Discontinuous controllers for high-order nonholonomic systems in power chained form

We address the problem of asymptotic convergence for a class of high-order nonholonomic systems in power chained form. This particular class of nonlinear systems is an extension of a nonholonomic system in chained form that has received considerable attention in the past few years. The nonholonomic system considered in this paper is not necessarily affine in the control variables and therefore cannot be handled by existing methods. Sufficient conditions are presented under which a discontinuous state feedback control law can be recursively constructed, using the so-called adding a power integrator technique proposed by Lin et al. (1999). We also illustrate how the result can be extended to multi-input systems in power chained form