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

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.

### MSC:

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