Synthesis Of Distributed Controllers Research Articles

Platoon Control of Connected Vehicles from a Networked Control Perspective: Literature Review, Component Modeling, and Controller Synthesis

The platooning of connected and automated vehicles has the potential to significantly benefit the road traffic, including enhancing highway safety, improving traffic capacity, and reducing fuel consumption. This paper presents a four-component analysis framework for platoon systems from a networked control perspective, including a literature review by network awareness, unified models of key components, and two application cases for controller synthesis. The networked control perspective naturally decomposes a platoon into four interrelated components, namely, 1) node dynamics (ND), 2) information flow topology (IFT), 3) formation geometry (FG), and 4) distributed controller (DC). The existing literature is categorized under this framework and analyzed according to the component features. The unified mathematical models are derived for platoons with linear dynamics and distributed controllers. As a case study, a distributed controller synthesis method is introduced for homogeneous platoons, which guarantees the internal stability in the presence of a broad class of topologies with/without uniform time-delays. The effectiveness is demonstrated by numerical simulations.

Distributed Safety Controller Synthesis for Unknown Interconnected Systems via Graph Neural Networks

This paper focuses on distributed controller synthesis for ensuring the safety of large-scale systems with unknown dynamics and known interconnection structures, employing control barrier certificates. Our approach centers on a distributed framework tailored to create control barrier certificates for safety, utilizing the interconnections within large-scale systems. We introduce a novel application of graph neural networks to synthesize these certificates and distributed controllers in a data-driven fashion. The formal correctness of trained networks is subsequently validated through data-driven techniques involving the solution of a sampling-based optimization problem. To illustrate the effectiveness of our methodology, we conduct experiments on a complex interconnected system comprising as many as 1000 components.

Cooperative Output Regulation of Heterogeneous Multiagent Systems: A Global Distributed Control Synthesis Approach

Agent-wise local design methods to synthesize distributed control gains focus on the individual dynamics of each agent to guarantee the overall stability of the system. They are powerful tools due to their scalability. However, the agent-wise local design methods are incapable of maximizing the overall system performance through, for example, decay rate assignment. On the other hand, design methods, which are predicated on a global condition, leads to nonconvex optimization problems. This article considers a global design of an internal model-based distributed dynamic state feedback control law for the linear cooperative output regulation problem. We present a convex formulation of this global design problem based on a structured Lyapunov inequality. Then, the existence of solutions to the structured Lyapunov inequality is investigated. Specifically, we analytically show that the solutions exist for the systems satisfying the agent-wise local sufficient condition. Finally, we compare the proposed method with the agent-wise local design method through numerical examples in terms of conservatism, performance maximization, graph dependency, and scalability.

Formula omitted] output containment control of heterogeneous multi-agent systems via distributed dynamic output feedback

This paper addresses the problem of output containment control of heterogeneous multi-agent systems (MASs), which aims to drive the outputs of all followers to a dynamic convex hull spanned by the outputs of multiple leaders. The considered MAS consists of heterogeneous linear agent dynamics with possibly non-identical state dimensions and subject to unknown external disturbances. New distributed control protocols via dynamic output feedback are proposed, such that the output containment control problem can be decomposed into independent H∞ stabilization subproblems for the follower agents. The resulting distributed control synthesis conditions are formulated as linear matrix equations plus linear matrix inequalities, which can be solved efficiently via convex optimization. Both continuous-time and discrete-time output containment control problems are addressed under a unifying framework. Two examples have been used to demonstrate the effectiveness of the proposed approaches.

Cooperative output regulation of multi-agent systems with switched leader dynamics

ABSTRACTIn this paper, the cooperative output regulation problem for heterogeneous multi-agent systems is addressed by considering a switched leader dynamics. The switched leader dynamics consists of multiple linear models and a switching rule governing the switches among them. A switched leader is capable of generating various sophisticated reference signals for more complicated multi-agent coordination tasks. A novel distributed hybrid impulsive switching control scheme is proposed to achieve cooperative output regulation. Distributed switching stability is established using the average dwell-time technique with multiple Lyapunov functions. Moreover, the associated distributed control synthesis conditions are formulated in terms of linear matrix inequalities plus linear matrix equations. As a result, both switching rules for the leader and distributed switching protocols for the followers can be jointly synthesised via efficient semi-definite programming. An example has been used to demonstrate the effectiveness of the proposed approach.

Cooperative [formula omitted] output regulation of heterogeneous parameter-dependent multi-agent systems

This paper addresses the cooperative output regulation problem for heterogeneous multi-agent systems with parameter-dependent linear fractional transformation (LFT) dynamics and unknown local, external perturbations. A novel distributed semi-LFT gain-scheduling protocol is proposed to achieve cooperative output regulation and H∞ disturbance attenuation performance. This new distributed control scheme advances existing techniques in two important ways: (1) more general heterogeneous uncertain agent dynamics are considered under a directed communication topology; and (2) new distributed control synthesis conditions are derived and formulated as independent sets of linear matrix inequalities (LMIs) plus linear matrix equations, such that the optimal distributed control solution can be obtained effectively via convex optimization. Two examples have been used to demonstrate the effectiveness and usefulness of the proposed approach in multi-agent consensus and formation control, respectively.

Convex Distributed Controller Synthesis for Interconnected Heterogeneous Subsystems Via Virtual Normal Interconnection Matrices

Based on a previously introduced framework for distributed controller synthesis, in this note a novel transformation of interconnection matrices is proposed that enables to consider arbitrary, time-varying and directed interaction topologies. It represents any interconnection as a virtual interconnection matrix that has the property of being normal, i.e., that guarantees the existence of a unitary diagonalizing transformation, which admits to decompose the synthesis problem in terms of the entire interconnected system into problems of subsystem scale, which can then be solved by standard convex multiplier-based gain-scheduling synthesis methods with complexity in the order of a single subsystem. When compared with a method from the literature, the method shows superior performance in both a numerical example and the leader-follower formation control problem of nonlinear quadrocopter models.

A Tool Support to Distributed Control Synthesis and Grafcet Implementation for Discrete Event Manufacturing Systems

Current production systems are becoming more complex: manufactured products are increasingly technical, production components are more specific, and control specifications are rapidly changing. Thus, formal methods and tools are becoming essential to support the automated development of control systems. We propose to develop a tool for the synthesis and implementation of modular/distributed supervisory control for Automated Manufacturing Systems (AMS). To reduce the computational complexity, we divide the control problem into local and global controls. Local Controllers (LCs) are designed for the individual subsystems, then global dependencies are added to the LCs to cooperatively execute the control actions. The tool provides a distributed control, interpreted as Grafcet (standard IEC 60848), that can be lately converted into any suitable IEC 61131-3 standard programming language for PLC programming purposes. It is based on Model-to-Model (M2M) transformations implemented in an Eclipse Modeling Framework (EMF) environment.

Towards an approach of synthesis, validation and implementation of distributed control for AMS by using events ordering relations

We study distributed control synthesis and validation for automated manufacturing systems (AMS) in the framework of supervisory control theory. To reduce the size of the control problem, we view an AMS as comprised of asynchronous subsystems which are coupled through imposed logical Boolean specifications. The principle of the distributed control approach is the decomposition of the global monolithic control action into local coordinated control strategies for the individual subsystems. Owing to its importance in a distributed scheme, the order in which events occur arouses interest. By extending our previous results, we develop a set of rules of events precedence ordering, under which the control strategy via decomposition promises the subsystems synchronisation and coordination. We show how these rules contribute to reduce the size of the controller models used in the verification/validation and implementation steps. The effectiveness of the proposed approach is demonstrated by means of an industrial AMS example.

Robust distributed model predictive control of linear systems with structured time-varying uncertainties

ABSTRACTIn this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min–max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.

A synthesis approach to distributed supervisory control design for manufacturing systems with Grafcet implementation

In supervisory control, computational complexity and implementation flexibility represent major challenges when a large number of local components compose a target system. To overcome these difficulties, we propose a formal approach to distributed control synthesis and implementation for automated manufacturing systems (AMS). We assume that the system is modelled with automata in a local modular fashion. Local control specifications are defined for each local subsystem by means of logical equations to construct local controllers (LCs). Then, global control specifications, stated as logical implications, are applied to the LCs, which allows synchronisation and cooperative interaction among the subsystems. This paper makes two contributions. First, it outlines a formal method for constructing minimally restrictive and deadlock-free distributed controllers (DCs). Second, it proposes a method for the interpretation of these DCs into Grafcet, which is a graphical modelling formalism widely used to design the controller’s dynamic behaviour for AMS. An experimental manufacturing system illustrates the approach.

Synthesis of Distributed Robust H-Infinity Controllers for Interconnected Discrete Time Systems

This paper presents an algorithm for the synthesis of robust distributed controllers for interconnected linear discrete-time systems. For a network of interconnected uncertain linear time-invariant systems, the distributed controller achieves robust stability and a guaranteed level of robust performance in a well-defined H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> sense. The setting of this paper is in discrete time. Based on the theory of dissipative dynamical systems, conditions for the analysis of robust stability and robust performance of networks are derived in terms of feasibility tests of linear matrix inequalities. From these conditions, computationally tractable synthesis conditions are derived. An iterative D-K type of synthesis algorithm is proposed that yields a robust distributed controller. Convergence properties of the algorithm are inferred.

Distributed synthesis and stability of cooperative distributed model predictive control for linear systems

This paper presents a new formulation and synthesis approach for stabilizing cooperative distributed model predictive control (MPC) for networks of linear systems, which are coupled in their dynamics. The controller is defined by a network-wide constrained optimal control problem, which is solved online by distributed optimization. The main challenge is the definition of a global MPC problem, which both defines a stabilizing control law and is amenable to distributed optimization, i.e., can be split into a number of appropriately coupled subproblems. For such a combination of stability and structure, we propose the use of a separable terminal cost function, combined with novel time-varying local terminal sets. For synthesis, we introduce a method that allows for constructing these components in a completely distributed way, without central coordination. The paper covers the nominal case in detail and discusses the extension of the methodology to reference tracking. Closed-loop functionality of the controller is illustrated by a numerical example, which highlights the effectiveness of the proposed controller and its time-varying local terminal sets.

Distributed control for alpha-heterogeneous dynamically coupled systems

This paper concerns the problem of distributed controller synthesis for a class of heterogeneous distributed systems composed of α (2 or more) different kinds of subsystems, interacting with one another according to a certain given graph topology. We will show that by employing Linear Matrix Inequalities (LMIs) tools, namely the full-block S-procedure, we can derive a control synthesis method based on L2 gain performance. This synthesis method guarantees stability and performance of a whole set of possible interconnection graphs, and its computational complexity does not depend on the number of subsystems involved but only on the number of different kinds of subsystems. The effectiveness of the new method is verified on a test case.

Rabin's theorem in the concurrency setting: A conjecture

Rabin's theorem says that the monadic second order theory of the infinite binary tree is decidable. This result has had a far reaching influence in the theory of branching time temporal logics. A simple consequence of Rabin's theorem is that for every finite state transition system, the monadic second order theory of its computation tree is decidable. Concurrency theory strongly suggests that finite 1-safe Petri nets (or simply, net systems) are a natural generalization of the notion of a finite state transition system while labelled event structures arising as the unfoldings of net systems are the proper counterparts to the computation trees obtained by unwinding finite (sequential) transition systems. It is easy to define the monadic second order theory of such event structures. It turns out that unlike the sequential case, not every net system (i.e. its event structure unfolding) has a decidable monadic second order theory. This gives rise to the question: Which net systems admit a decidable monadic second order theory? Here we present a conjecture based on a property called grid-freeness. Our conjecture is that a net system has a decidable monadic second order theory iff its event structure unfolding is grid-free. We show that it is decidable whether a net system has this property. We also prove that the monadic second order theory of a net system is undecidable if its event structure unfolding is not grid-free. In addition we show that our conjecture can be effectively reduced to the sub-class of free choice net systems. Finally we point out how the positive resolution of our conjecture will settle the decidability of a range of distributed controller synthesis problems.

Conservatism of Analysis and Controller Synthesis of Decomposable Systems

Recently, distributed controller synthesis approaches for decomposable systems, a subclass of distributed systems with identical subsystems, where the interconnection can be described as LFT interconnection, have been proposed. In order to make these approaches tractable for systems containing a very large number of subsystems, constraints on the Lyapunov matrix and the multiplier matrices are introduced that render the complexity of analysis and controller synthesis smaller and in best case independent on the number of subsystems. Those assumptions have to be paid for with conservatism, which is investigated in this work. It is proven that the conservatism is not reduced if either only the Lyapunov or only the multiplier matrices are constrained, when compared with having constraints on both simultaneously.

Computational Methods for Distributed Control of Heterogeneous Cyclic Interconnection Structures

We address the problem of fast system analysis and controller synthesis for heterogeneous subsystems interconnected in a loop. Such distributed systems have state-space realizations with a special matrix structure, which we show to be a generalization of the Sequentially Semi-Separable (SSS) structure employed in recent research on systems interconnected in a Cartesian array. By extending the O(N) structure-preserving SSS arithmetic to the matrices induced by this circular type of interconnection, we introduce a new cyclic SSS matrix structure and arithmetic which leads to fast and efficient procedures for linear computational complexity optimal distributed controller synthesis for arbitrarily heterogeneous subsystems connected in a loop. In the homogeneous case, where all subsystems are identical, the computational complexity reduces to O(1) and an interesting relationship with the infinite case is demonstrated. CSSS matrices can be non-Toeplitz (as compared to circulant matrices), a great expansion of domain, but when restricted to be Toeplitz (and thus circulant), the arithmetic reduces to O(1), a huge cost-savings. The procedures are demonstrated on two computational examples, using a freely available MATLAB toolbox implementation of these algorithms.

Dissipativity based distributed control synthesis

A control synthesis approach for plant-wide processes from a network perspective based on dissipativity theory is presented. Dynamic supply rates, expressed as quadratic differential forms, are used in an effort to render dissipativity based control design methodologies less conservative. In this paper, a convex algorithm for designing a plant-wide control system is presented, which, ensures plant-wide closed loop internal stability and performance in the form of weighted H∞ norm bounds. This is achieved by encoding these requirements as dissipativity conditions on the individual controllers and subsequently synthesizing suitably dissipative controllers. This approach to plant-wide control design is applicable to distributed control design with arbitrary communication topology as well as decentralized and centralized control. An example is provided to illustrate these results.

Practical Distributed Control Synthesis

Classic distributed control problems have an interesting dichotomy: they are either trivial or undecidable. If we allow the controllers to fully synchronize, then synthesis is trivial. In this case, controllers can effectively act as a single controller with complete information, resulting in a trivial control problem. But when we eliminate communication and restrict the supervisors to locally available information, the problem becomes undecidable. In this paper we argue in favor of a middle way. Communication is, in most applications, expensive, and should hence be minimized. We therefore study a solution that tries to communicate only scarcely and, while allowing communication in order to make joint decision, favors local decisions over joint decisions that require communication.

Distributed Control in Multiple Dimensions: A Structure Preserving Computational Technique

We consider the problem of analysis and control of discretely distributed systems in multidimensional arrays. For spatially invariant systems in one spatial dimension, we build an efficient arithmetic that preserves the rational Laurent operator structure, leading to fast iterative methods of solving Lyapunov and Riccati equations and block diagonalizations, and thus arbitrarily non-conservative stability analysis and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> distributed controller synthesis. These one-dimensional results are then used to build an efficient arithmetic and controller synthesis procedure in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> -dimensions by induction. The extension of these techniques from Laurent operators with rational symbols to sequentially semi-separable matrices yields a procedure for linear computational complexity analysis and controller synthesis for finite extent heterogeneous multidimensional systems with boundary conditions. The procedures are demonstrated on two computational examples.