A robust model reference adaptive control for nonminimum phase systems

In this paper, a new direct model reference adaptive control method for nonminimum phase systems is presented. The parameter estimation scheme combines adaptive data filtering with a recursive least-squares algorithm with parameter projection and signal normalization. The problem of minimum phase of the plant is handled by adaptive input output data filtering. This data filtering permits one to relocate the reros of the plant estimated model inside the unit circle and to define a good data model, which is a key issue for robust control. The scheme robustness with respect to unmodeled dynamics is also simultaneously improved. The performance of the control algorithm is illustrated by numerical examples.     

Stochastic adaptive control of nonminimum phase systems in the presence of unmodelled dynamics

We consider the problem of robust stochastic adaptive control of not necessarily minimum phase systems in the presence of unmodelled dynamics. Stochastic gradient algorithms with parameter projection and modified gain sequence are used for the estimation of the unknown controller parameters. Global stability of the adaptive system is achieved without requiring the strictly positive real condition and the persistency exciting condition to be satisfied.This work was supported by NSF Grant ECS-88-02924.     

Identification of nonminimum phase FIR systems via fourth-order cumulants and genetic algorithm

In this paper, the problem of estimating the parameters of an FIR system from only the fourth-order cumulants of the noisy system output is considered. The FIR system is driven by a symmetric, independent, and identically distributed (i.i.d) non-Gaussian sequence. We propose a new formula called Weighted Overdetermined C(q, k) (WOC(q, k)) by extending the conventional C(q, k) formula. The optimal selection of the weights in WOC(q, k) is performed by using the Genetic Algorithm (GA) optimization method which minimizes a nonlinear error function based on the fourth-order cumulants alone. Simulations are provided to reveal the effectiveness and the superiority of this novel technique over the C(q, k) and other existing techniques.     

New criteria for blind deconvolution of nonminimum phase systems(channels)

A necessary and sufficient condition for blind deconvolution (without observing the input) of nonminimum-phase linear time-invariant systems (channels) is derived. Based on this condition, several optimization criteria are proposed, and their solution is shown to correspond to the desired response. These criteria involve the computation only of second- and fourth-order moments, implying a simple tap update procedure. The proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the (unobserved) input sequence. It is shown that in several important cases (e.g. when the additive noise is Gaussian), the proposed criteria are essentially unaffected     

Active RC nonminimum phase network using the DVCCS/DVCVS

A new configuration for realizing a second-order nonminimum phase transfer function using the differential voltage controlled current source, differential voltage controlled voltage source (DVCCS/ DVCVS) as the active building block is given. The special cases of a notch filter and an all-pass network are considered. Recently [1], the DVCCS/DVCVS [2]-[3] was used as the active building block in the realization of bandpass and lowpass filters. In this letter the synthesis of a second-order nonminimum phase transfer function using the DVCCS/DVCVS is considered.     

One- and two-dimensional minimum and nonminimum phase retrieval bysolving linear systems of equations

The discrete phase retrieval problem is to reconstruct a discrete time signal whose support is known and compact from the magnitude of its discrete Fourier transform. We formulate the problem as a linear system of equations; our methods do not require polynomial rooting, tracking zero curves of algebraic functions, or any sort of iteration like previous methods. Our solutions obviate the stagnation problems associated with iterative algorithms, and our solutions are computationally simpler and more stable than alternative noniterative algorithms. Furthermore, our methods can explicitly accommodate noisy Fourier magnitude information through the use of total least squares type techniques. We assume either of the following two types of a priori knowledge of the signal: (1) a band of known values (which may be zeros) or (2) some known values of a subminimum phase signal (whose zeros lie inside a disk of radius greater than unity). We illustrate our methods with nonminimum-phase one-dimensional (1-D) and two-dimensional (2-D) signals     

Generation of nonminimum phase from amplitude-only data

A method is presented for the generation of nonminimum phase from amplitude-only data. The nonminimum phase is generated utilizing the principles of causality and the Hilbert transform. The application of the theory has been applied to some antenna radiation-power patterns and to measured transfer functions of microwave filters to illustrate the applicability of this approach     

Direct adaptive longitudinal control of vehicle platoons

An important aspect of an automated highway system design is the synthesis of an automatic vehicle following system. Associated with automatic vehicle following systems is the problem of the stability of a string of vehicles, i.e., the problem of spacing error propagation, and in some cases, amplification upstream from one vehicle to another, due to some disturbance at the head of the string. Realistic vehicle following designs must also address parametric uncertainties such as mass of the vehicle, aerodynamic drag, and tire drag. The mass of the vehicle varies with the number of passengers. At small intervehicular separations, aerodynamic drag force changes significantly with the distance to be maintained. We address the problem of stability of a vehicle string in the presence of parametric uncertainty and present a Lyapunov-based decentralized adaptive control algorithm to compensate for such parametric variations. We examine this direct adaptive control algorithm for platoon performance and parameter convergence. We present the simulation results to demonstrate the effectiveness of the adaptive controller     

Noncausal nonminimum phase ARMA modeling of non-Gaussian processes

A method is presented for the estimation of the parameters of a noncausal nonminimum phase ARMA model for non-Gaussian random processes. Using certain higher order cepstra slices, the Fourier phases of two intermediate sequences (h_min(n) and h_max(n)) can be computed, where h_min(n) is composed of the minimum phase parts of the AR and MA models, and h_max(n) of the corresponding maximum phase parts. Under the condition that there are no zero-pole cancellations in the ARMA model, these two sequences can be estimated from their phases only, and lead to the reconstruction of the AR and MA parameters, within a scalar and a time shift. The AR and MA orders do not have to be estimated separately, but they are by product of the parameter estimation procedure. Through simulations it is shown that, unlike existing methods, the estimation procedure is fairly robust if a small order mismatch occurs. Since the robustness of the method in the presence of additive noise depends on the accuracy of the estimated phases of h_min(n) and h_max(n), the phase errors due to finite length data are studied and their statistics are derived     

Bibliography on adaptive control systems

This bibliography contains the references to the major papers and reports on adaptive systems. The refmences listed are divided into two main sections, one for books and the other for journal, papers, reports, dissertations, patents, and conference papers. In the second section, papers, reports, etc., are indexed into categories e.g., applications, model reference systems, self-oscillating systems, etc.     

Cumulant based identification approaches for nonminimum phase FIRsystems

Recursive and least squares methods for identification of non-minimum-phase linear time-invariant (NMP-LTI) FIR systems are developed. The methods utilize the second- and third-order cumulants of the output of the FIR system whose input is an independent, identically distributed (i.i.d.) non-Gaussian process. Since knowledge of the system order is of utmost importance to many system identification algorithms, new procedures for determining the order of an FIR system using only the output cumulants are also presented. To illustrate the effectiveness of the methods, various simulation examples are presented     

Multirate adaptive robust control for discrete-time non-minimum phase systems and application to linear motors

It is well known that a plant becomes non-minimum phase in discrete-time domain when the relative degree of the original continuous-time plant is greater than 2 even if the plant is minimum-phase in continuous-time domain. Thus, it was difficult to apply the conventional adaptive controllers directly to these systems. In this paper, multirate adaptive robust control (MARC) is proposed for these systems. This scheme is developed by the good combination of perfect tracking control (PTC) with multirate feedforward control which has been proposed by the first author and discontinuous projection based adaptive robust control (ARC) which has been proposed by the second author. Although the original PTC can assure perfect tracking only for nominal plant, the proposed MARC can guarantee: 1) perfect tracking for plant with parametric uncertainty and 2) overall stability even if there exist modeling error and disturbance. The proposed scheme is applied to the high-speed position control of a linear motor, and the advantages are demonstrated through experiments.     

Optimum open eye equalizer design for nonminimum phase channels

This paper contains results on the design of optimum equalizers to eliminate intersymbol interference (ISI) in linear nonminimum phase channels conveying binary signals. The optimization is with respect to an open eye condition with a delay d. For causal stable channels with n _c nonminimum phase zeros, we argue that this problem requires only the consideration of the n_c-tap FIR modified channel that has all the n_c nonminimum phase zeros of the original channel. We show that if this modified channel can be equalized to yield an equalized system that is open eye with delay d, then the optimizing equalizer is, in fact, (d-n_c)-tap FIR with all zeros outside the unit circle. We also give a simple necessary and sufficient condition to determine if for a particular d, a given channel can be equalized to achieve an equalized response that is open eye with delay d     

New conversion methods for realizing nonminimum phase transfer functions

New methods are described for converting second-order active-RC low-pass, high-pass, and bandpass filters to obtain nonminimum phase-transfer characteristics. Some of the realizations obtained are superior to other realizations arrived at using well-known conversion methods. Design equations for each realization are summarized in a table. Experimental results are included.     

Fourier series based nonminimum phase model for statistical signalprocessing

In this paper, a parametric Fourier series based model (FSBM) for or as an approximation to an arbitrary nonminimum-phase linear time-invariant (LTI) system is proposed for statistical signal processing applications where a model for LTI systems is needed. Based on the FSBM, a (minimum-phase) linear prediction error (LPE) filter for amplitude estimation of the unknown LTI system together with the Cramer-Rao (CR) bounds is presented. Then, an iterative algorithm for obtaining the optimum LPE filter with finite data is presented that is also an approximate maximum-likelihood algorithm when data are Gaussian. Then three iterative algorithms using higher order statistics (HOS) with finite non-Gaussian data are presented to estimate parameters of the FSBM followed by some simulation results as well as some experimental results with real speech data to support the efficacy of the proposed algorithms using the FSBM. Finally, we draw some conclusions     

Actively adaptive control for nonlinear stochastic systems

An adaptive control method can be classified into two categories, actively adaptive or passively adaptive, according to how the available information is being utilized in the on-line calculation of the control. An actively adaptive controller utilizes, in addition to the , available real-time information, the knowledge that future observations will be made, and regulates its adaptation (learning). This is done by anticipating how future estimation will be beneficial to the control objective. On the other hand, a passively adaptive controller, while utilizing the available real-time measurements, does not account for the fact that future observations will be made. Thus any learning in such a case will occur in an accidental manner. This paper summarizes a recent research effort in the development of an actively adaptive control method for nonlinear stochastic systems. A new and simpler set of equations for the original algorithm is given that provides further insight into the concepts of probing and caution in adaptive control. Several examples are chosen to illustrate the actively adaptive control method.     

Motion measurement using shape adaptive phase correlation

For video objects that have large displacements between frames, standard motion estimation techniques may not be suitable. A modification to the phase correlation motion measurement technique is proposed that avoids using frequency components from the background and offers a better compromise between range and accuracy of measured motion parameters     

An improved scheme for direct adaptive control of dynamical systems using backpropagation neural networks

This paper presents an improved direct control architecture for the on-line learning control of dynamical systems using backpropagation neural networks. The proposed architecture is compared with the other direct control schemes. In this scheme the neural network interconnection strengths are updated based on the output error of the dynamical system directly, rather than using a transformed version of the error employed in other schemes. The ill effects of the controlled dynamics on the on-line updating of the network weights are moderated by including a compensating gain layer. An error feedback is introduced to improve the dynamic response of the control system. Simulation studies are performed using the nonlinear dynamics of an underwater vehicle and the promising results support the effectiveness of the proposed scheme.     

Blind equalization of nonminimum phase channels: higher ordercumulant based algorithm

Higher order cumulant analysis is applied to the blind equalization of linear time-invariant (LTI) nonminimum-phase channels. The channel model is moving-average based. To identify the moving average parameters of channels, a higher-order cumulant fitting approach is adopted in which a novel relay algorithm is proposed to obtain the global solution. In addition, the technique incorporates model order determination. The transmitted data are considered as independently identically distributed random variables over some discrete finite set (e.g., set {±1, ±3}). A transformation scheme is suggested so that third-order cumulant analysis can be applied to this type of data. Simulation examples verify the feasibility and potential of the algorithm. Performance is compared with that of the noncumulant-based Sato scheme in terms of the steady state MSE and convergence rate     

Adaptive identification of nonminimum phase ARMA models usinghigher order cumulants alone

An adaptive identification algorithm for causal nonminimum phase ARMA models in additive colored Gaussian noise is proposed. The algorithm utilizes higher order cumulants of the observed signal alone. It estimates the AR and MA parameters successively in each iteration without computing the residual time series. The steepest descent method is used for parameter updating