SINGULAR OPTIMAL CONTROL
Abstract
The Singular Optimal Control Problem has been solved using the Moore-Penrose inverse for the case of a singularity of order 1. In the present research, an extension to higher order singularities is explored for more general systems. The linear regulator problem is first formulated to serve as a basic study and the state feedback control is obtained. Nonlinear problems are then introduced and results from the linear regulator problem are modified to get solutions to these problems. We apply many standard theorems from regular optimal control theory to the singular optimal control problem. An extension of the Matrix Riccati Equation to the Matrix Riccati Inequality for singular problems is discussed. A duality theory between the linear quadratic singular optimal control problem and the linear state estimation problem is also developed and investigated. We also show how the free-terminal-time control problem can be solved by using a transformation on the state and time, and the results are just an extension of the results for the fixed-terminal-time problem.
Degree
Ph.D.
Subject Area
Electrical engineering
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