A receding horizon stabilization approach to constrained nonholonomic systems in power form

The control of nonholonomic systems with practical requirements is still a challenging problem but finds many industrial applications. This paper studies the receding horizon control (RHC)-based stabilization problem of a class of constrained nonholonomic systems in power form. A non-quadratic cost function is constructed by using the homogeneous norm of the nonholonomic system in power form. With this novel cost function, two kinds of RHC algorithms are designed, of which one ensures the convergence of the closed-loop system states, and the other ensures the ρ-exponential stability. The feasibility of the designed algorithms and the closed-loop convergence are analyzed and ensured theoretically under mild conditions. The comparison and application results are provided, showing that (1) the proposed RHC algorithms are effective and the theoretical results are valid, and (2) the proposed algorithms can stabilize the nonholonomic systems with a much faster convergence rate than the conventional time-varying stabilizable controllers.