Stefen Hui

Application of feedforward neural networks to dynamical system identification and control

Methods for identification and control of dynamical systems by adalines, two-layer, and three-layer feedforward neural networks (FNNs) using generalized weight adaptation algorithms are discussed. The FNNs considered contain odd nonlinear operators in both the neurons and the weight adaptation algorithms. Two application examples, each involving a nonlinear dynamical system, are considered. The first is identification of the systems forward and inverse dynamics. The second is control of the system using coordination of feedforward and feedback control combined with inverse system dynamics identification. Simulation results are used to verify the methods feasibility and to examine the effect of ENN parameter changes. Specifically the effect that the type of nonlinear activation functions present in the neurons and the type of nonlinear functions present in the weight adaptation algorithms have on FNN system dynamics identification performance is investigated. >

On solving constrained optimization problems with neural networks: a penalty method approach

Deals with the use of neural networks to solve linear and nonlinear programming problems. The dynamics of these networks are analyzed. In particular, the dynamics of the canonical nonlinear programming circuit are analyzed. The circuit is shown to be a gradient system that seeks to minimize an unconstrained energy function that can be viewed as a penalty method approximation of the original problem. Next, the implementations that correspond to the dynamical canonical nonlinear programming circuit are examined. It is shown that the energy function that the system seeks to minimize is different than that of the canonical circuit, due to the saturation limits of op-amps in the circuit. It is also noted that this difference can cause the circuit to converge to a different state than the dynamical canonical circuit. To remedy this problem, a new circuit implementation is proposed.

Dynamical analysis of the brain-state-in-a-box (BSB) neural models

A stability analysis is performed for the brain-state-in-a-box (BSB) neural models with weight matrices that need not be symmetric. The implementation of associative memories using the analyzed class of neural models is also addressed. In particular, the authors modify the BSB model so that they can better control the extent of the domains of attraction of stored patterns. Generalizations of the results obtained for the BSB models to a class of cellular neural networks are also discussed.

An analysis of a class of neural networks for solving linear programming problems

A class of neural networks that solve linear programming problems is analyzed. The neural networks considered are modeled by dynamic gradient systems that are constructed using a parametric family of exact (nondifferentiable) penalty functions. It is proved that for a given linear programming problem and sufficiently large penalty parameters, any trajectory of the neural network converges in finite time to its solution set. For the analysis, Lyapunov-type theorems are developed for finite time convergence of nonsmooth sliding mode dynamic systems to invariant sets. The results are illustrated via numerical simulation examples.

Brief paper: Sliding-mode observers for systems with unknown inputs: A high-gain approach

Sliding-mode observers can be constructed for systems with unknown inputs if the so-called observer matching condition is satisfied. However, most systems do not satisfy this condition. To construct sliding-mode observers for systems that do not satisfy the observer matching condition, auxiliary outputs are generated using high-gain approximate differentiators and then employed in the design of sliding-mode observers. The state estimation error of the proposed high-gain approximate differentiator based sliding-mode observer is shown to be uniformly ultimately bounded with respect to a ball whose radius is a function of design parameters. Finally, the unknown input reconstruction using the proposed observer is analyzed and then illustrated with a numerical example.

Solving linear programming problems with neural networks: a comparative study

In this paper we study three different classes of neural network models for solving linear programming problems. We investigate the following characteristics of each model: model complexity, complexity of individual neurons, and accuracy of solutions. Simulation examples are given to illustrate the dynamical behavior of each model.

On discrete-time variable structure sliding mode control

The purpose of this paper is to show the limitations of discrete-time variable structure sliding mode control and that the equivalent control must be used in order to have sliding in a neighborhood of the switching surface. Conflicting requirements for the sliding mode controller behavior in the continuous and discrete-time domains are revealed and analyzed. A linear control law for an uncertain discrete-time linear plant, with bounded uncertainties, is analyzed and its superiority over nonlinear controllers is demonstrated. The conclusion of the obtained results is that in the discrete-time variable structure sliding mode controller design, unlike in the continuous-time, the designer may have limited flexibility in selecting controller architectures.

Synthesis of Brain-State-in-a-Box (BSB) based associative memories

Presents a novel synthesis procedure to realize an associative memory using the Generalized-Brain-State-in-a-Box (GBSB) neural model. The implementation yields an interconnection structure that guarantees that the desired memory patterns are stored as asymptotically stable equilibrium points and that possesses very few spurious states. Furthermore, the interconnection structure is in general non-symmetric. Simulation examples are given to illustrate the effectiveness of the proposed synthesis method. The results obtained for the GBSB model are successfully applied to other neural network models.

Robust control synthesis for uncertain/nonlinear dynamical systems

This paper addresses the problem of robust output-feedback controller design for uncertain and nonlinear dynamic systems. First a robust state-feedback nonlinear control law is synthesized. This control strategy practically stabilizes the closed-loop system. Then a state estimator for the nonlinear/uncertain plant is designed and its performance analyzed. Finally the control law and the estimator are combined and the practical stability region is estimated. The results are illustrated by their application to a benchmark problem for robust control design proposed by Wie and Bernstein (1990).

Sliding Modes in Solving Convex Programming Problems

Sliding modes are used to analyze a class of dynamical systems that solve convex programming problems. The analysis is carried out using concepts from the theory of differential equations with discontinuous right-hand sides and Lyapunov stability theory. It is shown that the equilibrium points of the system coincide with the minimizers of the convex programming problem, and that irrespective of the initial state of the system the state trajectory converges to the solution set of the problem. The dynamic behavior of the systems is illustrated by two numerical examples.