Stabilization of affine systems by bounded control
The authors consider the control of \[ \dot x_{i} = x_{i+1},\quad i=1,\ldots,n-1, \qquad \dot x_{n} = f(x) + g(x)u(t),\quad |u(t)|\leq u_{*} \] with \(f,g\in C^{\infty}(\Omega)\). Introducing the auxiliary control \[ w=f(x) + g(x)u, \] the constrained control \(w\) is synthezised for the linearized system \[ \dot x_{i} = x_{i+1},\quad i=1,\ldots,n-1, \qquad\dot x_{n} = w,\quad |w|\leq u_{**}, \] and then \(u\) is computed. Feasibility conditions are deduced.
scientific article; zbMATH DE number 1940514