A Topological Obstruction in a Control Problem

The reach control problem (RCP) characterizes a control design approach, based on computer science notions of object triangulation, that has been extensively developed as a means of guiding the complete transient response of a system, entirely within a desired polytopic region of state-space operation characterized by linear constraints on its states. This thesis expands upon results achieved in the area of RCP problem solvability under continuous feedback, identifying new necessary conditions. It accomplishes this using algebraic topology constructs, mapping the reach control problem to an equivalent topological one to successfully demonstrate conditions under which topological obstructions are generated. These obstructions, which render the RCP unsolvable by continuous feedback are then used to characterize equivalent conditions necessary for solvability of the problem. This thesis also serves to formally demonstrate the substantial advantages of the RCP design approach over more conventional industry techniques, by solving real-world problems with complex specifications.MAS