Backstepping Stabilization of Nonlinear Dynamical Systems Under State Constraints

Abstract

The problem of stabilizing the zero value of the state vector of constrained nonlinear dynamical systems written in a special form is solved. The proposed control design accounts for magnitude constraints on the values of state variables and is based on the integrator backstepping approach using logarithmic Lyapunov barrier functions. The obtained stabilizing feedbacks, in contrast to similar known results, are based on the use of linear virtual stabilizing functions that do not grow unbounded as state variables approach the boundary values. As an example, we consider a state constraints aware solution to the control problem of positioning an autonomous underwater vehicle at a given point in space.