Local controllability of 2D nonlinear systems. (English) Zbl 0941.93005

Klamka, Jerzy

Bull. Pol. Acad. Sci., Tech. Sci. 47, No. 2, 153-161 (1999).

The author considers constrained controllability for nonlinear discrete 2D systems of the form \[ x(i+ 1,j+1)= f(x(i, j), x(i+ 1,j), x(i,j+1), u(i,j), u(i+ 1, j),u(i,j+ 1)),\tag{1} \] \(x(i,j)\in \mathbb{R}^n\), \(u(i,j)\in \mathbb{R}^m\) are the state and input vectors at the point \((i,j)\) and \(f: \mathbb{R}^n\times \mathbb{R}^n\times \mathbb{R}^n\times \mathbb{R}^m\times \mathbb{R}^m\times \mathbb{R}^m\to \mathbb{R}^n\). Using some mapping theorems and linear approximations of (1) sufficient conditions for constrained controllability are established. The paper extends some previous results of the author.

Reviewer: T.Kaczorek (Warszawa)

MSC:

93B05	Controllability
93C35	Multivariable systems, multidimensional control systems
93C55	Discrete-time control/observation systems
93B18	Linearizations
93C10	Nonlinear systems in control theory

Keywords:

linearization; constrained controllability; nonlinear discrete 2D systems