Distributed Model Predictive Control Design for Parameter-Invariant and Parameter-Varying Spatially-Distributed Systems in Input/Output Form
Final Report Abstract
In this project, we have addressed the constrained control problem of the class of distributed systems whose subsystems interact with nearest neighbors and are equipped with sensing and actuating capabilities. Instead of considering the system as a whole, distributed MPC design exploits the localized dynamics of subsystems, such that the terminal controller design, as well as the online optimization problem can be realized at the subsystem level, independent of the number of subsystems. Considered here are distributed systems whose subsystems exhibit linear time- and spaceinvariant (LTSI) dynamics, as well as systems whose subsystem dynamics are linear time-/space-varying (LTSV) and can be characterized as linear parameter-varying (LPV) models. Of importance in this work is that we explored the possibilities of distributed MPC design in input-output (I-O) form, such that no estimator is required for online implementation. The developed results can be applied to partial differential equation (PDE) governed distributed parameter systems. Examples include vibration control of flexible structure, irrigation canals, paper-making machine, etc. In the project description, we have proposed to solve the terminal control law problem in terms of bilinear matrix inequalities (BMIs), due to the well known fact that fixed-structure controller design leads to non-convex synthesis conditions. Based on solving BMI constraints, an approach to distributed MPC design for LTSI systems has been reported, whereas distributed control design for distributed LPV/LFT systems has been developed, whose results can be directly employed to design terminal control law in distributed MPC for LTSV systems. During the course of the project, we have discovered that by reformulating the I-O implicit representation into a nonminimal state space model, it is possible to solve the terminal controller design problem in the form of numerically more attractive linear matrix inequalities (LMIs). Meanwhile, due to that the states consist of time- and space-shifted inputs and outputs, no estimation is needed; thus, the I-O properties are preserved. This novel framework has been developed for LTSI systems and extended to solve analogous problems for LTSV systems. Another important issue has been addressed: Subsystems exchange their predicted state trajectory with their neighbors. When parallel implementation of the online optimization problem at all subsystems is considered, it is inevitable that there exists a one-step delay in the exchanging information. It means that the actual state trajectory of one subsystem deviates from the one assumed by its neighbors. We have proposed modified consistency constraints to ensure that the actual and the assumed trajectories do not deviate far from each other. Sufficient conditions have been derived such that recursive feasibility of the distributed MPC is guaranteed. All developed approaches have been evaluated using numerical examples as shown in the respective publications. It can bee concluded that when systems are subject to actuator constraints (it is a case for all systems in practice), the designed distributed MPC can guarantee stability and performance of the closed-loop system.
Publications
- Distributed Model Predictive Control of Constrained Spatially-Invariant Interconnected Systems in Input-Output Form, IEEE Proceeding of American Control Conference, Boston, 2016
Q. Liu, H. S. Abbas, J. Mohammadpour Velni, S. Wollnack, and H. Werner
(See online at https://doi.org/10.1109/ACC.2016.7525472) - An LMI-based Approach to Distributed Model Predictive Control Design for Spatially-Interconnected Systems. Automatica, Volume 95, September 2018, Pages 481-487
Q. Liu, H. S. Abbas and J. Mohammadpour Velni
(See online at https://doi.org/10.1016/j.automatica.2018.06.024)
