Optimal Control An Introduction to the Theory and Its Applications

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Other than learning basic calculus, I don't really have an advanced background. I was curious to learn about Optimal Control the theory that involves, bang-bang, Potryagin's Maximum Principle etc.

In short, I am lost. Can someone suggest me a path I should take to learn more about Optimal Control from the very basics? My field is mathematical programming, and I tend to look at optimal control as just optimization with ODEs in the constraint set; that is, it is the optimization of dynamic systems. I would start by studying some optimization theory not LPs but NLPs and getting an intuitive feel for the motivations behind stationarity and optimality conditions -- that will lead naturally into optimal control theory.

I should mention there is another facet of optimal control, related to control systems. The systems considered are discrete time as opposed to continuous in PMP therefore it's difference equations instead of differential equations. It is this latter type of optimal control that is actually applied in industry. The Pontryagin principle, while useful for analysis, is generally intractable for real-time application to nontrivial plants. It explains the basics of control theory, optimal control inclusive, as mathematicians see it - geared towards advanced undergrads but useful for all.


Pontryagin's Minimum Principle for Fuzzy Optimal Control Problems

The easier books to read are for and by engineers - nothing against them, I'm one - but if you want a mathematical text that gives the whole story I suggest you look at Sontag's. One potential tactic would be start with Estimation Theory rather than Control Theory.

I've enjoyed the approach taken in H. It might help to understand what background you already have.

Optimal Control: An Introduction to the Theory and Its Applications

Have you taken any courses in ordinary differential equations? What mathematics courses have you taken? What kind of background do you have in engineering approaches to dynamical systems? Have you taken an introductory course in linear systems?


Are you familiar with basic concepts like feedback? A very good little book on the subject is Analytical Methods of Optimization by D. Lawden, available from Dover Press.

Download Optimal Control An Introduction to the Theory with Applications Oxford Applied Mathematics

It covers Pontryagin's principal, Hamiltonian and Lagrangian formulations, and should be accessible to a person with your background. Another great book is "Optimal control theory: An introduction to the theory and its applications" by Peter Falb and Michael Athans, also published by Dover. If you have a background in differential geometry, you will probably like the two books of Jurdjevic, Geometric Control Theory , and Optimal Control and Geometry: Integrable Systems , both from Cambridge Univesity Press. Kamien and Schartwz is an extremely complete book on this subject.

It can occasionally be oblique, but is otherwise quite helpful.

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The Economists' Mathematical Manual contains all of Kamien and Schwartz's results and much more in a handy summary format. Try Singiresu S. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. How do I approach Optimal Control?

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Viewed 8k times. Legend Legend 2 2 gold badges 3 3 silver badges 10 10 bronze badges. To keep the mathematical level at that of graduate students in engineering, rigorous proofs of many important results are not given, while the interested reader is referred to more mathematical sources. Problem sets are included. Skip to main content. Description Description Optimal control theory is a mathematical optimization method with important applications in the aerospace industry.

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No Access Table of Contents and Preface pp. No Access Historical Background pp. Index pp.