Aleksandar Kojic

Brief Adaptive control of nonlinearly parameterized systems with a triangular structure

This paper deals with adaptive control of a class of nonlinear systems with a triangular structure and nonlinear parameterization. In Kojic et al. [(Systems Control Lett. 37 (1999) 267)] it was shown that a class of second-order nonlinearly parameterized systems can be adaptively controlled in a globally stable manner. In this paper, we extend our approach to all nth order systems that have a triangular structure. Global boundedness and convergence to within a desired precision @e is established for both regulation and tracking. Extensions to cascaded systems containing linear dynamics and static nonlinearities are also presented.

Parameter convergence in nonlinearly parameterized systems

A large class of problems in parameter estimation concerns nonlinearly parametrized systems. Over the past few years, a stability framework for estimation and control of such systems has been established. We address the issue of parameter convergence in such systems in this paper. Systems with both convex/concave and general parameterizations are considered. In the former case, sufficient conditions are derived under which parameter estimates converge to their true values using a min-max algorithm. In the latter case, to achieve parameter convergence a hierarchical min-max algorithm is proposed where the lower level consists of a min-max algorithm and the higher level component updates the bounds on the parameter region within which the unknown parameter is known to lie. Using this hierarchical algorithm, a necessary and sufficient condition is established for global parameter convergence in systems with a general nonlinear parameterization. In both cases, the conditions needed are shown to be stronger than linear persistent excitation conditions that guarantee parameter convergence in linearly parametrized systems. Explanations and examples of these conditions and simulation results are included to illustrate the nature of these conditions. A general definition of nonlinear persistent excitation that leads to parameter convergence is proposed at the end of this paper.

Adaptive control of a class of nonlinear systems with convex/concave parameterization

Abstract This paper deals with adaptive control of a class of second-order nonlinear systems with a triangular structure and convex/concave parameterization. In Annaswamy et al. (Automatica 33(11) (1998) 1975 –1995) it was shown that nonlinearly parameterized systems that satisfy certain matching conditions can be adaptively controlled in a stable manner. In this paper, we relax these matching conditions and include additional dynamics between the nonlinearities and the control input. Global boundedness and convergence to within a desired precision e is established. No overparameterization of the adaptive controller is required.

Brief Adaptive estimation of discrete-time systems with nonlinear parameterization

This paper concerns adaptive estimation of dynamic systems which are nonlinearly parameterized. A majority of adaptive algorithms employ a gradient approach to determine the direction of adjustment, which ensures stable estimation when parameters occur linearly. These algorithms, however, do not suffice for estimation in systems with nonlinear parameterization. We introduce in this paper a new algorithm for such systems and show that it leads to globally stable estimation by employing a different regression vector and selecting a suitable step size. Both concave/convex parameterizations as well as general nonlinear parameterizations are considered. Stable estimation in the presence of both nonlinear parameters and linear parameters which may appear multiplicatively is established. For the case of concave/convex parameterizations, parameter convergence is shown to result under certain conditions of persistent excitation.

Adaptive control of nonlinearly parametrized systems with a triangular structure

This paper deals with adaptive control of a class of nonlinear systems with a triangular structure and nonlinear parametrization. In our previous paper (1999) it was shown that a class of second-order nonlinearly parametrized systems can be adaptively controlled in a globally stable manner. In this paper, we extend our approach to all nth order systems that have a triangular structure. Global boundedness and convergence to within a desired precision /spl epsiv/ is established for both regulation and tracking. No overparametrization of the adaptive controller is required. Global boundedness in the presence of bounded disturbances is also established.

Adaptive control of a class of second order nonlinear systems with convex/concave parametrization

This paper deals with adaptive control of a class of second-order nonlinear systems with a triangular structure and concave/convex parametrization. In the paper by Annaswamy et al. (1998), it was shown that nonlinearly parametrized systems that satisfy certain matching conditions can be adaptively controlled in a stable manner. In this paper, we relax these matching conditions and include additional dynamics between the nonlinearities and the control input. Global boundedness and convergence to within a desired precision /spl epsiv/ is established. No over-parametrization of the adaptive controller is required.

A convergent frequency estimator

Online identification of sinusoidal components is an important problem that occurs in active noise control, vibration suppression, online health monitoring, and radar, sonar, and seismic applications. We adopt an approach to this identification problem which consists of the utilization of the underlying nonlinearity and an algorithm that is based on the nonlinear parameterization. The algorithm is shown to result in global convergence in the presence of two unknown frequencies. Extensions to n unknown frequencies for n/spl ges/2 that have unknown amplitudes are also discussed.

Global parameter identification in systems with a sigmoidal activation function

Parameter identification in a 2-node network with sigmoidal activation functions is considered. Given the nonlinearity in the weights, standard estimation algorithms based on linear parametrization are inadequate tools for studying global parameter convergence. In this paper, we provide an alternative approach for studying parameter identification in the presence of sigmoidal parametrization. Conditions under which a simple back propagation algorithm can lead to global convergence are considered.

Global parameter convergence in systems with monotonic parameterization

We consider parameter identification in a class of monotonically parameterized nonlinear systems, one example of which is a neural network. A gradient algorithm is employed to determine the parameter estimates. We determine sufficient conditions on the input under which the estimates converge globally to their true values. We show that new analytical tools that exploit the monotonicity of the underlying nonlinearity and properties of the gradient algorithm can be developed so as to result in global convergence.