Distributed and Localized Model Predictive Control

Abstract

The power grid, the internet, a city of autonomous cars, neural networks in humans and intelligent systems, and the microbiome are just a few examples of large-scale distributed bio- and cyber-physical systems (CPS). Our reliance on these systems has been dramatically accelerating, yet we lack the principled theory to control their behavior that we have for more traditional applications such as in aerospace, chemical process, and robotic systems. Often, CPS are used in safety-critical applications and it is imperative that our control algorithms are able to robustly handle diverse constraints despite diverse uncertainties, and that they enjoy theoretical guarantees for feasibility and stability. Model Predictive Control (MPC) is the foundational method to address these challenges, and it has proven very successful in a wide variety of applications. However, most of these applications require a centralized MPC controller with poor scalability. For bio and CPS networks, its online realtime requirements quickly make communications and computing intractable. The work in this thesis responds to this need and provides a novel optimal and robust control framework based on MPC that is able to achieve stringent requirements with highly-scalable communications and computing. We show how these results extend naturally to the data-driven case where no models are available and control is based on past observations only. We also provide novel hardware implementations that exploit GPU technology to further accelerate computations. In order to achieve this, we leverage a feature of large-scale distributed systems that is often neglected: their sparsity. A major challenge of most distributed control algorithms to date is the fact that the global information exchanges that one achieves in the centralized case are hindered by the fact that these systems often exhibit great sparsity. Contrary to prior works, we take advantage of such sparsity, and illustrate that by integrating ideas from control theory, optimization and learning into this framing, we can develop a completely new set of algorithms, theoretical results and architectures to optimally control distributed cyber-physical systems for safety-critical applications. To do so, we introduce locality constraints in the formulation, which restrict each subsystem in the network to only communicate and influence a small neighborhood of subsystems as opposed to the entire network. By doing so, we achieve the following contributions:

1. Distributed and localized synthesis and implementation of closed-loop model predictive controllers (MPC). We present for the first time a MPC algorithm for large-scale linear systems where both its synthesis as well as implementation can be performed in a distributed and localized way without strong assumptions. We call our algorithm Distributed and Localized Model Predictive Control (DLMPC). In this scheme, only local state and model information needs to be exchanged between subsystems for the computation and implementation of control actions. Moreover, the resulting distributed algorithms are robust to various types of additive disturbances and computations scale independent of the side of the network for the first time, making this approach scalable for arbitrary sizes of the systems.

2. Minimally conservative guarantees for asymptotic stability and recursive feasibility. In the existing literature, the introduction of these guarantees either led to excessive conservatism in the solution provided by the algorithms or resulted in additional computational burden while still introducing some conservatism. In this thesis we provide theoretical results and algorithms to compute theoretical guarantees for stability and feasibility of MPC.