Person:

Chen, Xudong

In this thesis, we investigate a special class of multi-agent systems, which we call reciprocal multi-agent (RMA) systems. The evolution of agents in a RMA system is governed by interactions between pairs of agents. Each interaction is reciprocal, and the magnitude of attraction/repulsion depends only on distances between agents. We investigate the class of RMA systems from four perspectives, these are two basic properties of the dynamical system, one formula for computing the Morse indices/co-indices of critical formations, and one formation control model as a variation of the class of RMA systems. An important aspect about RMA systems is that there is an equivariant potential function associated with each RMA system so that the equations of motion of agents are actually a gradient flow. The two basic properties about this class of gradient systems we will investigate are about the convergence of the gradient flow, and about the question whether the associated potential function is generically an equivariant Morse function. We develop systematic approaches for studying these two problems, and establish important results. A RMA system often has multiple critical formations and in general, these are hard to locate. So in this thesis, we consider a special class of RMA systems whereby there is a geometric characterization for each critical formation. A formula associated with the characterization is developed for computing the Morse index/co-index of each critical formation. This formula has a potential impact on the design and control of RMA systems. In this thesis, we also consider a formation control model whereby the control of formation is achieved by varying interactions between selected pairs of agents. This model can be interpreted in different ways in terms of patterns of information flow, and we establish results about the controllability of this control system for both centralized and decentralized problems.

As the fraction of electricity generation from intermittent renewable sources—such as solar or wind—grows, the ability to store large amounts of electrical energy is of increasing importance. Solid-electrode batteries maintain discharge at peak power for far too short a time to fully regulate wind or solar power output(^{1, 2}). In contrast, flow batteries can independently scale the power (electrode area) and energy (arbitrarily large storage volume) components of the system by maintaining all of the electro-active species in fluid form(^{3, 4, 5}). Wide-scale utilization of flow batteries is, however, limited by the abundance and cost of these materials, particularly those using redox-active metals and precious-metal electrocatalysts(^{6, 7}). Here we describe a class of energy storage materials that exploits the favourable chemical and electrochemical properties of a family of molecules known as quinones. The example we demonstrate is a metal-free flow battery based on the redox chemistry of 9,10-anthraquinone-2,7-disulphonic acid (AQDS). AQDS undergoes extremely rapid and reversible two-electron two-proton reduction on a glassy carbon electrode in sulphuric acid. An aqueous flow battery with inexpensive carbon electrodes, combining the quinone/hydroquinone couple with the (Br_2/Br^-) redox couple, yields a peak galvanic power density exceeding 0.6 W cm^{−2} at 1.3 A cm^{−2}. Cycling of this quinone–bromide flow battery showed >99 per cent storage capacity retention per cycle. The organic anthraquinone species can be synthesized from inexpensive commodity chemicals(^8). This organic approach permits tuning of important properties such as the reduction potential and solubility by adding functional groups: for example, we demonstrate that the addition of two hydroxy groups to AQDS increases the open circuit potential of the cell by 11% and we describe a pathway for further increases in cell voltage. The use of π-aromatic redox-active organic molecules instead of redox-active metals represents a new and promising direction for realizing massive electrical energy storage at greatly reduced cost.