In this paper, we address a neural-network-based control design for a discrete-time nonlinear system. Our design approach is to approximate the nonlinear system with a multilayer perceptron of which the activation functions are of the sigmoid type symmetric to the origin. A linear difference inclusion representation is then established for this class of approximating neural networks and is used to design a state-feedback control law for the nonlinear system based on the certainty equivalence principle. The control design equations are shown to be a set of linear matrix inequalities where a convex optimization algorithm can be applied to determine the control signal. Further, the stability of the closed-loop is guaranteed in the sense that there exists a unique global attraction region in the neighborhood of the origin to which every trajectory of the closed-loop system converges. Finally, a simple example is presented so as to illustrate our control design procedure.

optimization algorithms to be possible. The closedIn this paper we address a neural network-based control design for a discrete-time nonlinear system. Our design approach is to approxiniate the nonlinear system with a niultilayer perceptron o f which the activation functions are o f the sigmoid type s~~n~n i e t r i c to the origin. A linear difference inclusion representation is then established for this class o f approxiniating neural networks and is used to design a state-feedback control law for the nonlinear system based on the Certainty Equivalence Principle. The control design equations are shown to be a set o f linear niatrix inequalities where a convex optimization algorithm can be applied to determine the control signal. Further, the stability of the closed-loop is guaranteed in the sense that there exists a unique global attraction region in the neighborhood of the origin to which every trajectory of the closed-loop system converges. Finally, a siniple example is presented so as to illustrate our control design procedure.

In this paper we address the adaptive and nonadaptive model reference control problem for a class of multivariable linear time-varying plants, namely index-invariant ones. We show that, under appropriate controllability and observability conditions, this class of plants admits a fractional description in terms of polynomial differential operators and, as such, allows for a polynomial equation-based controller design. We also show that, for a model reference control objective, the controller can be designed by solving a set of algebraic equations. Further, when the plant parameters are only partially known, we employ a gradient-based adaptive law with projection and normalization to update the controller parameters and establish the stability and tracking properties of adaptive closed-loop plant. Finally, we present a simple example to illustrate the design and realization of both the adaptive and nonadaptive control laws.

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In this paper we address the problem of improving the asymptotic performance guarantees of a class of model reference adaptive controllers under insufficient excitation and in the presence of perturbations such as non-parametric uncertainty and bounded disturbances. We show that for a class of perturbations whose normalized effect is bounded by an a priori known function of time an estimate of the parametric uncertainty set can be obtained on-line via a set membership estimator. Furthermore, by incorporating this estimate as an additional constraint in the adaptive law generating the controller parameters, we show that the resulting adaptive controller offers dead-zone-like performance guarantees in the lim-sup sense while preserving the desirable root-mean-square performance guarantees of gradient-based algorithms. KEY WORDS Model reference adaptive control Root-mean-square performanceLim-sup performance Set membership estimation Parameter projection