Application of Integrator Backstepping to Nonholonomic Control Problems

Abstract Smooth time-periodic feedback laws for stabilization of nonholonomic dynamic systems are constructed. The construction procedure is based on Pomet ’s method and the integrator back-stepping approach. As an application, feedback laws for nonholonomic systems in extended power form are presented. The proposed technique is also applicable to stabilization problems for nonholonomic systems whose models include actuator dynamics. As an illustration, we develop smooth time-periodic feedback laws for the knife-edge with augmented actuator dynamics. We also present a nonsmooth time-periodic feedback law for this example.

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