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Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. Minimize the continuous-time cost functionaland using the initial and turn-T conditions, the functions can be solved to yieldForm the Hamiltonian and differentiate:subject to the algebraic constraintsAnother related optimal control problem may be to find the way to drive the car so as to minimize its fuel consumption, given that it must complete a given course in a time not exceeding some amount.
For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure.
Or the dynamical system could be a nation's economy, with the object We attempt to model how social insects, say a population of bees, determine the makeup of their society. etc.) Optimal Control brings together many of the important advances in 'nonsmooth' optimal control over the last several decades concerning necessary conditions, minimizer regularity, and global optimality conditions associated with the Hamilton–Jacobi equation. Excellent book if you want to know the background of optimal control. It has numerous applications in both science and engineering. Very helpful is the summary/overview of the derived equations at the end of the chapter plus … We used this book for half of the semester, but covered the entire book (the first half was spend on the linear algebra requirements such stability, Jordan Canonical Mappings, etc. * authoritative, coherent, and accessible coverage of the role of nonsmooth analysis in investigating minimizing curves for optimal control* a comprehensive overview is provided for specialists and nonspecialistsThis service is more advanced with JavaScript available* explains the necessary conditions for nonconvex problems* chapter coverage of dynamic programming and the regularity of minimizersOver 10 million scientific documents at your fingertipsThis book is an excellent presentation of the foundations and applications of nonsmooth optimal control for postgraduates, researchers, and professionals in systems, control, optimization, and applied mathematics. Nothing compares to the Bible of Optimal control.
You will be guided to see the derivation of the optimal controller in a very neat way. Lewis lacks insight. Yet another related control problem may be to minimize the total monetary cost of completing the trip, given assumed monetary prices for time and fuel.For the finite horizon LQ problem, the Riccati equation is integrated backward in time using the terminal boundary condition
Optimal Control of Partial Differential Equations International Conference in Chemnitz, Germany, April 20-25, 1998 The next example is from Chapter 2 of the book Caste and Ecology in Social Insects, by G. Oster and E. O. Wilson [O-W]. The book suggested by Rami Maher is the best book that gives the mathematical foundations of Optimal Control. A more abstract framework goes as follows.
Masada is fantastic teacher, but his course is brutally demanding. About this book A NEW EDITION OF THE CLASSIC TEXT ON OPTIMAL CONTROL THEORY As a superb introductory text and an indispensable reference, this new edition of Optimal Control will serve the needs of both the professional engineer and the advanced student in mechanical, electrical, and aerospace engineering.