Multi-Objective Control of Phase-Type Semi-Markov Jump Linear Systems Applied to Software-In-The-Loop Aircraft Control

In this work, we tackle the multi-objective control for phase-type semi-Markov jump linear systems in the context of partial observation of the jump variable. Design conditions for state feedback controllers depending on cluster observations, which ensure bounds on the $H_2$, $H_{\infty }$, and energy-to-peak performance indices, are given in terms of linear matrix inequalities. The robust case in which the system matrices are uncertain and described by suitable polytopes is also considered. By restricting to the pure Markov jump linear system case with perfect observation of the Markov chain, we show that the $H_2$ and $H_{\infty }$ conditions yield the optimal controllers when solved separately. For validating the results, two types of simulation for controlling an aircraft subject to faults are presented, namely, a conventional Model-in-the-Loop setting, in which the controller and the plant are simulated in the same scientific software; and a Software-in-the-Loop simulation, in which a realistic flight simulator is employed. The simulation results illustrate the effectiveness of the proposed method and are close to the theoretical predictions, suggesting a powerful tool for validating semi-Markov jump controllers in practical settings.