Robustness of prediction based delay compensation for nonlinear systems
Control of systems where the controller, actuator, and sensor are decentralized, e.g. connected only via a communication network, can be challenging. Information transmitted between controller, sensors, and actuators can be lost or delayed, leading to instability or poor performance of the closed loop. One way to improve the performance and to guarantee stability is the use of prediction based compensation schemes. Instead of a single input a sequence of (predicted) future controls is submitted and implemented at the actuator. Assuming that suitable, so-called prediction consistent compensation and control schemes, such as certain predictive control approaches, are used, stability of the closed loop in the presence of delays and packet losses can be guaranteed. In this paper, we show that control schemes employing prediction based delay compensation approaches for discrete time nonlinear systems do posses inherent robustness properties. Specifically, if the nominal closed loop system without delay compensation is ISS with respect to perturbation and measurement errors, then the closed loop system employing prediction based delay compensation techniques is robustly stable. Additionally, we analyze the influence of the prediction horizon on the robustness gains and illustrate the results by a numerical simulation.