Random Matrix Recursions and Estimation and Control over Lossy Networks
Many of the future applications of systems and control that will pertain to cyber-physical systems are those related to problems of (possibly) distributed estimation and control of multiple agents over lossy networks. Examples include areas such as distributed sensor networks, control of distributed autonomous agents, collision avoidance, distributed power systems, etc. Unfortunately, to date, the tools for analyzing such systems are woefully lacking, ostensibly because the [Lyapunov and Riccati] recursions are both nonlinear and random, and hence intractable if one wants to analyze them exactly. We exploit tools from the theory of large random matrices to find the asymptotic eigendistribution of the matrices in the random Riccati recursions when the number of states in the system, n, is large. The main idea of the approach is to replace a high-dimensional matrix-valued nonlinear stochastic recursion by a scalar-valued deterministic functional recursion (involving an appropriate transform of the eigendistribution), which is much more amenable to analysis and computation.
Submitted by Babak Hassibi
on
Many of the future applications of systems and control that will pertain to cyber-physical systems are those related to problems of (possibly) distributed estimation and control of multiple agents over lossy networks. Examples include areas such as distributed sensor networks, control of distributed autonomous agents, collision avoidance, distributed power systems, etc. Unfortunately, to date, the tools for analyzing such systems are woefully lacking, ostensibly because the [Lyapunov and Riccati] recursions are both nonlinear and random, and hence intractable if one wants to analyze them exactly. We exploit tools from the theory of large random matrices to find the asymptotic eigendistribution of the matrices in the random Riccati recursions when the number of states in the system, n, is large. The main idea of the approach is to replace a high-dimensional matrix-valued nonlinear stochastic recursion by a scalar-valued deterministic functional recursion (involving an appropriate transform of the eigendistribution), which is much more amenable to analysis and computation.
Submitted by Babak Hassibi
on