New Results in Stabilization of Uncertain Nonholonomic Systems: An Event-Triggered Control Approach

Abstract

This paper reports latest developments in event-triggered and self-triggered control of uncertain nonholonomic systems in the perturbed chained form. In order to tackle the effects of drift uncertain nonlinearities, nonholonomic constraints and nonsmooth aperiodic sampling in event-based control, a novel systematic design scheme is proposed by integrating set-valued maps with state-separation and state-scaling techniques. The stability analysis of the closed-loop event-triggered control system is based on the cyclic-small-gain techniques that overcome the limitation of Lyapunov theory in the construction of Lyapunov functions for nonsmooth dynamical systems and enjoy inherent robustness properties due to the use of gain-based characterization of robust stability. More specifically, the closed-loop event-triggered control system is transformed into an interconnection of multiple input-to-state stable systems, to which the cyclic-small-gain theorem is applied for robust stability analysis. New self-triggered mechanisms are also developed as natural extensions of the event-triggered control result. The proposed event-based control design approach is new and original even when the system model is reduced to the ideal unperturbed chained form. Interestingly, the proposed methodology is also applicable to a broader class of nonholonomic systems subject to state and input-dependent uncertainties. The efficacy of the obtained event-triggered controllers is validated by a benchmark example of mobile robots subject to parametric uncertainties and a measurement noise such as bias in the orientation.