Robust Control: From Continuous-State Systems to Finite State Machines

This brief aims to introduce the concept of robust control from continuous-state systems to the field of finite state machines (FSMs). It expands on the concept of observability by proposing current state observability and current state set observability for FSMs. The concept of robust controllability is introduced for FSMs, including robust controllability between states and robust controllability between states and state sets. An existence condition for robust controllers of FSMs is established. Consequently, a robust controller is designed to enable FSMs with uncertainty to possess robust controllability, ensuring that FSMs exhibit the desired state evolution behavior under uncertain disturbances. Unlike the robust control of continuous-state systems, the built robust control systems of FSMs use reference states that represent the desired state transitions as the reference inputs of the closed-loop systems. Additionally, a brief discussion is conducted on how to further investigate robust control problems of FSMs within the STP framework.