Adaptive control with multiple event-triggering settings under mismatched uncertainties in control and feedback paths

It is technically challenging to achieve stable tracking control for strict-feedback systems in the presence of mismatched uncertainties in control and feedback paths. The underlying problem becomes even more complicated if the plant states and the actuation signal as well as the adaptive estimated parameters are triggered simultaneously as the virtual control signals in regular backstepping design methods are no longer differentiable under such settings. In this work we develop a new strategy in which the state sensoring, control signal transmitting and adaptive parameter updating are executed intermittently via three triggering units respectively, for saving communication-energy resources and alleviating computation burden. To circumvent the non-differentiability associated with virtual controllers arising from multiple event-triggering actions, we first develop a continuous adaptive control scheme under regular state feedback, based on which we construct an adaptive multiple event-triggered control scheme by replacing the variables in the preceding scheme with the triggered ones, respectively. Several useful lemmas are elaborately derived to ensure closed-loop system stability under such replacement. It is shown that semi-global uniform boundedness of all internal signals is ensured without Zeno behavior; and the output tracking error is steered into an assignable residual set around zero. Numerical simulation verifies the benefits and efficiency of the proposed method.