Kumpati S. Narendra

Identification and control of dynamical systems using neural networks

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.

Adaptive control using multiple models

Intelligent control may be viewed as the ability of a controller to operate in multiple environments by recognizing which environment is currently in existence and servicing it appropriately. An important prerequisite for an intelligent controller is the ability to adapt rapidly to any unknown but constant operating environment. This paper presents a general methodology for such adaptive control using multiple models, switching, and tuning. The approach was first introduced by Narendra et al. (1992) for improving the transient response of adaptive systems in a stable fashion. This paper proposes different switching and tuning schemes for adaptive control which combine fixed and adaptive models in novel ways. The principal mathematical results are the proofs of stability when these different schemes are used in the context of model reference control of an unknown linear time-invariant system. A variety of simulation results are presented to demonstrate the efficacy of the proposed methods.

A new adaptive law for robust adaptation without persistent excitation

A new adaptive law motivated by the work of loannou and Kokotovic (1983) is proposed for the robust adaptive control of plants with unknown parameters. In this adaptive law the output error plays a dual role in the adjustment of the control parameter vector. The advantages of using the adaptive law over others proposed in the literature are discussed. In the ideal case the adaptive system has bounded solutions; in addition, the origin of the error equations is exponentially stable when the reference input is persistently exciting and has a sufficiently large amplitude. The adaptive system is also shown to be robust under bounded external disturbances. Finally, it is shown that, by suitably modifying the adaptive law, the overall system can be made robust in the presence of a class of unmodeled dynamics of the plant. Simulation results are presented throughout the paper to complement the theoretical developments.

Gradient methods for the optimization of dynamical systems containing neural networks

An extension of the backpropagation method, termed dynamic backpropagation, which can be applied in a straightforward manner for the optimization of the weights (parameters) of multilayer neural networks is discussed. The method is based on the fact that gradient methods used in linear dynamical systems can be combined with backpropagation methods for neural networks to obtain the gradient of a performance index of nonlinear dynamical systems. The method can be applied to any complex system which can be expressed as the interconnection of linear dynamical systems and multilayer neural networks. To facilitate the practical implementation of the proposed method, emphasis is placed on the diagrammatic representation of the system which generates the gradient of the performance function.

A common Lyapunov function for stable LTI systems with commuting A-matrices

The paper demonstrates that a common quadratic Lyapunov function exists for all linear systems of the form x/spl dot/=A/sub i/x, i=1,2,/spl middot//spl middot//spl middot/,N, where the matrices A/sub i/ are asymptotically stable and commute pairwise. This in turn assures the exponential stability of a switching system x/spl dot/(t)=A(t)x(t) where A(t) switches between the above constant matrices A/sub i/. >

Stable adaptive controller design, part II: Proof of stability

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.

Learning Automata - A Survey

Stochastic automata operating in an unknown random environment have been proposed earlier as models of learning. These automata update their action probabilities in accordance with the inputs received from the environment and can improve their own performance during operation. In this context they are referred to as learning automata. A survey of the available results in the area of learning automata has been attempted in this paper. Attention has been focused on the norms of behavior of learning automata, issues in the design of updating schemes, convergence of the action probabilities, and interaction of several automata. Utilization of learning automata in parameter optimization and hypothesis testing is discussed, and potential areas of application are suggested.

An iterative method for the identification of nonlinear systems using a Hammerstein model

An iterative method is proposed for the identification of nonlinear systems from samples of inputs and outputs in the presence of noise. The model used for the identification consists of a no-memory gain (of an assumed polynomial form) followed by a linear discrete system. The parameters of the pulse transfer function of the linear system and the coefficients of the polynomial non-linearity are alternately adjusted to minimize a mean square error criterion. Digital computer simulations are included to demonstrate the feasibility of the technique.

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

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. >

Adaptation and learning using multiple models, switching, and tuning

This article presents a general methodology for the design of adaptive control systems which can learn to operate efficiently in dynamical environments possessing a high degree of uncertainty. Multiple models are used to describe the different environments and the control is effected by switching to an appropriate controller followed by tuning or adaptation. The study of linear systems provides the theoretical foundation for the approach and is described first. The manner in which such concepts can be extended to the control of nonlinear systems using neural networks is considered next. Towards the end of the article, the applications of the above methodology to practical robotic manipulator control is described. >