Zhuquan Zang

Iterative weighted least-squares identification and weighted LQG control design

Many practical applications of control system design based on input-output measurements permit the repeated application of a system identification procedure operating on closed-loop data together with successive refinements of the designed controller. Here we develop a paradigm for such an iterative design. The key to the procedure is to account for evaluated modelling error in the control design and, equally, to let the closed-loop controller requirements determine the identification criterion. With an H-2 control problem, this is achieved by frequency weighting the linear-quadratic Gaussian (LQG) control criterion with filters that reflect the closed-loop plant/model mismatch, and by filtering the identifier signals used in a least-squares identification scheme in a logical and mutually supportive fashion.

H/sub 2/ iterative model refinement and control robustness enhancement

Many practical applications of control system design based on input-output measurements permit the repeated application of a system identification procedure operating on closed-loop data together with successive refinement of the designed controller. A paradigm is developed for such an iterative design. The key to the procedure is to account for evaluated modeling error in the control design and, equally, to allow for the requirements of the closed-loop controller in performing the identification. With an H/sub 2/ control problem, this is achieved by frequency weighting the linear quadratic control criterion and by filtering the identifier signals in a logical fashion.<<ETX>>

A semi-infinite quadratic programming algorithm with applications to array pattern synthesis

This paper presents a new extended active set strategy for optimizing antenna arrays by semi-infinite quadratic programming. The optimality criterion is either to maximize the directivity of the antenna or to minimize its sidelobe energy when subjected to a specified peak sidelobe level. Additional linear constraints are used to form the mainlobe. The design approach is applied to a numerical example that deals with the design of a narrow-band circular antenna array for the far field.

New weight transform schemes for delayless subband adaptive filtering

Very long adaptive filters are used for controlling the acoustic echo due to the acoustic echo of the loudspeaker and microphone. Subband adaptive filters have been proposed to save computations as well as speed up convergence. Delayless subband adaptive filters remove the additional signal path delay due to the analysis-synthesis system in their conventional counterpart by transforming the subband filters to a corresponding fullband one and cancelling the echo using the fullband filter. The weight transform from subband to fullband plays a crucial role in the delayless subband adaptive filters. In this paper, a defect of the FFT-stacking weight transform is identified, and new transform schemes are proposed. Simulation results show that significant performance improvements can be achieved by employing the proposed weight transform schemes.

Semi-infinite linear programming: a unified approach to digital filter design with time- and frequency-domain specifications

Using the recently developed semi-infinite linear programming techniques and Caratheodorys dimensionality theory, we present a unified approach to digital filter design with time and/or frequency-domain specifications. Through systematic analysis and detailed numerical design examples, we demonstrate that the proposed approach exhibits several salient features compared to traditional methods: 1) using the unified approach, complex responses can be handled conveniently without resorting to discretization; 2) time domain constraints can be included easily; and 3) any filter structure, recursive or nonrecursive, can be employed, provided that the frequency response can be represented by a finite-complex basis. More importantly, the solution procedure is based on the numerically efficient simplex extension algorithms. As numerical examples, a discrete-time Laguerre network is used in a frequency-domain design with additional group-delay specifications, and in a /spl Hscr//sub /spl infin//-optimal envelope constrained-filter design problem. Finally, a finite impulse response phase equalizer is designed with additional frequency domain /spl Hscr//sub /spl infin// robustness constraints.

Continuous-time envelope-constrained filter design via laguerre filters and H∞ optimization methods

The envelope-constrained filtering problem is concerned with the design of a time-invariant filter to process a given input signal such that the noiseless output of the filter is guaranteed to lie within a specified output mask while minimizing the noise gain of the filter. An algorithm is developed to solve the continuous-time envelope-constrained filter design problem with the /spl Hscr//sub /spl infin// norm of the filter as the cost and an orthonormal set of basis filters. It is shown that the problem can be reformulated and solved as a constrained /spl Hscr//sub /spl infin// model-matching problem. To illustrate the effectiveness of the design method, two numerical examples are presented that deal with the design of equalization filters for digital transmission channels.

A comparison of various low-pass filter architectures for sigma-delta demodulators

A comparison of various low-pass filter architectures that are commonly used in Sigma-Delta(/spl Sigma/-/spl Delta/) demodulators is presented in the paper. In this comparison the conventional demodulator filter architectures such as the optimal FIR filter, Sinc/sup k/ filter and non-linear Zoomer filter are considered. It is shown that the optimum FIR filter provides the most attractive properties among the conventional demodulator low-pass filters. As an alternative to the optimal FIR filter, optimal Laguerre IIR filter architecture is then proposed in the paper. A design scheme for the optimal IIR filter is presented via the use of orthonormal Laguerre functions. In comparison with the conventional FIR filter approach, this design offers several attractive features. The proposed IIR filter design problem is easy to solve and numerically robust. Furthermore, the optimal IIR filter is easy to implement because it needs only a small number of components and therefore well suited for VLSI implementations.

Envelope-constrained IIR filter design via H/sub /spl infin// optimization methods

Previously, the envelope-constrained (EC) filtering problem was formulated as designing an infinite impulse response (IIR) filter such that the filters l/sub 2/ norm is minimized, subject to the constraint that its response to a specified input pulse lies within a prescribed envelope. In this paper we recast this filter design problem as a frequency-domain H/sub /spl infin// optimization problem with time-domain constraints. Motivations for solving this problem are given. Then, the recently developed H/sub /spl infin// optimization techniques are used for the design of the required IIR filter. For illustration, we apply the approach to two numerical examples which deal with the design of equalization filters for digital transmission channels.

Transient bounds for adaptive control systems

Adaptive control systems are essentially nonlinear and mechanisms to analyze their stability and transient response typically derive from more general nonlinear theories such as small gain arguments or passivity. In this note, we consider how these theories may be applied to adaptive control to quantify transient response. This involves the explicit description of the constants appearing in the passivity theorem and/or the small gain theorem which characterize both system gains and initial condition effects. The result is a fundamental connection between transient response bounds and uniform plant controllability, which connects initial state conditions with the input-output analysis. Applying these general theorems to adaptive control, we are able to interpret the uniform controllability condition as a persistency of excitation requirement and thereby to provide local bounds on transient response. The implication of these sufficient results is that without both bounds upon initial conditions and guarantees of excitation, potentially extreme transient excursions of system variables are possible even though global convergence and asymptotic performance are guaranteed. >

A dual approach to continuous-time envelope-constrained filter design via orthonormal filters

The envelope-constrained (EC) filtering problem was initially posed in the continuous-time domain as a constrained L/sup 2/ space optimization problem. However, only the discretized version has been solved, using various approaches. In this paper we consider the continuous-time EC filtering problem formulated using an orthonormal basis defined on a Hilbert vector space. Caratheodorys theorem and the dual parametrization method are used to obtain a dual finite-dimensional optimization problem. Two iterative algorithms based on the gradient flow technique are then developed for solving this dual problem. The design of an EC optimal equalization filter for a communication channel is solved to illustrate the effectiveness of the proposed algorithm.