It is demonstrated that neural networks can be used effectively for the identification and control of nonlinear dynamical systems. The emphasis is on models for both identification and control. Static and dynamic backpropagation methods for the adjustment of parameters are discussed. In the models that are introduced, multilayer and recurrent networks are interconnected in novel configurations, and hence there is a real need to study them in a unified fashion. Simulation results reveal that the identification and adaptive control schemes suggested are practically feasible. Basic concepts and definitions are introduced throughout, and theoretical questions that have to be addressed are also described. >

Identification and control of dynamical systems using neural networks

This paper examines the robustness properties of existing adaptive control algorithms to unmodeled plant high-frequency dynamics and unmeasurable output disturbances. It is demonstrated thai there exist two infinite-gain operators in the nonlinear dynamic system which determines the time-evolution of output and parameter errors. The pragmatic implication of the existence of such infinite-gain operators is that 1) sinusoidal reference inputs at specific frequencies and/or 2) sinusoidal output disturbances at any frequency (including dc), can cause the loop gain to increase without bound, thereby exciting the unmodeled high-frequency dynamics, and yielding an unstable control system. Hence, it is concluded that existing adaptive control algorithms as they are presented in the literature referenced in this paper, cannot be used with confidence in practical designs where the plant contains unmodeled dynamics because instability is likely to result. Further understanding is required to ascertain how the currently implemented adaptive systems differ from the theoretical systems studied here and how further theoretical development can improve the robustness of adaptive controllers.

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Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics

The paper presents a proof of stability of model reference adaptive control systems using direct control. The structure of the adaptive system is similar to that considered by Monopoli [1] and Narendra and Valavani [2] but contains an additional feedback term which ensures that the time derivative of the parameter error vector belongs to the L2space. The output of the plant is shown to be bounded by expressing the plant feedback loop as an exponentially stable system with a time-varying gain \dot{\phi}(\cdot)\in L^{2} in the feedback path.

Stable adaptive controller design, part II: Proof of stability

An integrated approach to the design of practical adaptive control algorithms is presented. Many existing ideas are brought together, and the effect of various design parameters available to a user is explored. The theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators. It is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics. >

Design issues in adaptive control

A well-known problem in adaptive control is the poor transient response which is observed when adaptation is initiated. In this paper we develop a stable strategy for improving the transient response by using multiple models of the plant to be controlled and switching between them. The models are identical except for initial estimates of the unknown plant parameters. The control to be applied is determined at every instant by the model which best approximates the plant. Simulation results are presented to indicate the improvement in performance that can be achieved. >

Improving transient response of adaptive control systems using multiple models and switching

The paper presents a proof of stability of the model reference adaptive control problem for the discrete case.

Yuan-Hao Lin

Papers

Stable discrete adaptive control