This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The research goal of this integrated research and educational endeavor is to advance the fundamental understanding of the behavior of interconnected systems by studying the influence of delays on their stability and performance. The proposed theoretical approach builds on a hybrid system formulation for networked systems with delays. The novelty lies in expressing the Lyapunov exponent ?a measure of stability- as a path average and characterizing the discrete structure associated with the hybrid system (the underlying graph). The statistical properties of the induced random walk on the underlying graphs will be used to quantify stability and performance properties of the networked system in terms of the moments of the delay distribution. This is achieved by combining techniques and tools of dynamical systems techniques (Lyapunov exponent, cell-to-cell mapping), discrete mathematics (graph theory and generating functions) and statistical physics (random matrix products, random walks).
Systems of communicating components have impacted a broad range of applications including space exploration, mobile sensor networks, teleoperated surgical robots, control of teams of vehicles, and integrated building systems. With the proliferation of embedded processors interacting through networks, the analysis of communicating dynamic components is timely and important. Such systems are common in chemical/nuclear plants, cars, aircrafts, and thus questions regarding their stability and performance should be rigorously studied. Due to network traffic, the signal delays can only be statistically characterized. The fundamental contribution of this proposal is a novel theoretical and computational framework for studying stability and performance of interconnected systems with random time delays. The education goal is to excite students about the possibilities in science and engineering through engaging courses and involvement in a multidisciplinary and multilevel project emphasizing practical problem solving, creative design, and the scientific method. To integrate educational activities with experimental validation of the proposed theory, a distributed testbed of vehicles/robots will be built by a multidisciplinary and multilevel team supervised by the PI.
