Control Theory and State Estimation¶
Lecture notes on Control Theory and Estimation based on a class I taught in the Department of Mathematics at Ohio University.
Control theory combines rigorous mathematics of optimization, differential equations, dynamical systems, linear algebra, calculus of variations, probability, and other more theoretical areas of mathematics with practical use of computer programming, numerical methods and engineering applications. As such, the goal is twofold, first to introduce the more theory oriented students to the beautiful world of engineering applications in control theory, a perfect example of the use of the higher level mathematics in the `real world’, and second, to give a sound theoretical footing to those students that are more applied and engineering oriented.
In parallel, I am developing a Cloud based interactive Controls and Simulation Toolbox that can be accessed at:
Warning: These notes are a work in progress.
References:¶
Optimal Control and Estimation, Robert F. Stengel
Calculus of Variations and Optimal Control Theory, Daniel Liberzon
Optimal Control Theory for Applications, David G. Hull
Applied Optimal Control, Arthur E. Bryson, Jr and Yu-Chi Ho
"An optimal guidance law for planetary landing", Christopher D'Souza, paper, Guidance, Navigation, and Control Conference
Probabilistic Robotics, Sebastian Thrun, Wolfram Burgard, and Dieter Fox
A Course in Robust Control Theory: a convex approach, Geir E. Dullerud and Fernando G. Paganini
Robust and Adaptive Control with Aerospace Applications, Eugene Lavretsky and Kevin A. Wise
Теория автоматического управления, Гольдфарб Л. С, Балтрушевич А. В., Нетушил А. В. и др.
Model References:¶
2D Car model - I found the original system without the derivation in "Optimal Control and Estimation" by Robert F. Stengel. After not finding a satisfying derivation of the equations in other references I derived it myself as shown in the first section below. Interestingly, the right-hand side of the rate of orientation change turned out to be different from the original model in Stengel.
Landing Spacecraft - Christopher D'Souza. "An optimal guidance law for planetary landing", Guidance, Navigation, and Control Conference, http://dx.doi.org/10.2514/6.1997-3709. Thanks to Ronald Sostaric, NASA, for the suggestion of this paper, which is also used for the Module 2 project.
Table of Context¶
Module 1 - Classical Control¶
Project 1 - Adaptive Cruise Control
Module 2 - Optimal Control¶
Optimal Control using Calculus of Variations
Hamilton-Jacobi-Bellman Equation
The Linear Quadratic Regulator
Project 2 - Planetary Landing Guidance