[Legacy Report] Prof. Frank Lewis: Stability vs. Optimality of Cooperative Multiagent Control

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Everyone is welcome to a public lecture given by the world-renowned expert on methods for optimal control of cooperative multiagent systems - professor Frank Lewis. The talk will be given at K14 seminar room at Karlovo namesti 13/E (see http://aa4cc.dce.fel.cvut.cz/content/contact-information for the instructions on how to get there) and will start at 10am. It will take about one hour. After the talk there will be an opportunity to discuss scientific issues with the lecturer. The talk is given within the IEEE Control Systems Society Distinguished Lecturer Program (http://www.ieeecss.org/member-activities/distinguished-lecturers-program).

Abstract: Distributed systems of agents linked by communication networks only have access to information from their neighboring agents, yet must achieve global agreement on team activities to be performed cooperatively. Examples include networked manufacturing systems, wireless sensor networks, networked feedback control systems, and the internet. Sociobiological groups such as flocks, swarms, and herds have built-in mechanisms for cooperative control wherein each individual is influenced only by its nearest neighbors, yet the group achieves consensus behaviors such as heading alignment, leader following, exploration of the environment, and evasion of predators. It was shown by Charles Darwin that local interactions between population groups over long time scales lead to global results such as the evolution of species.
Natural decision systems incorporate notions of optimality, since the resources available to organisms and species are limited. This talk investigates relations between the stability of cooperative control and optimality of cooperative control.

Stability: A method is given for the design of cooperative feedbacks for the continuous-time multi-agent tracker problem (also called pinning control or leader-following) that guarantees stable synchronization on arbitrary graphs with spanning trees. It is seen that this design is a locally optimal control with infinite gain margin. In the case of the discrete-time cooperative tracker, local optimal design yields stability on graphs that satisfy an additional restriction based on the Mahler instability measure of the local agent dynamics.

Optimality: Global optimal control of distributed systems is complicated by the fact that, for general LQR performance indices, the resulting optimal control is not distributed in form. Therefore, it cannot be implemented on a prescribed communication graph topology. A condition is given for the existence of any optimal controllers that be implemented in distributed fashion. This condition shows that for the existence of global optimal controllers of distributed form, the performance index weighting matrices must be selected to depend on the graph structure.

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