Optimal control and stability analysis of networked communication systems with Time-Varying Delays

Abstract

The integrated system of physical plants, sensors, controllers, actuators, and communication networks with digital communication channels is called a networked control system (NCS). Scalability and flexibility are achieved with a networked implementation at the cost of delays caused by communication that can significantly affect closed-loop performance and destabilization of the controlled system. The situation gets more complex if the delays between the sensor and the controller and between the controller and the actuators are not deterministic but time-varying, and the bandwidth over which the communication occurs is limited. Event triggered control can effectively reduce unnecessary transmissions, while predictive control can cope with the delay caused by the network. Yet optimal control performance, adaptive triggering of communication, two channel time-varying delays and stringent stability guarantees are still important mathematical control problems that have not been solved yet. In this paper, we propose an optimal predictive control framework for linear networked control systems with bounded time-varying communication delays by considering the communication properties. The formulation models the existing delays from the sensor to the controller and the delay from the controller to the actuators as separate delays, and as a time-varying delay function. A dynamic event triggering mechanism is determined to decide when the state information is supposed to be sent, and a delay-compensating state predictor is designed to predict the plant state at the future actuation instant. The performance index adds an explicit communication-activity penalty to the traditional quadratic state/control penalty. Based on this, a Lyapunov–Krasovskii functional of delay type is then built, and sufficient LMIs are formulated for delay-dependent stability and quadratic performance. The numeric evaluation is conducted based on the study configuration, which consists of system parameters and control schemes that are provided. The obtained delay-compensation, communication-reduction and performance measures show the combined dependency of delay-compensation and communication-reduction on closed-loop regulation.