Intellectual merit: This project involves the design and analysis of control and estimation algorithms for nonlinear dynamic systems consisting of multiple interacting agents. Each agent has its own dynamics which are affected by the agent's local control action and possibly also by disturbances or by uncontrolled interactions with other agents. The salient features of the systems considered are that 1) the controllers are decentralized, namely, each agent decides on a control action based solely on information it receives through its sensors or through direct communication with neighboring agents, and 2) whether or not two agents are neighbors is a function of their states, so that the topology of the network of interconnected agents changes with time as the states of the agents evolve. The focus of the proposed work is on the simultaneous control and estimation of these networked systems: decisions about local control actions are based on current estimates of the parameters of the entire collection of agents, so that the controller and estimator dynamics affect each other through feedback interactions. These complex nonlinear interactions prevent the application of any simple separation principle; as a result, the estimators are taken into account in the design of the controllers (and/or vice versa). This project will provide specific algorithms for the combined decentralized control and estimation of these multi-agent systems, with performance properties demonstrated both through mathematical analysis and through simulation. Applications of the proposed algorithms may include single-team objectives, such as formation control or the optimal distribution of mobile sensors, or multi-team objectives such as multi-player pursuit/evasion.
Before being modified to work with estimators, the controllers must be designed first to work under full information. An important class of local controllers are the gradient controllers in which each agent applies a control action in the steepest descent direction relative to the agent's individual cost (which may or may not be the same as the costs of the other agents). One goal of the proposed work is to identify classes of cost functions for which these gradient schemes have appropriate global convergence properties (for example, any equilibrium corresponding to an undesirable configuration should be unstable). Another goal is to incorporate auxiliary control objectives into the basic descent strategies, such as collision/obstacle avoidance (in the case of mobile agents) or the maintenance of network connectivity. For decentralized implementation, local control algorithms will rely on estimators for information needed about the collection but not available from local sensors. Such estimators must be dynamic in the sense that the signals they estimate are changing with time as the states of the agents evolve. Inputs to the estimators come from local sensors or from direct communication with neighboring agents. Goals of the proposed work include the design and analysis of appropriate estimators, with an emphasis on their convergence properties, estimator gain optimizations, and adaptation schemes.
Broader impacts: The proposed work will provide tools for the design of multi-agent systems, potentially contributing to a variety of applications in the fields of mobile robots, sensor networks, manufacturing (e.g., self-assembly of smart parts), and multi-player games (e.g., coordinated automated battlefield or search-and-rescue scenarios). Graduate students funded through this proposal will benefit from the interdisciplinary perspective gained through their involvement with the Northwestern Institute on Complex Systems, where they share ideas with researchers from diverse areas (e.g., economics, medicine, physics, chemistry, and engineering). In addition, a sophomore-level undergraduate student will participate in the project through a Fellow Assistant Researcher Award sponsored by Northwestern's Residential College program. This undergraduate student will benefit from the opportunity to make a significant contribution to a research project, an important step in preparing the student for a scientific career.
