Saturated Control of Chained Nonholonomic Systems

Plenty of approaches to stabilize chained nonholonomic systems have been proposed in the literature. However, the stabilization with constrained inputs is seldom addressed. This problem has practical importance since all physical nonholonomic systems have actuator limitations. In this article, a novel switching control design is proposed. The design strategy is inspired by the structural similarity between chained nonholonomic systems and multiple-integrator systems. The key idea is to make u1 to be piecewise constant, which renders the rest of the states a chain of constant weighted integrators. Moreover, since the saturation control u2 eventually works in a linear region with fixed eigenvalues, a buffer zone for x1 is introduced to ensure the convergence of the rest of the states. The effectiveness of the proposed design is verified by computer simulations.