A New Neuro-FDS Definition for Indirect Adaptive Control of Unknown Nonlinear Systems Using a Method of Parameter Hopping

Abstract

The indirect adaptive regulation of unknown nonlinear dynamical systems is considered in this paper. The method is based on a new neuro-fuzzy dynamical system (neuro-FDS) definition, which uses the concept of adaptive fuzzy systems (AFSs) operating in conjunction with high-order neural network functions (FHONNFs). Since the plant is considered unknown, we first propose its approximation by a special form of an FDS and then the fuzzy rules are approximated by appropriate HONNFs. Thus, the identification scheme leads up to a recurrent high-order neural network (RHONN), which however takes into account the fuzzy output partitions of the initial FDS. The proposed scheme does not require a priori experts' information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions. Once the system is identified around an operation point, it is regulated to zero adaptively. Weight updating laws for the involved HONNFs are provided, which guarantee that both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. The existence of the control signal is always assured by introducing a novel method of parameter hopping, which is incorporated in the weight updating law. Simulations illustrate the potency of the method and comparisons with conventional approaches on benchmarking systems are given. Also, the applicability of the method is tested on a direct current (dc) motor system where it is shown that by following the proposed procedure one can obtain asymptotic regulation.

Direct adaptive neuro‐fuzzy trajectory tracking of uncertain nonlinear systems

“…In this section, we investigate trajectory tracking problems on the basis of the F-RHONNs formulation developed in [25] for systems having an MVMI form. Tracking is known as our attempt to force the state of the actual system to follow the state of a given dynamical system.…”

“…These centers can be obtained by experts or by offline techniques based on gathered data. The F-RHONN approximation offers a number of advantages in comparison with traditional adaptive fuzzy or neural formulations because it reduces the a priori experts knowledge to be incorporated into the model and transforms the global approximation task into many simpler ones, resulting in better overall approximation performance [25].…”

“…Therefore, the projection of the updating vector on the boundary surface is of no use. To cope with this situation, an alternative technique termed 'parameter hopping' has been introduced in [25]. With the use of concepts from multidimensional vector geometry, this technique modifies the updating law such that when the weight vector approaches (within a safe distance  ij ), the forbidden hyper-plane N x g ij W g ij D 0 and the direction of updating are toward the forbidden hyper-plane; it introduces a hopping that drives the weights in the direction of the updating but on the other side of the space, where here the weight space is divided into two sides by the forbidden hyper-plane.…”

“…This way the proposed method is less vulnerable to initial design assumptions, and the parameter identification is easily addressed by HONNs. In recent papers [25,26], the proposed neuro-fuzzy approximator has been used to regulate affine in the control plants with indirect or direct methods in the presence of only parametric uncertainties. This paper is motivated by the approximation superiority of the F-RHONN formulation.…”

“…Depending on the type of discontinuity and the direction of the vector field before and after the point of discontinuity, the system may have a Caratheodory or a Filippov [34] solution [33,35]. Here, because of the construction of the underlying F-RHONN approximator, we do not apply projection but employ a different choice called parameter hopping [25], in a modified form, which is incorporated in the weight updating laws. The slight modification of the hopping method aims to eliminate the possibility of activating an unnecessary repetitive hopping loop, when the hopping condition is actuated.…”