Recursive and Delayed Reconstruction of Unknown Inputs for Dynamical Systems

Abstract

Most dynamical systems have inputs driving the system and the resulting outputs. The inputs to the system can be known or unknown. Unknown inputs in a dynamical system may represent unknown external drivers, input uncertainty, state uncertainty, or instrument faults. In this dissertation we consider delayed recursive reconstruction of states and unknown inputs of a systems. That is, we develop filters that use current measurements to estimate past states and reconstruct past inputs. We further derive results for convergence of these filters in terms of multivariable zeros and show that these methods are a more general form of the methods in the literature. Next, we explore the applicability of input reconstruction methods above to address command following problems in which the objective is to ensure that the system output follows a desired reference command. The key idea is to assume that a control input exists that yields the desired reference output exactly and then use input reconstruction methods to estimate that control input. With this end in view we explore a few control schemes based on the filter-based approach to input reconstruction and demonstrate the efficacy of these methods with illustrative numerical examples.