduced using balanced truncation or optimal Hankel approximation leading to the final finite-dimensional approximation to the original infinite-dimensional model. This model has been tested on several transfer functions of the time-delay type with promising results. >

Linear and nonlinear algorithms for identification in H/sub infinity / with error bounds

A linear algorithm and a nonlinear algorithm for the problem of system identification in H/sub infinity / posed by Helmicki et al. (1990) for discrete-time systems are presented. The authors derive some error bounds for the linear algorithm which indicate that it is not robustly convergent. However, the worst-case identification error is shown to grow as log(n), where n is the model order. A robustly convergent nonlinear algorithm is derived, and bounds on the worst-case identification error (in the H/sub infinity / norm) are obtained. >

Stabilizability conditions of multivariable uncertain systems via output feedback control

A stabilizability condition is established for stabilizing multivariable uncertain dynamical systems with matched uncertainties by linear static output feedback control. It is shown that under the assumptions of minimum phase and nonsingular high-frequency gain for the nominal plant, stabilization with linear static output feedback control is achievable. A necessary and sufficient condition is also obtained for the existence of constant output feedback which makes the closed-loop system strictly positive real. >

A new method for computing delay margins for stability of linear delay systems

This note is concerned with stability properties of linear time-invariant delay systems. We consider retarded delay systems modeled both as a high order scalar differential difference equation and as a set of first order differential-difference equations expressed in state space form. We provide a computational method that can be used to compute a delay interval such that the delay system under consideration is stable for all delay values that lie in the computed interval. This method requires computing only the eigenvalues and generalized eigenvalues of certain constant matrices and it can be implemented efficiently. Based on this method, we further state a simple necessary and sufficient condition concerning stability independent of delay for each of the two types of the models.<<ETX>>

Technical Communique: Robust stabilization of MIMO nonlinear systems by backstepping

The problem of global robust stabilization is investigated for a class of multi-input, minimum-phase nonlinear systems with unknown time-varying parameters or disturbances belonging to a given compact set. It is assumed that the systems admit a special structure, which is much more general than strict feedback form. It is shown that such a structure makes it possible to construct both Lyapunov functions and robust stabilizing controllers by the backstepping method.

Bifurcation Stabilization with Local Output Feedback

Local output feedback stabilization with smooth nonlinear controllers is studied for parameterized nonlinear systems for which the linearized system possesses either a simple zero eigenvalue or a pair of imaginary eigenvalues and the bifurcated solution is unstable at the critical value of the parameter. It is assumed that the unstable mode corresponding to the critical eigenvalue of the linearized system is not linearly controllable. Results are established for bifurcation stabilization using output feedback where the critical mode can be either linearly observable or linearly unobservable. The stabilizability conditions are characterized in explicit forms that can be used to synthesize stabilizing controllers. The results obtained in this paper are applied to rotating stall control for axial flow compressors as an application example.

Two algorithms for frequency domain design of robust control systems

Two algorithms are described that are useful in the computer-aided design implementation of the robust controller design scheme proposed by Horowitz (1963) and Horowitz and Sidi (1972).

Identification in H ∞ using Pick's interpolation

The problem of system identification in H∞ is studied using the Pick interpolation theorem. A tuned nonlinear interpolation algorithm is proposed and the resulting error bound in H∞ norm is derived. An example is used to illustrate the use of the interpolation algorithm.

Networked Stabilization of Multi-Input Systems with Channel Resource Allocation ⋆

Abstract In this paper, we study the problem of stabilizing a linear time-invariant discrete-time system with information constraints in the input channels. The information constraint in each input channel is modelled as a sector uncertainty. Equivalently, the transmission error of an input channel is modelled as an additive system uncertainty with a bound in the induced norm. We attempt to find the least information required, or equivalently the largest allowable uncertainty bound, in each input channel which renders the stabilization possible. The solution for the single-input case, which gives a typical H∞ optimal control problem, is available in the literature and is given analytically in terms of the Mahler measure or topological entropy of the plant. The main purpose of this paper is to address the multi-input case. In the multi-input case, if the information constraint in each input channel is given a priori, then our stabilization problem turns out to be a so-called µ synthesis problem, a notoriously hard problem. In this paper, we assume that the information constraints in the input channels are determined by the network resources assigned to the channels and they can be allocated subject to a total recourse constraint. With this assumption, the resource allocation becomes part of the design problem and a modified µ synthesis problem arises. Surprisingly, this modified µ-synthesis problem can be solved analytically and the solution is also given in terms of the Mahler measure or topological entropy as in the single-input case.

Optimal Cooperative Sensing using a Team of UAVs

The authors investigates the joint optimal estimation of both the position and velocity of a ground moving target (GMT) using pulse Doppler radars on-board unmanned aerial vehicles (UAVs). The problem of cooperative estimation using a UAV team and the optimization of the teams configuration to achieve optimal GMT position and velocity estimates are addressed. Based on the Cramer-Rao bound, the minimum achievable error variance of the GMT position and velocity estimates is derived. The expression of the minimum achievable estimation error variance for unbiased estimation provided by the Cramer-Rao bound is minimized yielding the optimal configuration of the UAV team. Our solution is complete in that it addresses various GMT tracking scenarios and an arbitrary number of UAVs. Optimal sensor geometries for typical applications are illustrated