Model-following neuro-adaptive control design for non-square, non-affine nonlinear systems

Abstract

This paper proposes a new model-following adaptive control design technique for a class of non-affine and nonsquare nonlinear systems using neural networks. An appropriate stabilizing controller is assumed available for a nominal system model. This nominal controller may not be able to guarantee stability/satisfactory performance in the presence of unmodeled dynamics (neglected algebraic terms in the mathematical model) and/or parameter uncertainties present in the system model. In order to ensure stable behavior, an online control adaptation procedure is proposed in this paper. The controller design is carried out in two steps: (i) synthesis of a set of neural networks which capture matched unmodeled (neglected) dynamics or model uncertainties due to parametric variations and (ii) synthesis of a controller that drives the state of the actual plant to that of a desired nominal model. The neural network weight update rule is derived using Lyapunov theory, which guarantees both stability of the error dynamics (in a practical stability sense) and boundedness of the weights of the neural networks. A desirable characteristic of the adaptation procedure presented in this paper is that it is independent of the technique used to design the nominal controller; and hence can be used in conjunction with any known control design technique. Numerical results for two challenging illustrative problems are presented in this paper which demonstrate these features and clearly bring out the potential of the proposed approach.

Electrohydraulic Control Using Neural MRAC Based on a Modified State Observer

“…Ideally, the closed-loop system is asymptotically stable when γ 1 = 0. Combining (8), (15), and (31), the final expression for the proposed controller is (40) x ≤ λ max (P ) (2 P bε * /λ min (Q) + 2λ min (K 2 P )) 2 Note that the controller will drive the tracking error asymptotically to zero.…”

“…This paper develops a new neural network MRAC with improved transient performance and asymptotic stability. Based on the MRAC neural network controller, the uncertainty-state neural network observer structure is modified in the manner of [40]. In this modification, instead of introducing additional filters, a factor of the observer error is added to the neural network observer structure and, as a result, this new method enables further increases in the adaptive gain, leading to improved tracking performance.…”

Estimation of tip-sample interaction in tapping mode AFM using a neural-network approach

“…K can be chosen as a diagonal matrix with the inverse of time constants on its diagonal [21]. By defining the state-approximation-error as â e X X   and weight-approximation-error asŴ W W    , the state error dynamics can be expressed as,…”

“…To ensure bounds on state error a e and to also on the adaptive weight Ŵ , the stabilizing weight update rule given by [21],…”

“…Our approach utilizes a Neural-Network (NN) model because NNs are known for their ability to model complex and unknown functions, they have been successfully demonstrated in a wide variety of applications, and they can be solved in parallel, which is critical for real-time implementation [21], [22]. The objective of this paper is to evaluate the NN technique in simulation using simple models of the probe dynamics and tip-sample forces in order to determine potential efficacy for the AFM problem as well as identify key areas for future research and development.…”