Showing papers by "Anthony N. Michel published in 1992"

Asymptotic stability of discrete-time systems with saturation nonlinearities with applications to digital filters

Abstract: New results for an established for the global asymptotic stability of the equilibrium x=0 of nth order discrete-time systems with state saturations, x(k+1)=sat(Ax(k)), utilizing a class of positive definite and radially unbounded Lyapunov functions, v. When v is a quadratic form, necessary and sufficient conditions are obtained under which positive definite matrices H can be used to generate a Lyapunov function v(w)=w/sup T/Hw with the properties that v(Aw(k)) is negative semidefinite, and that v(sat(w)) >

A training algorithm for binary feedforward neural networks

Abstract: The authors present a new training algorithm to be used on a four-layer perceptron-type feedforward neural network for the generation of binary-to-binary mappings. This algorithm is called the Boolean-like training algorithm (BLTA) and is derived from original principles of Boolean algebra followed by selected extensions. The algorithm can be implemented on analog hardware, using a four-layer binary feedforward neural network (BFNN). The BLTA does not constitute a traditional circuit building technique. Indeed, the rules which govern the BLTA allow for generalization of data in the face of incompletely specified Boolean functions. When compared with techniques which employ descent methods, training times are greatly reduced in the case of the BLTA. Also, when the BFNN is used in conjunction with A/D converters, the applicability of the present algorithm can be extended to accept real-valued inputs. >

A learning and forgetting algorithm in associative memories: the eigenstructure method

Abstract: The authors develop a design technique for associative memories with learning and forgetting capabilities via artificial feedback neural networks. The proposed synthesis technique utilizes the eigenstructure method. Networks generated by this method are capable of learning new patterns as well as forgetting existing patterns without the necessity of recomputing the entire interconnection weights and external inputs. In many respects, the results represent significant improvements over the outer product method, the projection learning rule, and the pseudo-inverse method with stability constraints. Several specific examples are given to illustrate the strengths and weaknesses of the methodology advocated. >

Verification of the self-stabilization mechanism in robust stochastic adaptive control using Lyapunov function arguments

Abstract: The objective of this paper is to propose a new algorithm for self-tuning control in the presence of unmodeled dynamics. The algorithm is a modified version of the well-known stochastic gradient scheme. It is shown (with probability one) that the resulting closed-loop system is globally stable and the mean-square tracking error is proportional to the size of unmodeled dynamics. In the absence of unmodeled dynamics, the algorithm produces the minimum-variance self-timing control. It is analytically verified that the proposed algorithm has self-stabilization property; i.e., possible occurrence of instability results in mean-square bounded signals. Global stability of the adaptive system is achieved without imposing persistency exciting condition on the regressor and positive real assumption on the system noise dynamics.

Asymptotic stability of discrete-time systems with saturation nonlinearities

Abstract: The authors present results for the global asymptotic stability of the equilibrium x=0 of n/sup th/ order, discrete-time systems with state saturations. The results are used to establish conditions for the non-existence of limit cycles in n/sup th/-order fixed point digital filters. It is demonstrated that the present results are easier to apply and are less conservative than corresponding existing results. >

Stability and Boundedness Analysis of Discrete Event Systems

Abstract: Recently it has been shown that the conventional notions of stability in the sense of Lyapunov and asymptotic stability can be used to characterize the stability properties of "logical" discrete event systems (DES). Moreover, it has been shown that stability analysis via the choice of appropriate Lyapunov functions can be used for DES and can be applied to several DES applications including manufacturing systems and computer networks [1,2]. In this paper we extend the conventional notions and analysis of uniform boundedness, uniform ultimate boundedness, practical stability, and finite time stability so that they apply to the class of logical DES that can be defined on a metric space. Within this framework we show that the standard Petri net-theoretic notions of boundedness are special cases of Lagrange stability and uniform boundedness. In addition we show that the Petri net-theoretic approach to boundedness analysis is actually a Lyapunov approach in that the net-theoretic analysis actually produces an appropriate Lyapunov function. Moreover, via the Lyapunov approach we provide a sufficient condition for the uniform ultimate boundedness of General Petri nets. Several applications are provided.

Comparison theory for general motions of dynamical systems with applications to discrete event systems

Abstract: A comparison theory is developed for the qualitative analysis of general dynamical systems, making use of stability preserving mapping. The qualitative aspects addressed pertain to Lyapunov and Lagrange stability. The theory is general enough to include as special cases most of the existing deterministic results for dynamical systems described on finite- and infinite-dimensional spaces. In addition, the results are applicable to contemporary systems, such as discrete-event systems. >

Qualitative equivalence of dynamical systems with applications to discrete event systems

Abstract: Stability preserving mappings are used to identify general dynamical systems having equivalent qualitative properties. The authors establish sufficient conditions for a mapping to have stability preserving properties and they use stability preserving mappings to formulate comparison theorems for general dynamical systems. The results developed include most of the corresponding comparison results reported in the literature as special cases. In addition, the present results are applicable to certain classes of general dynamical systems, such as discrete event systems, which cannot be addressed by corresponding previous results. For such systems, the motions which make up a dynamical system are not determined by equations, as is required by the existing results. The applicability of the results developed is demonstrated on a class of discrete event systems. >

A Unified Approach to Robust Stochastic and Deterministic Adaptive Control

Abstract: This paper presents a new methodology for the global stability analysis, and consequently, for the design of robust deterministic and stochastic adaptive control, filtering and prediction. The methodology advocated herein represents a mathematical formalization of the self-stabilization mechanism which is a natural characteristic of every properly designed adaptive system. The effectiveness of the proposed approach is demonstrated by solving the robust deterministic and stochastic adaptive control problems. It is shown that very small algorithm gains ?, may produce very large signals in the adaptive loop, which are unacceptable for practical applications. The intensity of the admissible unmodelled dynamics does not depend on the algorithm design parameters and it is specified in terms of the corresponding H? norm.

Adaptive control and self-stabilization

Abstract: This paper presents a new methodology for the global stability analysis, and consequently, for the design of robust deterministic and stochastic adaptive control, filtering and prediction. The methodology advocated herein represents a mathematical formalization of the self-stabilization mechanism which is a natural characteristic of every properly designed adaptive system. The effectiveness of the proposed approach is demonstrated by solving the robust deterministic and stochastic adaptive control problems. It is shown that very small algorithm gains μ, may produce very large signals in the adaptive loop, which are unacceptable for practical applications. The intensity of the admissible unmodelled dynamics does not depend on the algorithm design parameters and it is specified in terms of the corresponding H ∞ norm.

Unlearning algorithm in associative memories: eigenstructure method

Abstract: Unlearning capabilities are incorporated into a synthesis procedure for a class of discrete-time neural networks. The proposed technique increases storing capacity while maximizing the domain of attraction of each desired pattern to be stored. Making use of learning, forgetting, and unlearning capabilities, networks generated by the method advanced herein are capable of learning new patterns as well as forgetting learned patterns without the necessity of recomputing all the interconnection weights and external inputs. The unlearning algorithm developed is then utilized to equalize the basins of attraction for each desired pattern to be stored in a given network, and to minimize the number of spurious states. Examples are given to illustrate the strengths and weaknesses of the methodologies. >

Nonlinear model-matching design of servomechanisms

Abstract: This paper examines the design and realization of nonlinear multivariable servomechanisms utilizing higher-order spectral information about the plant. Specifically, the simultaneous design for specified output responses and reasonable control signals is addressed. For a desired output behavior and a given plant, a systematic model-matching procedure is employed which exploits the higher-order concepts contained in the multidimensional transfer function representations of the Volterra kernels of the plant and its compensation. The method applies to the design of nonlinear output feedback dynamics and to higher-order feedforward excitation of the closed-loop system. A recursive algorithm for realization of the higher-order kernel transforms obtained in the design is presented in detail. The potential improvement in performance is demonstrated in two applications, in which the design goals are partial feedback linearization with associated decoupling.