Time decision for multi-input and multi-output networked control systems

In a networked control system with multiple inputs and multiple outputs, the send time is the time instant at which a sensor sends the sampling signal to the controllers, and the perform time is the time instant at which an actuator starts performing the control commands. The relationship between the send time and perform time is nonlinear from the traditional perspective. This article formulates such a nonlinear timing relationship as a linear form based on a special algebraic structure. An algorithm is developed to find all legal send times that allow the control commands to be performed at the given time. It is pointed out that the problem for finding all legal send times is nondeterministic polynomial (NP)-hard. In addition, the method for finding the latest legal send time is presented, which has a polynomial complexity. This article also analyzes the robustness of networked control systems with perturbations, which decides the send time such that the actuators can perform the control commands at the specified time no matter how the time delays vary in bounded intervals. Numerical examples are used to illustrate the presented algorithm.