Local controllability of 2D nonlinear systems (Q1302662)

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.