Model-free robust tracking control of LTI systems with Markov jump target: A data informativity approach

In this paper, the data-driven robust output tracking problem for unknown linear time-invariant system is studied where the reference signal is generated by Markov jump systems. Unlike constructing controllers for known systems, this paper, based on data informativity, aims to develop common controllers for a family of systems corresponding to the observed data, thereby circumventing the need for persistent excitation conditions required for identifying specific dynamics. The core mission of this study is, based on observed data, to delve into the design of the sufficient and/or necessary conditions for achieving transmission zeros, controllability, and stochastic stability. Furthermore, this paper integrates these conditions through comprehensive analysis to derive the data informativity conditions that achieve robust output tracking. According to the stochastic stability criterion in the form of the data-based linear matrix inequality, the controller gains are derived. Ultimately, a mathematical model of the unmanned vehicle is established and some simulation experiments are conducted, and the effectiveness and robustness of the proposed control strategy are verified.