Dimitris C. Theodoridis

INDIRECT ADAPTIVE CONTROL OF UNKNOWN MULTI VARIABLE NONLINEAR SYSTEMS WITH PARAMETRIC AND DYNAMIC UNCERTAINTIES USING A NEW NEURO-FUZZY SYSTEM DESCRIPTION

The indirect adaptive regulation of unknown nonlinear dynamical systems with multiple inputs and states (MIMS) under the presence of dynamic and parameter uncertainties, is considered in this paper. The method is based on a new neuro-fuzzy dynamical systems description, which uses the fuzzy partitioning of an underlying fuzzy systems outputs and high order neural networks (HONNs) associated with the centers of these partitions. Every high order neural network approximates a group of fuzzy rules associated with each center. The indirect regulation is achieved by first identifying the system around the current operation point, and then using its parameters to device the control law. Weight updating laws for the involved HONNs are provided, which guarantee that, under the presence of both parameter and dynamic uncertainties, both the identification error and the system states reach zero, while keeping all signals in the closed loop bounded. The control signal is constructed to be valid for both square and non square systems by using a pseudoinverse, in Moore-Penrose sense. The existence of the control signal is always assured by employing a novel method of parameter hopping instead of the conventional projection method. The applicability is tested on well known benchmarks.

Dynamical recurrent neuro-fuzzy identification schemes employing switching parameter hopping.

In this paper we analyze the identification problem which consists of choosing an appropriate identification model and adjusting its parameters according to some adaptive law, such that the response of the model to an input signal (or a class of input signals), approximates the response of the real system for the same input. For identification models we use fuzzy-recurrent high order neural networks. High order networks are expansions of the first-order Hopfield and Cohen-Grossberg models that allow higher order interactions between neurons. The underlying fuzzy model is of Mamdani type assuming a standard defuzzification procedure such as the weighted average. Learning laws are proposed which ensure that the identification error converges to zero exponentially fast or to a residual set when a modeling error is applied. There are two core ideas in the proposed method: (1) Several high order neural networks are specialized to work around fuzzy centers, separating in this way the system into neuro-fuzzy subsystems, and (2) the use of a novel method called switching parameter hopping against the commonly used projection in order to restrict the weights and avoid drifting to infinity.

Direct adaptive regulation of unknownnonlinear systems with analysis of themodel order problem

A new method for the direct adaptive regulation of unknown nonlinear dynamical systems is proposed in this paper, paying special attention to the analysis of the model order problem. The method uses a neurofuzzy (NF) modeling of the unknown system, which combines fuzzy systems (FSs) with high order neural networks (HONNs). We propose the approximation of the unknown system by a special form of an NF-dynamical system (NFDS), which, however, may assume a smaller number of states than the original unknown model. The omission of states, referred to as a model order problem, is modeled by introducing a disturbance term in the approximating equations. The development is combined with a sensitivity analysis of the closed loop and provides a comprehensive and rigorous analysis of the stability properties. An adaptive modification method, termed ‘parameter hopping’, is incorporated into the weight estimation algorithm so that the existence and boundedness of the control signal are always assured. The applicability and potency of the method are tested by simulations on well known benchmarks such as ‘DC motor’ and ‘Lorenz system’, where it is shown that it performs quite well under a reduced model order assumption. Moreover, the proposed NF approach is shown to outperform simple recurrent high order neural networks (RHONNs).

A new direct adaptive regulator with robustness analysis of systems in Brunovsky form.

The direct adaptive regulation of unknown nonlinear dynamical systems in Brunovsky form with modeling error effects, is considered in this paper. Since the plant is considered unknown, we propose its approximation by a special form of a Brunovsky type neuro-fuzzy dynamical system (NFDS) assuming also the existence of disturbance expressed as modeling error terms depending on both input and system states plus a not-necessarily-known constant value. The development is combined with a sensitivity analysis of the closed loop and provides a comprehensive and rigorous analysis of the stability properties. The existence and boundness of the control signal is always assured by introducing a novel method of parameter hopping and incorporating it in weight updating laws. Simulations illustrate the potency of the method and its applicability is tested on well known benchmarks, as well as in a bioreactor application. It is shown that the proposed approach is superior to the case of simple recurrent high order neural networks (HONNs).