Robust Distributed Stabilization of Interconnected Multiagent Systems

Many large-scale systems can be modeled as groups of individual dynamics, e.g., multi-vehicle systems, as well as interconnected multiagent systems, power systems and biological networks as a few examples. Due to the high-dimension and complexity in configuration of these infrastructures, only a few internal variables of each agent might be measurable and the exact knowledge of the model might be unavailable for the control design purpose. The collective objectives may range from consensus to decoupling, stabilization, reference tracking, and global performance guarantees. Depending on the objectives, the designer may choose agent-level low-dimension or multiagent system-level high-dimension approaches to develop distributed algorithms. With an inappropriately designed algorithm, the effect of modeling uncertainty may propagate over the communication and coupling topologies and degrade the overall performance of the system. We address this problem by proposing single- and multi-layer structures. The former is used for both individual and interconnected multiagent systems. The latter, inspired by cyber-physical systems, is devoted to the interconnected multiagent systems. We focus on developing a single control-theoretic tool to be used for the relative information-based distributed control design purpose for any combinations of the aforementioned configuration, objective, and approach. This systematic framework guarantees robust stability and performance of the closed-loop multiagent systems. We validate these theoretical results through various simulation studies

Event-based synchronisation of linear discrete-time dynamical networks

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The Total s-Energy of a Multiagent System

We introduce the "total s-energy" of a multiagent system with time-dependent links. This provides a new analytical lens on bidirectional agreement dynamics, which we use to bound the convergence rates of dynamical systems for synchronization, flocking, opinion dynamics, and social epistemology

Design and implementation of predictive control for networked multi-process systems

This thesis is concerned with the design and application of the prediction method in the NMAS (networked multi-agent system) external consensus problem. The prediction method has been popular in networked single agent systems due to its capability of actively compensating for network-related constraints. This characteristic has motivated researchers to apply the prediction method to closed-loop multi-process controls over network systems. This thesis conducts an in-depth analysis of the suitability of the prediction method for the control of NMAS. In the external consensus problem, NMAS agents must achieve a common output (e.g. water level) that corresponds to the designed consensus protocol. The output is determined by the external reference input, which is provided to only one agent in the NMAS. This agreement is achieved through data exchanges between agents over network communications. In the presence of a network, the existence of network delay and data loss is inevitable. The main challenge in this thesis is thus to design an external consensus protocol with an efficient capability for network constraints compensation. The main contribution of this thesis is the enhancement of the prediction algorithm’s capability in NMAS applications. The external consensus protocol is presented for heterogeneous NMAS with four types of network constraints by utilising the developed prediction algorithm. The considered network constraints are constant network delay, asymmetric constant network delay, bounded random network delay, and large consecutive data losses. In the first case, this thesis presents the designed algorithm, which is able to compensate for uniform constant network delay in linear heterogeneous NMAS. The result is accompanied by stability criteria of the whole NMAS, an optimal coupling gains selection analysis, and empirical data from the experimental results. ‘Uniform network delay’ in this context refers to a situation in which the agent experiences a delay in accessing its own information, which is identical to the delay in data transfer from its neighbouring agent(s) in the network In the second case, this thesis presents an extension of the designed algorithm in the previous chapter, with the enhanced capability of compensating for asymmetric constant network delay in the NMAS. In contrast with the first case—which required the same prediction length as each neighbouring agent, subject to the same values of constant network delay—this case imposed varied constant network delays between agents, which required multi-prediction lengths for each agent. Thus, to simplify the computation, we selected a single prediction length for all agents and determined the possible maximum value of the constant network delay that existed in the NMAS. We tested the designed control algorithm on three heterogeneous pilotscale test rig setups. In the third case, we present a further enhancement of the designed control algorithm, which includes the capability of compensating for bounded random network delay in the NMAS. We achieve this by adding delay measurement signal generator within each agent control system. In this work, the network delay is considered to be half of the measured total delay in the network loop, which can be measured using a ramp signal. This method assumes that the duration for each agent to receive data from its neighbouring agent is equal to the time for the agent’s own transmitted data to be received by its neighbouring agent(s). In the final case, we propose a novel strategy for combining the predictive control with a new gain error ratio (GER) formula. This strategy is not only capable of compensating for a large number of consecutive data losses (CDLs) in the external consensus problem; it can also compensate for network constraints without affecting the consensus convergence time of the whole system. Thus, this strategy is not only able to solve the external consensus problem but is also robust to the number of CDL occurrences in NMAS. In each case, the designed control algorithm is compared with a Proportional-Integral (PI) controller. The evaluation of the NMAS output performance is conducted for each by simulations, analytical calculations, and practical experiments. In this thesis, the research work is accomplished through the integration of basic blocks and a bespoke Networked Control toolbox in MATLAB Simulink, together with NetController hardware

Fast, Robust, Quantizable Approximate Consensus

We introduce a new class of distributed algorithms for the approximate consensus problem in dynamic rooted networks, which we call amortized averaging algorithms. They are deduced from ordinary averaging algorithms by adding a value-gathering phase before each value update. This results in a drastic drop in decision times, from being exponential in the number n of processes to being polynomial under the assumption that each process knows n. In particular, the amortized midpoint algorithm is the first algorithm that achieves a linear decision time in dynamic rooted networks with an optimal contraction rate of 1/2 at each update step. We then show robustness of the amortized midpoint algorithm under violation of network assumptions: it gracefully degrades if communication graphs from time to time are non rooted, or under a wrong estimate of the number of processes. Finally, we prove that the amortized midpoint algorithm behaves well if processes can store and send only quantized values, rendering it well-suited for the design of dynamic networked systems. As a corollary we obtain that the 2-set consensus problem is solvable in linear time in any dynamic rooted network model

Tight Bounds for Asymptotic and Approximate Consensus

We study the performance of asymptotic and approximate consensus algorithms under harsh environmental conditions. The asymptotic consensus problem requires a set of agents to repeatedly set their outputs such that the outputs converge to a common value within the convex hull of initial values. This problem, and the related approximate consensus problem, are fundamental building blocks in distributed systems where exact consensus among agents is not required or possible, e.g., man-made distributed control systems, and have applications in the analysis of natural distributed systems, such as flocking and opinion dynamics. We prove tight lower bounds on the contraction rates of asymptotic consensus algorithms in dynamic networks, from which we deduce bounds on the time complexity of approximate consensus algorithms. In particular, the obtained bounds show optimality of asymptotic and approximate consensus algorithms presented in [Charron-Bost et al., ICALP'16] for certain dynamic networks, including the weakest dynamic network model in which asymptotic and approximate consensus are solvable. As a corollary we also obtain asymptotically tight bounds for asymptotic consensus in the classical asynchronous model with crashes. Central to our lower bound proofs is an extended notion of valency, the set of reachable limits of an asymptotic consensus algorithm starting from a given configuration. We further relate topological properties of valencies to the solvability of exact consensus, shedding some light on the relation of these three fundamental problems in dynamic networks

Optimal Computation in Leaderless and Multi-Leader Disconnected Anonymous Dynamic Networks

We give a simple characterization of which functions can be computed deterministically by anonymous processes in disconnected dynamic networks, depending on the number of leaders in the network. In addition, we provide efficient distributed algorithms for computing all such functions assuming minimal or no knowledge about the network. Each of our algorithms comes in two versions: one that terminates with the correct output and a faster one that stabilizes on the correct output without explicit termination. Notably, these are the first deterministic algorithms whose running times scale linearly with both the number of processes and a parameter of the network which we call "dynamic disconnectivity". We also provide matching lower bounds, showing that all our algorithms are asymptotically optimal for any fixed number of leaders. While most of the existing literature on anonymous dynamic networks relies on classical mass-distribution techniques, our work makes use of a recently introduced combinatorial structure called "history tree", also developing its theory in new directions. Among other contributions, our results make definitive progress on two popular fundamental problems for anonymous dynamic networks: leaderless Average Consensus (i.e., computing the mean value of input numbers distributed among the processes) and multi-leader Counting (i.e., determining the exact number of processes in the network). In fact, our approach unifies and improves upon several independent lines of research on anonymous networks, including Nedic et al., IEEE Trans. Automat. Contr. 2009; Olshevsky, SIAM J. Control Optim. 2017; Kowalski-Mosteiro, ICALP 2019, SPAA 2021; Di Luna-Viglietta, FOCS 2022.Comment: 35 pages, 1 figure. arXiv admin note: text overlap with arXiv:2204.0212

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