An immune algorithm-optimised event-triggered observer design for adaptive control of stochastic Markov jump systems via sliding mode approach

This paper addresses the problem of adaptive sliding mode control for nonlinear Markov jump systems subjected to disturbances induced by Brownian motion, unknown nonlinearities, and malicious cyber attacks. Firstly, a novel dynamic event-triggered strategy is proposed, integrating an immune-algorithm-based parameter adaptation method that optimises the triggering condition in real time. Secondly, an integral sliding mode surface is designed to achieve sliding mode dynamics, and its mean-square stochastic stability is analyzed. Thirdly, an adaptive compensator-based sliding mode controller is developed to handle unknown nonlinearities and time-varying attack signals, without the need for prior knowledge of disturbance bounds. Additionally, it is shown that the sliding surface can be reached within a finite time, and Zeno behaviour is explicitly excluded. The effectiveness of the proposed control scheme is validated through simulation and comparative results.