Model description:
$$\begin{align*} x_1(k+1) &= 0.9x_1(k)\sin{[x_2(k)]} + \left(2 + 1.5 \dfrac{x_1(k)u_1(k)}{1+x_1^2(k)u_1^2(k)}\right)u_1(k) + \left(x_1(k) + \dfrac{2x_1(k)}{1+x_1^2(k)}\right)u_1(k)\\ x_2(k+1) &= x_3(k)(1+\sin{[4x_3(k)]}+ \dfrac{x_3(k)}{1+x_3^2(k)}\\ x_3(k+1) &= (3 + \sin{[2x_1(k)]})u_2(k)\\ y_1(k)&=x_1(k)\\ y_2(k)&=x_2(k) \end{align*}$$
Type:
Form:
Model order:
3
Time domain:
Linearity:
Publication details:
| Title | Adaptive control of nonlinear multivariable systems using neural networks |
| Publication Type | Conference Paper |
| Year of Publication | 1993 |
| Authors | Narendra, K.S., and Mukhopadhyay S. |
| Conference Name | Proceedings of the 32nd IEEE Conference on Decision and Control, 1993. |
| Date Published | 12/1993 |
| Publisher | IEEE |
| Conference Location | San Antonio, TX |
| ISBN Number | 0-7803-1298-8 |
| Accession Number | 4772091 |
| Keywords | adaptive control, multivariable systems, neural nets, nonlinear systems |
| Abstract | In this paper we examine the problem of control of multivariable systems using neural networks. The problem is discussed assuming different amounts of prior information concerning the plant and hence different levels of complexity. In the first stage it is assumed that the state equations describing the plant are known and that the state of the system is accessible. Following this the same problem is considered when the state equations are unknown. In the last stage the adaptive control of the multivariable system using only input-output data is discussed in detail. The objective of the paper is to demonstrate that results from nonlinear control theory and linear adaptive control theory can be used to design practically viable controllers for unknown nonlinear multivariable systems using neural networks. The different assumptions that have to be made, the choice of identifier and controller architectures and the generation of adaptive laws for the adjustment of the parameters of the neural networks form the core of the paper |
| DOI | 10.1109/CDC.1993.325299 |