Optimal Two Player LQR State Feedback With Varying Delay

This paper presents an explicit solution to a two player distributed LQR problem in which communication between controllers occurs across a communication link with varying delay. We extend known dynamic programming methods to accommodate this varying delay, and show that under suitable assumptions, the optimal control actions are linear in their information, and that the resulting controller has piecewise linear dynamics dictated by the current effective delay regime.Comment: Extended version of IFAC '14 submissio

Optimal Decentralized State-Feedback Control with Sparsity and Delays

This work presents the solution to a class of decentralized linear quadratic state-feedback control problems, in which the plant and controller must satisfy the same combination of delay and sparsity constraints. Using a novel decomposition of the noise history, the control problem is split into independent subproblems that are solved using dynamic programming. The approach presented herein both unifies and generalizes many existing results

System Level Synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty -- such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies.Comment: To appear in Annual Reviews in Contro

H2 Optimal Coordination of Homogeneous Agents Subject to Limited Information Exchange

Controllers with a diagonal-plus-low-rank structure constitute a scalable class of controllers for multi-agent systems. Previous research has shown that diagonal-plus-low-rank control laws appear as the optimal solution to a class of multi-agent H2 coordination problems, which arise in the control of wind farms. In this paper we show that this result extends to the case where the information exchange between agents is subject to limitations. We also show that the computational effort required to obtain the optimal controller is independent of the number of agents and provide analytical expressions that quantify the usefulness of information exchange

On Control and Estimation of Large and Uncertain Systems

This thesis contains an introduction and six papers about the control and estimation of large and uncertain systems. The first paper poses and solves a deterministic version of the multiple-model estimation problem for finite sets of linear systems. The estimate is an interpolation of Kalman filter estimates. It achieves a provided energy gain bound from disturbances to the point-wise estimation error, given that the gain bound is feasible. The second paper shows how to compute upper and lower bounds for the smallest feasible gain bound. The bounds are computed via Riccati recursions. The third paper proves that it is sufficient to consider observer-based feedback in output-feedback control of linear systems with uncertain parameters, where the uncertain parameters belong to a finite set. The paper also contains an example of a discrete-time integrator with unknown gain. The fourth paper argues that the current methods for analyzing the robustness of large systems with structured uncertainty do not distinguish between sparse and dense perturbations and proposes a new robustness measure that captures sparsity. The paper also thoroughly analyzes this new measure. In particular, it proposes an upper bound that is amenable to distributed computation and valuable for control design. The fifth paper solves the problem of localized state-feedback L2 control with communication delay for large discrete-time systems. The synthesis procedure can be performed for each node in parallel. The paper combines the localized state-feedback controller with a localized Kalman filter to synthesize a localized output feedback controller that stabilizes the closed-loop subject to communication constraints. The sixth paper concerns optimal linear-quadratic team-decision problems where the team does not have access to the model. Instead, the players must learn optimal policies by interacting with the environment. The paper contains algorithms and regret bounds for the first- and zeroth-order information feedback

An Online Data-Driven Method for Microgrid Secondary Voltage and Frequency Control with Ensemble Koopman Modeling

Low inertia, nonlinearity and a high level of uncertainty (varying topologies and operating conditions) pose challenges to microgrid (MG) systemwide operation. This paper proposes an online adaptive Koopman operator optimal control (AKOOC) method for MG secondary voltage and frequency control. Unlike typical data-driven methods that are data-hungry and lack guaranteed stability, the proposed AKOOC requires no warm-up training yet with guaranteed bounded-input-bounded-output (BIBO) stability and even asymptotical stability under some mild conditions. The proposed AKOOC is developed based on an ensemble Koopman state space modeling with full basis functions that combines both linear and nonlinear bases without the need of event detection or switching. An iterative learning method is also developed to exploit model parameters, ensuring the effectiveness and the adaptiveness of the designed control. Simulation studies in the 4-bus (with detailed inner-loop control) MG system and the 34-bus MG system showed improved modeling accuracy and control, verifying the effectiveness of the proposed method subject to various changes of operating conditions even with time delay, measurement noise, and missing measurements.Comment: Accepted by IEEE Transactions on Smart Grid for future publicatio