Event-triggered robust optimal control algorithm for strict-feedback nonlinear systems with dead-zone and external disturbance

Abstract

The paper proposes a novel event-triggered robust optimal control algorithm for strict-feedback nonlinear
systems (SNSs) affected by dead-zone and external disturbance. An event-triggered feed-forward control (EFFC)
law is designed on the basis of backstepping techniques and on the framework of an event-triggering mechanism
to transform the control problem of a strict-feedback nonlinear system to equivalent control problem of an affine
nonlinear system. Subsequently, an event-triggered robust optimal control (EROC) law is designed in order to
reject the dead-zone effect and external disturbance. Compared with the existing control algorithm, which
samples states periodically, EFFC and EROC only sample the states when a triggering error exceeds the defined
threshold, and thus mitigate the computational and communication complexity. In addition, EFFC and EROC
also remove the drift dynamic identification process, persistent excitation condition. By Lyapunov analysis, it is
guaranteed that the closed dynamics is stable, the approximation error is uniformly ultimately bounded, and the
cost function converges to the sub-optimal value. Finally, the effectiveness of the proposed algorithm is
confirmed through examples of controlling linear systems, Euler-Lagrange systems and Van der Pol oscillator
nolinear systems with saturated inputs.