Robust distributed control of constrained linear systems

This thesis presents new algorithms for the distributed control of a group of contrained, linear time-invariant (LTl) dynamic subsystems.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

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

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

Distributed Control for Cyber-Physical Systems

Networked Cyber-Physical Systems (CPS) are fundamentally constrained by the tight coupling and closed-loop control and actuation of physical processes. To address actuation in such closed-loop wireless control systems there is a strong need to re-think the communication architectures and protocols for maintaining stability and performance in the presence of disturbances to the network, environment and overall system objectives. We review the current state of network control efforts for CPS and present two complementary approaches for robust, optimal and composable control over networks. We first introduce a computer systems approach with Embedded Virtual Machines (EVM), a programming abstraction where controller tasks, with their control and timing properties, are maintained across physical node boundaries. Controller functionality is decoupled from the physical substrate and is capable of runtime migration to the most competent set of physical controllers to maintain stability in the presence of changes to nodes, links and network topology. We then view the problem from a control theoretic perspective to deliver fully distributed control over networks with Wireless Control Networks (WCN). As opposed to traditional networked control schemes where the nodes simply route information to and from a dedicated controller, our approach treats the network itself as the controller. In other words, the computation of the control law is done in a fully distributed way inside the network. In this approach, at each time-step, each node updates its internal state to be a linear combination of the states of the nodes in its neighborhood. This causes the entire network to behave as a linear dynamical system, with sparsity constraints imposed by the network topology. This eliminates the need for routing between “sensor → channel → dedicated controller/estimator → channel → actuator”, allows for simple transmission scheduling, is operational on resource constrained low-power nodes and allows for composition of additional control loops and plants. We demonstrate the potential of such distributed controllers to be robust to a high degree of link failures and to maintain stability even in cases of node failures

Optimal Control and Feedback Design of State-Constrained Parabolic Systems in Uncertainty Conditions

The paper concerns minimax control problems for linear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in the Dirichlet boundary conditions. The underlying parabolic control system is functioning under hard/pointwise constraints on control and state variables. The main goal is to design a feedback control regulator that ensures the required state performance and robust stability under any feasible perturbations and minimize an energy-type functional under the worst perturbations from the given area. We develop a constructive approach to the minimax control design of constrained parabolic systems that is based on certain characteristic features of the parabolic dynamics including the transient monotonicity with respect to both controls and perturbations and the turnpike asymptotic behavior on the infinite horizon. In this way, solving a number of associated open-loop control and optimization problems, we justify an easily implementable three-positional suboptimal structure of the feedback boundary regulator and compute its optimal parameters, ensuring thus the required state performance and robust stability of the closed-loop, highly nonlinear parabolic control system on the infinite horizon

Multigrid Methods for Elliptic Optimal Control Problems

In this dissertation we study multigrid methods for linear-quadratic elliptic distributed optimal control problems. For optimal control problems constrained by general second order elliptic partial differential equations, we design and analyze a $P_1$ finite element method based on a saddle point formulation. We construct a $W$-cycle algorithm for the discrete problem and show that it is uniformly convergent in the energy norm for convex domains. Moreover, the contraction number decays at the optimal rate of $m^{-1}$, where $m$ is the number of smoothing steps. We also prove that the convergence is robust with respect to a regularization parameter. The robust convergence of $V$-cycle and $W$-cycle algorithms on general domains are demonstrated by numerical results. For optimal control problems constrained by symmetric second order elliptic partial differential equations together with pointwise constraints on the state variable, we design and analyze symmetric positive definite $P_1$ finite element methods based on a reformulation of the optimal control problem as a fourth order variational inequality. We develop a multigrid algorithm for the reduced systems that appear in a primal-dual active set method for the discrete variational inequalities. The performance of the algorithm is demonstrated by numerical results

A Robust Distributed Model Predictive Control Framework for Consensus of Multi-Agent Systems with Input Constraints and Varying Delays

This paper studies the consensus problem of general linear discrete-time multi-agent systems (MAS) with input constraints and bounded time-varying communication delays. We propose a robust distributed model predictive control (DMPC) consensus protocol that integrates the offline consensus design with online DMPC optimization to exploit their respective advantages. More precisely, each agent is equipped with an offline consensus protocol, which is a priori designed, depending on its immediate neighbors' estimated states. Further, the estimation errors propagated over time due to inexact neighboring information are proved bounded under mild technical assumptions, based on which a robust DMPC strategy is deliberately designed to achieve robust consensus while satisfying input constraints. Moreover, it is shown that, with the suitably designed cost function and constraints, the feasibility of the associated optimization problem can be recursively ensured. We further provide the consensus convergence result of the constrained MAS in the presence of bounded varying delays. Finally, two numerical examples are given to verify the effectiveness of the proposed distributed consensus algorithm

Distributed Model Predictive Control for Reconfigurable Large-Scale Systems

Large-scale Systems are gaining more importance in the modern world requiring flexible techniques capable of handling interactions. This thesis is concerned with the development of suitable algorithms based on Model Predictive Control (MPC) that guarantee stability, recursive feasibility and constraint satisfaction. In the first part of this thesis, the main properties and control challenges for controlling an Large-Scale System are brought together, and the main distributed approaches for solving these problems are surveyed. Also, two novel Distributed MPC algorithms are presented. A non-centralised approach to the output-feedback variant of tube-based model predictive control of dynamically coupled linear time-invariant systems with shared constraints. A tube-based algorithm capable of handling the interactions–not rejecting them– that replaces the conventional linear disturbance rejection controller with a second MPC controller, as is done in tube-based nonlinear MPC. Following this, a smart-grids application of the developed algorithm is presented to solve the load frequency control for a power network. The approach achieves guaranteed constraint satisfaction, the recursive feasibility of the MPC problems and stability while maintaining on-line complexity similar to conventional MPC. The second part of the thesis covers reconfigurable distributed MPC. Two novel approaches are considered: a nominal MPC methodology that incorporates information of external disturbances, and a coalitional approach for robust distributed MPC. The first approach uses available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a disturbance, which may change from time step to time step, is resent in the model and on the system. We show how standard stabilising terminal conditions may be modified to account for the use of disturbances in the prediction model. Robust stability and feasibility are established under the assumption that the disturbance change across sampling instances is limited. The proposed coalitional approach to robust Distributed MPC aims to tackle the existing trade-off between communication and performance in Large-Scale System by exploiting the different network topologies of system dynamics. The algorithm employs a method to switch between topologies using a multi-rate control approach. The optimal topology selection problem is solved using a consensus approach appropriately constrained to reduce the effects of any combinatorial explosion. The robust control algorithm is capable of recomputing the necessary parameters online to readjust to new partitions. Robust constraint satisfaction, recursive and stability are guaranteed by the proposed algorithm