Optimisation-based adaptive event-triggered resilient control for nonlinear semi-Markov jump cyber-physical systems

This study focuses on investigating the stochastic finite-time stabilisation problem for nonlinear semi-Markov jump cyber-physical systems considering the impact of generally uncertain transition rates, gain fluctuations, multiple cyber-attacks and external disturbances through a secured adaptive event-triggered resilient control protocol. Specifically, the concepts of stochastic finite-time boundedness and stochastic input-output finite-time stability are jointly used to ensure that both the state and output remain limited during designated transient periods. Furthermore, a particle swarm optimisation algorithm is implemented to significantly reduce the cost function, thereby enhancing the overall efficiency of the analysed system. Thereafter, an adaptive event-triggered scheme is applied to achieve the desired objectives while ensuring minimal use of communication resources. To improve the robustness and security of the system, gain fluctuations and multiple cyber-attacks are incorporated into the controller framework. In particular, the incidence of multiple cyber-attacks, including deception and denial-of-service attacks are modelled using two distinct Bernoulli-distributed stochastic variables. Furthermore, by utilising the mode-dependent Lyapunov-Krasovskii functional and applying the integral inequality, suitable criteria are derived within the structure of linear matrix inequalities to ensure the targeted results. Finally, two numerical examples are offered to confirm the practicality and effectiveness of the designed control protocol.