Distributed Optimal Control and Application to Consensus of Multi-Agent Systems

This paper develops a novel approach to the consensus problem of multi-agent systems by minimizing a weighted state error with neighbor agents via linear quadratic (LQ) optimal control theory. Existing consensus control algorithms only utilize the current state of each agent, and the design of distributed controller depends on nonzero eigenvalues of the communication topology. The presented optimal consensus controller is obtained by solving Riccati equations and designing appropriate observers to account for agents' historical state information. It is shown that the corresponding cost function under the proposed controllers is asymptotically optimal. Simulation examples demonstrate the effectiveness of the proposed scheme, and a much faster convergence speed than the conventional consensus methods. Moreover, the new method avoids computing nonzero eigenvalues of the communication topology as in the traditional consensus methods

Consensusability of discrete-time multi-agent systems

The study of multi-agent systems (MAS) focuses on systems in which many intelligent agents interact within an environment. The agents are considered to be autonomous entities. MAS can be used to solve problems that are difficult or impossible for an individual agent to solve. The main feature which is achieved when developing MAS, if they work, is flexibility, since MAS can be added to, modified and reconstructed, without the need for detailed rewriting of the application. MAS can manifest self-organization as well as self-steering related complex behaviors even when the individual strategies of all their agents are simple. The goal of MAS research is to find methods that allow us to build complex systems composed of autonomous agents who, while operating on local knowledge and possessing only limited abilities, are nonetheless capable of enacting the desired global behaviors. We want to know how to take a description of what a system of agents should do and break it down into individual agent behaviors. This thesis investigates the problem when discrete-time MAS are consensusable under undirected graph. A discussion is provided to show how the problem differs from continuous time system. Then a consensusability condition is derived in terms of the Mahler measure of the agent system for single input single out systems (SISO) and result shows that there is an improved consensusability by a power of two. An algorithm is proposed for distributed consensus feedback control law when the consensusability holds. Also the case of output feedback is considered in which the consensusability problem becomes more complicated. To solve this we decompose the problem into two parts i.e. state feedback and state estimation. Simulation results demonstrate the effectiveness of the established results

Event-triggering architectures for adaptive control of uncertain dynamical systems

In this dissertation, new approaches are presented for the design and implementation of networked adaptive control systems to reduce the wireless network utilization while guaranteeing system stability in the presence of system uncertainties. Specifically, the design and analysis of state feedback adaptive control systems over wireless networks using event-triggering control theory is first presented. The state feedback adaptive control results are then generalized to the output feedback case for dynamical systems with unmeasurable state vectors. This event-triggering approach is then adopted for large-scale uncertain dynamical systems. In particular, decentralized and distributed adaptive control methodologies are proposed with reduced wireless network utilization with stability guarantees. In addition, for systems in the absence of uncertainties, a new observer-free output feedback cooperative control architecture is developed. Specifically, the proposed architecture is predicated on a nonminimal state-space realization that generates an expanded set of states only using the filtered input and filtered output and their derivatives for each vehicle, without the need for designing an observer for each vehicle. Building on the results of this new observer-free output feedback cooperative control architecture, an event-triggering methodology is next proposed for the output feedback cooperative control to schedule the exchanged output measurements information between the agents in order to reduce wireless network utilization. Finally, the output feedback cooperative control architecture is generalized to adaptive control for handling exogenous disturbances in the follower vehicles. For each methodology, the closed-loop system stability properties are rigorously analyzed, the effect of the user-defined event-triggering thresholds and the controller design parameters on the overall system performance are characterized, and Zeno behavior is shown not to occur with the proposed algorithms --Abstract, page iv

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

Containment Control of Multi-Agent Systems with Dynamic Leaders Based on a PInPI^n-Type Approach

This paper studies the containment control problem of multi-agent systems with multiple dynamic leaders in both the discrete-time domain and the continuous-time domain. The leaders' motions are described by $(n-1)$-order polynomial trajectories. This setting makes practical sense because given some critical points, the leaders' trajectories are usually planned by the polynomial interpolations. In order to drive all followers into the convex hull spanned by the leaders, a $PI^n$-type ($P$ and $I$ are short for {\it Proportion} and {\it Integration}, respectively; $I^n$ implies that the algorithm includes high-order integral terms) containment algorithm is proposed. It is theoretically proved that the $PI^n$-type containment algorithm is able to solve the containment problem of multi-agent systems where the followers are described by any order integral dynamics. Compared with the previous results on the multi-agent systems with dynamic leaders, the distinguished features of this paper are that: (1) the containment problem is studied not only in the continuous-time domain but also in the discrete-time domain while most existing results only work in the continuous-time domain; (2) to deal with the leaders with the $(n-1)$-order polynomial trajectories, existing results require the follower's dynamics to be $n$-order integral while the followers considered in this paper can be described by any-order integral; and (3) the "sign" function is not employed in the proposed algorithm, which avoids the chattering phenomenon. Furthermore, in order to illustrate the practical value of the proposed approach, an application, the containment control of multiple mobile robots is studied. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed algorithm