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. Note to Practitioners—The motivation of this paper is to address the control of uncertainty in Finite State Machines (FSMs), but it also has significant implications for other logic dynamic systems, such as Boolean networks, game systems, and finite-value systems. Existing control methods for FSMs are typically based on supervised control, which limits control over system uncertainty. Drawing inspiration from robust control in continuous state systems (CSS), this paper presents a robust control approach for FSMs. This approach enables the application of robust control methods from CSS to control the uncertainty in FSMs. The usage of this approach closely resembles the well-known and widely utilized robust control methods employed in practical industrial domains involving CSS. Several new concepts, ideas, and methods are proposed in this paper, followed by the design of a corresponding controller. Numerical examples demonstrate the feasibility of this approach, although it has not been validated in actual industrial systems. Nevertheless, the findings can undoubtedly be applied to many industrial systems in theory, such as communication and networks, control systems, embedded systems, and natural language processing. In future research, we will explore the application of the proposed robust control for FSMs in specific real-world industrial systems.