Distributed Control with Low-Rank Coordination

A common approach to distributed control design is to impose sparsity constraints on the controller structure. Such constraints, however, may greatly complicate the control design procedure. This paper puts forward an alternative structure, which is not sparse yet might nevertheless be well suited for distributed control purposes. The structure appears as the optimal solution to a class of coordination problems arising in multi-agent applications. The controller comprises a diagonal (decentralized) part, complemented by a rank-one coordination term. Although this term relies on information about all subsystems, its implementation only requires a simple averaging operation

Hierachical and Cooperative Control of Complex Distributed Systems

Zugleich: Dissertation, Universität Kassel, 201

Distributed optimal and predictive control methods for networks of dynamic systems

Several recent approaches to distributed control design over networks of interconnected dynamic systems rely on certain assumptions, such as identical subsystem dynamics, absence of dynamical couplings, linear dynamics and undirected interaction schemes. In this thesis, we investigate systematic methods for relaxing a number of simplifying factors leading to a unifying approach for solving general distributed-control stabilization problems of networks of dynamic agents. We show that the gain-margin property of LQR control holds for complex multiplicative input perturbations and a generic symmetric positive definite input weighting matrix. Proving also that the potentially non-simple structure of the Laplacian matrix can be neglected for stability analysis and control design, we extend two well-known distributed LQR-based control methods originally established for undirected networks of identical linear systems, to the directed case. We then propose a distributed feedback method for tackling large-scale regulation problems of a general class of interconnected non-identical dynamic agents with undirected and directed topology. In particular, we assume that local agents share a minimal set of structural properties, such as input dimension, state dimension and controllability indices. Our approach relies on the solution of certain model matching type problems using local linear state-feedback and input matrix transformations which map the agent dynamics to a target system, selected to minimize the joint control effort of the local feedback-control schemes. By adapting well-established distributed LQR control design methodologies to our framework, the stabilization problem of a network of non-identical dynamical agents is solved. We thereafter consider a networked scheme synthesized by multiple agents with nonlinear dynamics. Assuming that agents are feedback linearizable in a neighborhood near their equilibrium points, we propose a nonlinear model matching control design for stabilizing networks of multiple heterogeneous nonlinear agents. Motivated by the structure of a large-scale LQR optimal problem, we propose a stabilizing distributed state-feedback controller for networks of identical dynamically coupled linear agents. First, a fully centralized controller is designed which is subsequently substituted by a distributed state-feedback gain with sparse structure. The control scheme is obtained byoptimizing an LQR performance index with a tuning parameter utilized to emphasize/deemphasize relative state difference between coupled systems. Sufficient conditions for stability of the proposed scheme are derived based on the inertia of a convex combination of two Hurwitz matrices. An extended simulation study involving distributed load frequency control design of a multi-area power network, illustrates the applicability of the proposed method. Finally, we propose a fully distributed consensus-based model matching scheme adapted to a model predictive control setting for tackling a structured receding horizon regulation problem

Minimax Linear Regulator Problems for Positive Systems : with applications to multi-agent synchronization

Exceptional are the instances where explicit solutions to optimal control problems are obtainable. Of particular interest are the explicit solutions derived for minimax problems, as they provide a framework for addressing challenges involving adversarial conditions and uncertainties. This thesis presents explicit solutions to a novel class of minimax optimal control problems for positive linear systems with linear costs, elementwise linear constraints in the control policy, and worst-case disturbances. We refer to this class of problems, in the absence of disturbances, as the linear regulator (LR) problem. Two types of worst-case disturbances are considered in this thesis: bounded by elementwise-linear constraints and unconstrained positive disturbances. Using dynamic programming theory, explicit solutions to the Bellman equation (in the discrete-time setting) and the Hamilton-Jacobi-Bellman equation (in the continuous-time setting) are derived for both finite and infinite horizons. For the infinite horizon case, a fixed-point method is proposed to compute the solution of the HJB equation. Furthermore, a necessary and sufficient condition for minimiz- ing the l1-induced gain of the system is derived and characterized by the disturbance penalty in the cost function of the minimax problem. This condition characterizes the solution of the l1−induced gain minimization problem and demonstrates that, if a finite solution exists for the minimax problem under the presence of worst-case, unconstrained and positive disturbances, the solution to the minimax setting reduces to that of the LR problem in the absence of disturbances. This thesis also analyzes the stabilizability and detectability properties of the LR problem. Similar to the Linear-Quadratic Regulator (LQR) problem, the LR problem is shown to facilitate the stabilization of positive systems. A linear programming formulation is introduced to compute the associated stabilizing controller, if one exists. The scalability and practical advantages of this theoretical framework for large-scale applications are demonstrated through its implementation in an optimal voltage control problem for a DC power network and in the management of a large-scale water network. The second important contribution of this thesis is addressing positive synchronization on undirected graphs for homogeneous discrete and continuous-time positive systems. A static feedback protocol, derived from the Linear Regulator problem, is introduced. The stabilizing policy is derived by solving the linear programming formulation of the explicit solution to the LR problem under appropriate assumptions. Necessary and sufficient conditions are provided to ensure the positivity of each agent’s trajectory for all nonnegative initial conditions. The effectiveness of this approach is illustrated through simulations on large regular graphs with varying nodal degrees. Throughout the thesis, we demonstrate how the results can be applied to problems over networks with positive dynamics. Our results pave the way for robust networks that maintain stability and optimal performance despite adversarial conditions. By leveraging explicit solutions to minimax optimal control and multi-agent synchronization problems, this work provides a computationally efficient and scalable framework for controlling large-scale systems

Distributed design of ultra large-scale control systems:Progress, Challenges, and Prospects

The transition from large centralized complex control systems to distributed configurations that rely on a network of a very large number of interconnected simpler subsystems is ongoing and inevitable in many applications. It is attributed to the quest for resilience, flexibility, and scalability in a multitude of engineering fields with far-reaching societal impact. Although many design methods for distributed and decentralized control systems are available, most of them rely on a centralized design procedure requiring some form of global information of the whole system. Clearly, beyond a certain scale of the network, these centralized design procedures for distributed controllers are no longer feasible and we refer to the corresponding systems as ultra large-scale systems (ULSS). For these ULSS, design algorithms are needed that are distributed themselves among the subsystems and are subject to stringent requirements regarding communication, computation, and memory usage of each subsystem. In this paper, a set of requirements is provided that assures a feasible real-time implementation of all phases of a control solution on an ultra large scale. State-of-the-art approaches are reviewed in the light of these requirements and the challenges hampering the development of befitting control algorithms are pinpointed. Comparing the challenges with the current progress leads to the identification and motivation of promising research directions.</p

Distributed Linear Quadratic Control and Filtering:a suboptimality approach

Design of distributed protocols for multi-agent systems has received extensive attention in the past two decades. A challenging problem in this context is to develop distributed synchronizing protocols that minimize given cost criteria. Recent years have also witnessed an increasing interest in problems of distributed state estimation for large-scale systems. Two challenging problems in this context are the problems of distributed H-2 and H-infinity optimal filtering.In this dissertation, we study both distributed linear quadratic optimal control problems and distributed filtering problems. In the framework of distributed linear quadratic control, both for leaderless and leader-follower multi-agent systems we provide design methods for computing state-feedback-based distributed suboptimal synchronizing protocols. In the framework of distributed H-2 suboptimal control, both for homogeneous and heterogeneous multi-agent systems we establish design methods for computing state-feedback-based and output-feedback-based distributed suboptimal synchronizing protocols.The distributed H-2 and H-infinity optimal filtering problem are the problems of designing local filter gains such that the H-2 or H-infinity norm of the transfer matrix from the disturbance input to the output estimation error is minimized, while all local filters reconstruct the full system state asymptotically. Due to their non-convex nature, it is not clear whether optimal solutions exist. Instead of studying these optimal filtering problems, in this dissertation we therefore address suboptimality versions of these problems and provide conceptual algorithms for obtaining H-2 and H-infinity suboptimal distributed filters, respectively

Distributed LQR control of multi-agent systems

The thesis develops optimal control methods for designing distributed cooperative control schemes in multi-agent networks. First, the model of a completely connected multi-agent network is presented, consisting of identical dynamically decoupled agents controlled by a centralized LQR (Linear Quadratic Regulator) based controller. The structure of the solution, as well as controller's spectral and robustness properties are presented. A special case of centralized control where the optimal solution for the whole network can be constructed from the solution of single agent LQR system is given. The problem is extended to distributed control where the special structure is imposed onto the information flow between agents and only local interaction is considered. A systematic method is given for computing the performance loss of various distributed control configurations relative to the performance of the optimal centralized controller. Necessary and sufficient conditions are derived for which a distributed control configuration pattern arising from the optimal centralized solution does not entail loss of performance if the initial state vector lies is a certain subspace of state-space which is identified. It is shown that these conditions are always satisfied for systems with communication/control networks corresponding to complete graphs with a single link removed. The procedure is extended for the purposes of analysing the performance loss of an arbitrary distributed configuration. Cost increase due to decentralisation is quantified by introducing three cost measures corresponding to the worst-case, best-case and average directions in which the initial state of the system lies. Finally, a cooperative scheme is presented for controlling arbitrary formations of low speed experimental UAVs (Unmanned Aerial Vehicles) based on a distributed LQR design methodology. Each UAV acts as an independent agent in the formation and its dynamics are described by a 6-DOF (six degrees-offreedom) nonlinear model. This is linearised for control design purposes around an operating point corresponding to straight flight conditions and simulated for longitudinal motion. It is shown that the proposed controller stabilises the overall formation and can control effectively the nonlinear multi-agent system. Also, it is illustrated via numerous simulations that the system provides reference tracking and that is robust to environmental disturbances such as nonuniform wind gusts acting on a formation of UAVs and to the loss of communication between two neighbouring UAVs

Autonomous Teaming of Multileader System - Robust Cluster Formation Approach

The cluster consensus problem of Multileader MAS Is considered and the clustering problem of interconnected multileader systems is formulated as a disturbance attenuation problem. For the first time, it\u27s proved that the multileader MAS can reach cluster consensus without limiting the communication between the clusters. The combination of Small Gain Theorem and H8 optimization has been designed in the graphical differential game platform to prove the stability for the system. At the end, an online off-policy reinforcement learning algorithm is developed to find the solution to the H8 optimal problem of multileader MAS with completely unknown systems

Electric Vehicle Efficient Power and Propulsion Systems

Vehicle electrification has been identified as one of the main technology trends in this second decade of the 21st century. Nearly 10% of global car sales in 2021 were electric, and this figure would be 50% by 2030 to reduce the oil import dependency and transport emissions in line with countries’ climate goals. This book addresses the efficient power and propulsion systems which cover essential topics for research and development on EVs, HEVs and fuel cell electric vehicles (FCEV), including: Energy storage systems (battery, fuel cell, supercapacitors, and their hybrid systems); Power electronics devices and converters; Electric machine drive control, optimization, and design; Energy system advanced management methods Primarily intended for professionals and advanced students who are working on EV/HEV/FCEV power and propulsion systems, this edited book surveys state of the art novel control/optimization techniques for different components, as well as for vehicle as a whole system. New readers may also find valuable information on the structure and methodologies in such an interdisciplinary field. Contributed by experienced authors from different research laboratory around the world, these 11 chapters provide balanced materials from theorical background to methodologies and practical implementation to deal with various issues of this challenging technology. This reprint encourages researchers working in this field to stay actualized on the latest developments on electric vehicle efficient power and propulsion systems, for road and rail, both manned and unmanned vehicles