Switched Feedback Control of Higher-order Nonholonomic Systems with Multi-generators

Abstract

In this paper, we propose a discontinuous state feedback control algorithm for a class of nonholonomic symmetric affine systems with multi-generators. The controllability Lie algebra of a multi-generator system is structurally different from that of single-generator systems, such as conventional chained form systems. Due to this complexity of controllability structure, feedback control problem of multi-generator system is so awkward that the existing control method for chained systems are not valid any longer. In this paper, we take notice that a certain part of a multi-generator system is considered a single-generator systems and the subsystem can be stabilized by any conventional controller for chained systems. Then we propose a switching control algorithm that each generator is chosen in sequence and conrresponding sub-controllers are applied, where each sub-controller design is based on existing Astolfi’s and Sampei’s design method proposed for chained systems. The efficiency of the proposed strategy is evaluated via numerical simulations.