Distributed H∞ Method Design and Operation using Dis- tributed Computing

Abstract

Control systems have two significant components: controllers and filters. Controllers are used to control the output while filters are used to estimate the internal state of a system from a series of noisy output measurements. The design of both require modelling, i.e the formulation of a mathematical model, taking into account all the dynamics of the system. There are several model based, “optimal” controllers and filters, such as the Kalman filter. However, when subjected to unaccounted errors, their performance suffers. “Robust” methods, such as H∞ methods for control and filtering, are capable of providing satisfactory performance, with respect to a performance parameter, even in the presence of noise. They are extensively used in sensitive applications such as spacecraft navigation, where a model cannot possibly account for all the errors. Their design requires convex optimization to minimize a convex function with respect to Linear Matrix Inequalities (LMI). In large scale convex optimization problems, centralized algorithms cannot work satisfactorily, due to slow convergence, and the need for a system with high performance and large memory. Distributed algorithms solve this practical constraint on convex optimization problems. However, current distributed algorithms are centralized and capable of convex optimization only within an infinite time horizon, offering sub-optimal results in finite time. In this project, we attempt to develop a distributed infinite-horizon algorithm which converges to an accurate value within a feasible number of iterations, and offers a speedup of at least 50% over traditional methods.