| The research presented in this dissertation represents the first successful attempt at finding an optimal feedback control law for a particular class of stochastic control problems involving noisy measurements and optimization criteria based on the first two cumulants of an integral quadratic performance cost functional. For linear systems where the class of feedback controls is constrained to be a linear function of the optimal state estimate, we develop the Hamilton-Jacobi-Bellman formulation for the minimization of the second moment of the integral performance functional. We also develop the corresponding results for the minimization of the cost variance when the cost-to-go of the mean is constrained. We subsequently develop the corresponding differential equations which will generate the solution for the output feedback minimum cost variance control.; In order to demonstrate the implementation of this theory and develop insights into the properties of these controllers, we present a simple example of the application of this theory to a single degree-of-freedom structural system. We also apply the theory to the case of the benchmark problem competition being conducted for an active mass driver system implemented in a scale model three story building at the Structural Dynamics and Control/Earthquake Engineering Laboratory at the University of Notre Dame. |
