Model predictive control (MPC) is a popular advanced control technique that solves a constrained optimal control problem, on-line, at each sampling instant. The first control input of the optimized sequence is applied, and the optimization is repeated at each subsequent time step, inducing feedback. MPC excels in situations where it is prohibitively difficult to determine an explicit control law off-line: for example, when the system to be controlled is subject to constraints, delays or nonlinearities. The theoretical foundations for MPC are, by now, mature and its applications are widespread; however, some outstanding challenges remain, most notably in distributed and adaptive forms of MPC. Outstanding students are, therefore, sought for a research project at the interface of distributed, adaptive and robust MPC.
In distributed (or decentralized) MPC, the conventional MPC problem is decomposed and distributed to several control agents that make decisions locally and independently. This paves the way for the application of MPC to large-scale systems, since the computational bottleneck is removed. The basic challenge is how to coordinate the distributed decision making of agents so that stability of the overall system is maintained, and system-wide performance is acceptable. Many approaches have been proposed, and for an increasingly wide class of systems, but many problems are still open: for example, can the natural sub-optimality of distributed MPC be quantified or bounded? How can distributed MPC methods be made robust to the failure of existing subsystems or the addition of new subsystems? How robust are distributed MPC-controlled systems to cyber attacks?
In adaptive MPC, the dynamics of the system to be controlled are unknown and/or changing over time -- in either a continuous or a discrete (switched) way. The controller must learn a model of the system while the latter is being controlled. While seemingly straightforward, this raises several technical and theoretical difficulties, including how to guarantee the properties of stability and constraint satisfaction while probing the system and learning a new model.
This project aims to develop novel algorithms for the adaptive distributed MPC of large-scale systems. The goal is to devise an approach that combines computational tractability and design simplicity with strong theoretical guarantees of stability, constraint satisfaction, and learning.