ALGORITHMS AND SOFTWARE FOR SOLVING COUPLED DISCRETE-TIME RICCATI EQUATIONS VIA THE L-A-S LANGUAGE (COMPUTER-AIDED DESIGN, CONTROL, GAME THEORY).

摘要

This thesis conducts an in-depth study of the computational issues associated with solving a set of coupled discrete-time Riccati equations. Briefly, the organization of this study is as follows. First, the problem is motivated by discussing two game situations which give rise to coupled discrete-time Riccati equations. Next, the computational aspects of solving these coupled equations are investigated. Finally, algorithms and software are produced that iterate these equations in a numerically robust and computationally efficient manner. The thesis carries the coupled Riccati problem from formulation to software implementation with several theoretical advances along the way. However, the major contribution of this work is the Riccati solution method--i.e., the algorithms and software which solve the problem. As the algorithms are formulated, structured, and subsequently coded, the software engineering factors that influence good software design are addressed. Furthermore, the coupled Riccati software developed here is integrated into a well-known Computer-Aided Design (CAD) software package. Thus, the informal computer user has easy access to software which solves both single and coupled Riccati equations.