Robust Stability Analysis of Cyber-Physical Systems Controlled by Model Predictive Control

This thesis presents novel methods for analysing linear and nonlinear of constrained Networked Control Systems (NCS) controlled by Model Predictive Control (MPC), subject to a cyber-attack in the form of random packet losses and (bounded) additive disturbances. Conditions for (robust) stability and criteria for the Separation Principle design conditions of controllers and estimators are investigated. Stability conditions are presented through lemmas and theorems, with numerical examples provided to verify the proposed results.

Using a counterexample, this thesis shows that the Separation Principle does not hold when a TCP-like protocol is used. Further analysis uncovers a trade-off between estimation and controller prediction errors, suggesting that improving estimation performance can affect controller performance. Conditions are established under which the explicit control law is Piecewise Affine (PWA) and the cost function is Piecewise Quadratic (PWQ).

For discrete-time linear and nonlinear MPC-controlled systems with a buffer mechanism for packet losses mitigation, subject to input constraints and random packet losses, it is shown that, at best, the use of a buffer facilitates the transfer of the initial state to the terminal region but does not guarantee stability under consecutive packet losses. The number of consecutive packet losses the system can tolerate while maintaining stability is upper bounded by expressions dependent on system and controller parameters.

The last part extends the results by analysing the robustness of an MPC-controlled system under bounded additive disturbances. Conditions are derived under which the state remain in the region of attraction under consecutive packet losses. The results show that the use of the buffer does not provide the transfer of an initial state to the terminal region. However, we derive upper bounds on the number of consecutive packet losses that can be tolerated while maintaining robust stability if the disturbance is sufficiently small.