Research Progress on Control Synthesis of Complex Jump Systems

Complex jump systems are a kind of dynamic system model driven by continuous-time variables and discrete events, which are with hybrid state features, parameter time variability, disturbance diversity and structural uncertainty. Firstly, the models of complex jump systems are elaborated, including the continuous-time and discrete-time Markov jump systems and semi-Markov jump systems. Then, the research progress of continuoustime and discrete-time complex jump systems is introduced from stability analysis, control and filtering problems, respectively, including the completely known transition rate/probability cases, the partially known transition rate/probability cases and the general transition rate/probability cases. Additionally, the research results of hidden Markov jump model for the control and filtering problems of complex jumping systems with unknown mode information are introduced. Finally, the main content of this article is summarized and pointed out that how to deal with the modeling, analysis and control of complex nonlinear jump systems is still a difficult problem, how to establish a suitable mathematical model to describe various cyber-attacks that a complex jump system may encounter and how to solve its security control and filtering problems are also challenge for the complex jump systems, and the learning-based control, filtering and learning-based safety control and safety estimation of the complex jump systems also deserve further study.