Optimal Control - Theory and Applications

This course will cover the fundamentals of optimal control theory including applications from current research in aeronautics and robotics. Specific topics include: extrema of functions and functionals, Lagrange multipliers, calculus of variations, du Bois-Reymond equation, corner conditions, Legendre/Jacobi necessary conditions, isoperimetric problems and constrained optimization, variational approach to optimal control, bang-bang control, LQR, Pontryagin Maximum Principle (PMP), Dynamic programming and the HamiltonJacobi-Bellman (HJB) equations, relationship between PMP and Dynamic Programming, singular optimal control, and stochastic optimal control.

[1]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[2]  S. Brendle,et al.  Calculus of Variations , 1927, Nature.

[3]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[4]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[5]  E. Blum,et al.  The Mathematical Theory of Optimal Processes. , 1963 .

[6]  P. Hartman.  Ordinary Differential Equations , 1965 .

[7]  D. Naidu,et al.  Optimal Control Systems , 2018 .

[8]  S. Kahne,et al.  Optimal control: An introduction to the theory and ITs applications , 1967, IEEE Transactions on Automatic Control.

[9]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[10]  S. H. Crandall,et al.  Direct Variational Methods and Eigenvalue Problems in Engineering , 1976 .

[11]  Stephen Taylor.  Measure and Probability , 1977 .

[12]  E. Kreyszig.  Introductory Functional Analysis With Applications , 1978 .

[13]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[14]  Lester A. Rubenfeld,et al.  Advanced calculus and its applications to the engineering and physical sciences , 1980 .

[15]  Helena M. Pycior.  A History of the Calculus of Variations from the 17th through the 19th Century. By Herman H. Goldstine , 1983 .

[16]  Frank L. Lewis,et al.  Optimal Control , 1986 .

[17]  E. J. McShane.  The calculus of variations from the beginning through optimal control theory , 1989 .

[18]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[19]  E. R. Pinch,et al.  Optimal control and the calculus of variations , 1993 .

[20]  J. Troutman.  Variational Calculus and Optimal Control: Optimization with Elementary Convexity , 1995 .

[21]  Xuerong Mao,et al.  Stochastic differential equations and their applications , 1997 .

[22]  Victor L. Berdichevsky,et al.  Variational Principles of Continuum Mechanics , 2009 .

[23]  Mike Mesterton-Gibbons,et al.  A Primer on the Calculus of Variations and Optimal Control Theory , 2009 .

[24]  Toka Diagana,et al.  An Introduction to Stochastic Differential Equations , 2011 .

[25]  Daniel Liberzon,et al.  Calculus of Variations and Optimal Control Theory: A Concise Introduction , 2012 .

[26]  J. Janssen,et al.  Deterministic and Stochastic Optimal Control , 2013 .

[27]  F. Clarke.  Functional Analysis, Calculus of Variations and Optimal Control , 2013 .

[28]  H. Watanabe.  MEASURE AND PROBABILITY , 2022 .