Discrete-Time Linear-Quadratic Control: An Algebraic Approach

Linear-quadratic control is a fundamental technique for modern control systems. For example, the linear-quadratic estimator and extended Kalman filter are ubiquitous in the field of estimation. Kalman filters are used in diverse applications, including spacecraft attitude estimation and space weather prediction. Similarly, the linear-quadratic regulator and linear-quadratic-Gaussian controller are foundational control methods with broad application to NASA technologies such as spacecraft navigation and control, control of flexible space structures, control of spacecraft propulsion systems, and aircraft control. Despite the importance of linear-quadratic control, many students find the subject challenging to learn. This challenge is due, in part, to the mathematical tools that are used to derive the linear-quadratic estimator, regulator, and controller. Specifically, linear-quadratic results are typically derived using the principle of optimality and the Hamilton-Jacobi- Bellman equation, or using Pontryagin’s minimum principle and the Euler-Lagrange equation. These mathematical tools can make linear-quadratic control difficult to understand. The objective of this project is to develop textbook material on discrete-time linearquadratic control, which can be used for a new course on multivariable discrete-time control. The principal investigator is coauthoring a textbook manuscript on linear-quadratic control for continuous time and discrete time. In contrast to other textbooks on linear-quadratic control, the principal investigator’s book adopts an algebraic approach to linear-quadratic control. This approach relies on linear algebra and undergraduate calculus to derive and explain the fundamental results in linear-quadratic control. Thus, the textbook aims to provide a rigorous introduction to linear-quadratic control without resorting to mathematical tools that can make the material difficult to understand. This textbook manuscript will be used in a new discrete-time control course, which will be offered during the 2015-to-2016 academic year. While the course is intended for graduate students, the course will also be open to advanced undergraduates.