Simple Adaptive Control for MIMO Nonlinear Continuous-Time Systems Using Neural Networks

Abstract

This paper presents a method of continuous-time SAC (simple adaptive control) for MIMO (multi-input multi-output) nonlinear systems using neural networks. The control input is given by the sum of the output of the simple adaptive controller and the output of the neural network. The neural network is used to compensate the nonlinearity of plant dynamics that is not taken into consideration in the usual SAC. The role of the neural network is to construct a linearized model by minimizing the output error caused by nonlinearities in the control systems.

MRAC Combined Neural Networks for Ultra-Sonic Motor

“…To overcome non-linearity of the plant, MRAC combined with neural networks (NN) were proposed in Refs. (7) and (8). The proposed design schemes are almost similar.…”

“…The main contribution is to improve the architecture of NN incorporated in MRAC system proposed in Refs. (7) and (8). As a result, we derived very simple calculation expression of the Jacobian in the learning algorithm of NN.…”

“…In the proposed method, only output of NN is used as one input of NN instead of the synthesized output of MRAC and NN used in Refs. (7) and (8). As a result, we have proposed the very simple calculation method of the Jacobian used only one estimated value of the plant.…”

Application of Neural Networks to MRAC for the Nonlinear Magnetic Levitation System

“…In the conventional MRAC scheme, the controller is designed to realize a plant output convergence to reference model output based on the assumption that the plant can be linearized. Therefore, this scheme is effective for controlling a linear plant with unknown parameters in the ideal case, but it may not be assured to succeed in controlling a nonlinear plant with unknown structures in the real case (1), (4), (5) . The Neural Networks (NNs) are able to learn from example, recognize data, identify pattern, and determine approximation of a nonlinear function, and this makes it a prime candidate to be utilized in the area of nonlinear control systems.…”

“…The NN is required to better control complex uncertainty dynamical systems and to improve performance of the conventional control method (6) - (8) . Many researchers have employed the NN in their control design (5), (7) - (13) . For example, the neural networks have been applied in a direct adaptive control for unknown nonlinear systems (9) .…”