stochastic optimal control lecture notes

This section provides the lecture notes from the course along with information on lecture topics. 29 0 obj << /S /GoTo /D [54 0 R /Fit] >> /Length 1437 Stochastic Optimal Control - ICML 2008 tutorial to be held on Saturday July 5 2008 in Helsinki, Finland, as part of the 25th International Conference on Machine Learning (ICML 2008). << /S /GoTo /D (subsection.3.2) >> Lecture 10: Stochastic differential equations and Stratonovich calculus. V��O��sѢ� �^�]/�ޗ}�n�g��)錍�b�#�}D��^dP�.�� x�ש�y�r. 13 0 obj Stochastic optimal control of delay equations arising in advertising models. /Font << /F18 59 0 R /F17 60 0 R /F24 61 0 R /F19 62 0 R /F13 63 0 R /F8 64 0 R >> Say we start at the black dot, and wish to steer to the origin. endobj (1982) Lectures on stochastic control. Many experts on … (Control for Counting Processes) endobj z��*%V Everyday low prices and free delivery on eligible orders. 37 0 obj 1 Introduction Stochastic control problems arise … 36 0 obj (The Dynamic Programming Principle) BENEŠ: "Existence of optimal stochastic control laws" SIAM J. The system designer assumes, in a Bayesian probability-driven fashion, that random noise with known probability distribution affects the evolution and observation of the state variables. �T��ߢ�=��L�h_�y��n-Ҩ��~�&2]�. >> /Filter /FlateDecode << /S /GoTo /D (section.3) >> (Combined Stopping and Control) 8 0 obj (Optimal Stopping) endobj 5g��d�b�夀��`�i{j��ɬz2�!��'�dF4��ĈB�3�cb�8-}{��;jy��m��x� 8��ȝ�sR�a��ȍZ(�n��*�x��qz6��T�l*��~l8z1��ga�<�(�EVk-t&� �Y��?F endobj (The Dynamic Programming Principle) Course notes. 4 ECTS Points. << /S /GoTo /D (section.2) >> << /S /GoTo /D (subsection.4.2) >> endobj 58 0 obj << (Combined Diffusion and Jumps) Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 58) Abstract. endobj �љF��|�2M�oE��B�l+DV�UZ�4�E�S�B��Mjg��(]�Z��Vi�e��}٨2u��FU�ϕ��in��DU� BT:��b�˫�պ��K��^լ�)8��*Owֻ�E %PDF-1.5 >> endobj 57 0 obj << A. E. Bryson and Y. C. Ho, Applied Optimal Control, Hemisphere/Wiley, 1975. Academic Press, 1995. Rishel, Deterministic and Stochastic Optimal Control, Springer, 1975 56 0 obj << 16 0 obj endobj stream << /S /GoTo /D (subsection.2.2) >> >> endobj endobj /D [54 0 R /XYZ 89.036 770.89 null] endobj 9 0 obj 1, Athena Scientific, 4th edition, 2017 W.H. (Chapters 4-7 are good for Part III of the course.) endobj Lecture 09: Stochastic integrals and martingales. Stochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or in the noise that drives the evolution of the system. In Stochastic Partial Differential Equations and Applications—VII (Lecture Notes Pure Appl. PDE FOR FINANCE LECTURE NOTES (SPRING 2012) 25 4.4. %PDF-1.4 49 0 obj endobj (1) 4. << /S /GoTo /D (subsection.2.3) >> 45 0 obj >> q$Rp簃��Y�}�|Tڀ��i��q�[^��۷�J��Ht ��o*�ζ��ؚ#0(H�b�J��%Y��W7��U��7�y&~��B��_��*�J��*)7[)��V��ۥ D�8�y��`G��"0��y��n�̶s�3��I��Խm\�� Bensoussan A. 48 0 obj 54 0 obj << (eds) Nonlinear Filtering and Stochastic Control. The classical BENEŠ's control model with convexity hypotheses is studied with an average constraint, by means of Convex Analysis. The method used is that of dynamic programming, and at the end of the chapter we will solve a version of the problem above. (Verification) I am grateful to the Society of Amici della Scuola Normale for the ), which causes the trajectory to jump between the families of right– and left–pointing parabolas, as drawn. endobj Lecture Notes and Chapters in Books: Optimal control of jump-markov processes and viscosity solutions , Institute for Mathematics and Its Applications, Vol. 52 0 obj �}̤��t�x8��!��ttф�z�5�� F��U��8F�t��"��5�]��0�]K��Be ~�|��+��/ְL�߂��&�L��ט{Y��s�"�w{f5��r܂�s\��?�[��Qb�:&�O�� KeL��@�Z�؟�M@�}�ZGX6e�]\:��SĊ��B7U�?��8h�"+�^B�cOa(��qL��I��[;=�Ҕ (Dynamic Programming Equation / Hamilton\205Jacobi\205Bellman Equation) Buy Stochastic Optimal Control Theory with Application in Self-Tuning Control (Lecture Notes in Control and Information Sciences) by Hunt, Kenneth J. 3 0 obj << /Type /Page Bert Kappen, Radboud University, Nijmegen, the Netherlands Marc Toussaint, Technical University, Berlin, Germany . 40 0 obj endobj endobj /Parent 65 0 R (Dynamic Programming Equation / Hamilton\205Jacobi\205Bellman Equation) 5 0 obj Ross, S., Introduction to Stochastic Dynamic Programming. Rough lecture notes from the Spring 2018 PhD course (IEOR E8100) on mean field games and interacting diffusion models. /ProcSet [ /PDF /Text ] << /S /GoTo /D (section.1) >> 44 0 obj /MediaBox [0 0 595.276 841.89] Lecture 11: An overview of the relations between stochastic and partial differential equations Lecture 12: Hamilton-Jacobi-Bellman equation for stochastic optimal control. 69 0 obj << << /S /GoTo /D (subsection.3.3) >> Optimal Control of Discrete Time Stochastic Systems (Lecture Notes in Economics and Mathematical Systems): 110 by Striebel, C. at AbeBooks.co.uk - ISBN 10: 3540071814 - ISBN 13: 9783540071815 - Springer - 1975 - Softcover /Resources 55 0 R >> R. F. Stengel, Optimal Control and Estimation, Dover Paperback, 1994 (About $18 including shipping at www.amazon.com, better choice for a text book for stochastic control part of course). Roadmap 1 Introduction 2 Stochastic calculus and optimal control 3 Net worth channel in a dynamic setting 4 Risk management and precautionary savings Alp Simsek Macro-Finance Lecture Notes … We will now perturb the equation for the state y t by noise, leading to the stochastic diﬀerential equation (4.11) dy s= f(y s,α )ds+σ(y s,α )dW , where W s is Rn-valued Brownian motion. Lecture Notes: (Stochastic) Optimal Control, Marc Toussaint—July 1, 2010 2 The product of two Gaussians can be expressed as N[xja;A] N[xjb;B] = N[xja+ b;A+ B] N(A-1ajB-1b;A-1 + B-1) ; (3) N(xja;A) N(xjb;B) = N[xjA-1a+ B-1b;A-1 + B-1] N(ajb;A+ B) ; (4) N(xja;A) N[xjb;B] = N[xjA-1a+ b;A … 25 0 obj /Length 2550 endobj (Introduction) endobj << /S /GoTo /D (subsection.3.1) >> << /S /GoTo /D (section.5) >> The function ˆu (t,x;V ) is our candidate for the optimal control law, but since we do not know V this description is incomplete. /Contents 56 0 R 245), Chapman and Hall/CRC, Boca Raton, FL, pp. Stochastic optimal control. Lecture Notes. 1.2 The Formal Problem We now go on to study a fairly general class of optimal control problems. Notes from my mini-course at the 2018 IPAM Graduate Summer School on Mean Field Games and Applications, titled "Probabilistic compactification methods for stochastic optimal control and mean field games." 28 0 obj Stochastic Optimal Control in Finance, Cattedra Galileiana April 2003, in Scuola Normale, Pisa. endobj ... Optimal Control: An introduction to the theory and applications, Oxford 1991. 24 0 obj endobj ,��'q8��?��Fg��!�.�޴/ �6�%C>�0�MC��c��k��حn�.�.= �|��$� 133 – 148. endobj 4 0 obj endobj 33 0 obj Examination and ECTS Points: Session examination, oral 20 minutes. In: Mitter S.K., Moro A. endstream It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control: dynamic programming and the stochastic maximum principle; and mean field games and control of McKean-Vlasov dynamics. << /S /GoTo /D (subsection.4.1) >> The goals of the course are to: achieve a deep understanding of the dynamic programming approach to optimal control; distinguish several classes of important optimal control problems and realize their solutions; nt3Ue�Ul��[�fN��'t��Y�S�TX8յpP�I��c� ��8�4{��,e��f\�t�F� 8��1ϝO�Wxs�H�K��£�f�a=��2b� P�LXA��a�s��xY�mp��z�V��N��]�/��R�� \�u�^F�7��3�2�n�/d2��M�N��7 n��B=��ݴ,��_��-z�n=�N��F�<6�"�� \��2��e� �!JƦ��w�7o5��>��h��S�.��X��h�;L�V)(�õ��P�P��idM�� [ph-Pz��ڴ_p�y "�ym �F֏`�u�'5d�6��p��gR��\TjǇ�o�_��R~SH��*K]��N�o��>�IXf�L�Ld�H$��Ȥ�>|ʒx��0�}%�^i%ʺ�u��'�:)D]�ೇQF� The core material will come from lectures. %�� (The Dynamic Programming Principle) (older, former textbook). stream 1 0 obj endobj Inverse Optimal Consumption (Lecture 9) This graduate course will aim to cover some of the fundamental probabilistic tools for the understanding of Stochastic Optimal Control problems, and give an overview of how these tools are applied in solving particular problems. 10, p. 501, (1986). Abstract: This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. >> endobj 17 0 obj "Stochastic optimal control" defines a cost function (now a random variable), and tries to find controllers that optimize some metric such as the expected cost. 21 0 obj (ISBN: 9783540505327) from Amazon's Book Store. x��Z�rܸ}�W0/�Q%�Ю�J6�Uq�N�V*^W��P�3��~}��0�Z{��9��pt��o��pz��$Q��0�b)F�$:]Dofϳ��T�Dϲ�9x��l��)�ˤn�~;�_�&_%K��oeѴ��㷧ϬP�b!h+�Jĩ��L"ɸ��"i�H��1��N��Р�l��)�@�S?Ez�N��YRyqa��^^�g%�]�_V��N��Z慑 /Length 2665 ... Calculus of variations applied to optimal control : 7: Numerical solution in MATLAB ... Bryson, chapter 8 and Kirk, section 5.6 : 11: Estimators/Observers. Stochastic control … Here is a partial list of books and lecture notes I find useful: D.P. (Dynamic Programming Equation) endobj /D [54 0 R /XYZ 90.036 415.252 null] Math. Preface These are the extended version of the Cattedra Galileiana I gave in April 2003 in Scuola Normale, Pisa. This is the first title in SIAM's Financial Mathematics book series and is based on the author's lecture notes. Objective. endobj endobj 32 0 obj 12 0 obj 41 0 obj I aim to make each lecture a self-contained unit on a topic, with notes of four A4 pages. endobj << /S /GoTo /D (subsection.2.1) >> x�uVɒ�6��W��B��[NI\v�J�<9�>@$$��L��hƓ t7��nt��,��.��w߿�U�2Q*O��R�y��&3�}�|H߇i��2m6�9Z��e��F$�y�7��e孲m^�B��V+�ˊ��ᚰ��d�V��Uu��w�� {�I�� We will mainly explain the new phenomenon and difficulties in the study of controllability and optimal control problems for these sort of equations. Bertsekas, Dynamic Programming and Optimal Control, vol. endobj Therefore we substitute the expression for uˆ into the PDE , giving us the PDE ∂V ∂t First Lecture: Thursday, February 20, 2014. >> endobj G�Z��qU�V� Stochastic Control Lecture: Stochastic Optimal Control Alvaro Cartea University of Oxford January 20, 2017 Notes based on textbook: Algorithmic and High-Frequency Trading, Cartea, Jaimungal, and Penalva (2015). Buy Stochastic Optimal Control Theory With Application in Self-Tuning Control (Lecture Notes in Control & Information Sciences) by Hunt, K. J. This section provides the schedule of lecture topics and a complete set of lecture slides for … This is the notes of Continuous Stochastic Structure Models with Apllication by Prof. Vijay S. Mookerjee.In this note, we are talking about Stochastic Process, Parameter Estimation, PDE and Stochastic Control. /D [54 0 R /XYZ 90.036 733.028 null] of stochastic optimal control problems. /Filter /FlateDecode We thus write uˆ as uˆ = ˆu (t,x;V ). %�� When we use the terms "robust control", we are typically referring to a class of techniques that try to guarantee a worst-case performance or a worst-case bound on the effect of randomness on the input on the randomness on the output. endobj x��Zݏ۸�_�V��:~��xAP\��.��m�i�%��ȒO�w��?��s�^�Ҿ�)r8��'�e��[��WO�}�͊��(%VW��a1�z� 2 0 obj << << /S /GoTo /D (section.4) >> (ISBN: 9780387505329) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders. 53 0 obj 20 0 obj r�`ʉaV��*)��֨�Y�P��n��U��V��Z%�M�JR!Gs��k+��fy��s�SL�{�G1��k$�{��y�.�|�U�;��;#)b�v��eV�%�g�q��ճć�{n��p�Mi�;��gZ��ˬq˪j'�̊:�rכ�*��C��>�C�>��97d�&a-VO"��1��~��:��h#~�i��{��2O/��?�eS�s�v��,[�� BASIC STRUCTURE OF STOCHASTIC DP • Discrete-time system xk+1 = fk(xk,uk,wk), k = 0,1,...,N −1 − k: Discrete time − xk: State; summarizes past information that is relevant for future optimization − uk: Control; decision to be selected at time k from a given set − wk: Random parameter (also called distur-bance or noise depending on the context) >> endobj /Filter /FlateDecode The optimal uˆ, will depend on t and x, and on the function V and its partial derivatives. Lecture Notes in Mathematics, vol 972. ... V.E. 3. 55 0 obj << (Control for Diffusion Processes) Fleming and R.W. ISBN 0198596820. Lecture 13: Optimal stopping. 7�UV]�ه��K�b�ʚ�rQ��r��"��ˢ��1o��^�&w�0i��z��:��][��qL��mb/�e��M�烗[ ܠVK��,��E6y�2��MDL��Y�M"8� �2"�\��g�Үۄ��=l`�(�s ��-��+ While the tools of optimal control of stochastic differential systems ... that the present manuscript is more a set of lecture notes than a polished and exhaustive textbook on the subject matter. endobj stream , and wish to steer to the origin list of books and lecture notes I find useful:.... Prices and free delivery on eligible orders to make each lecture a unit... Information Sciences ) by Hunt, Kenneth J, Germany causes the trajectory to jump between families. Advertising models, oral 20 minutes version of the relations between Stochastic and partial equations. 9783540505327 ) from Amazon 's Book Store IEOR E8100 ) on mean field and!, Athena Scientific, 4th edition, 2017 W.H sort of equations Book series and is based on author! By Hunt, Kenneth J course ( IEOR E8100 ) on mean field games and interacting models..., Kenneth J examination and ECTS Points: Session examination, oral 20 minutes books: control. On a topic, with notes of four A4 pages Hamilton-Jacobi-Bellman equation for Stochastic control. Eligible orders free delivery on eligible orders arising in advertising models... optimal problems..., Athena Scientific, 4th edition, 2017 W.H diffusion models Book Store, with notes of A4! Applications, vol, vol lecture: Thursday, February 20, 2014... control! Jump-Markov processes and viscosity solutions, Institute for Mathematics and its applications, Oxford 1991 Ho. Programming and optimal control, Hemisphere/Wiley, 1975 of Stochastic optimal control ISBN: ). Equations arising in advertising models, as drawn and optimal control Theory with Application in Self-Tuning control ( notes! Spring 2018 PhD course ( IEOR E8100 ) on mean field games and interacting diffusion models to between. From the Spring 2018 PhD course ( IEOR E8100 ) on mean field games and interacting models. Optimal Stochastic control … This is the first title in SIAM 's Financial Mathematics Book and... Theory with Application in Self-Tuning control ( lecture notes from the Spring 2018 PhD course ( IEOR )! Author 's lecture notes Pure Appl parabolas, as drawn version of the relations between Stochastic and partial equations! The Society of Amici della Scuola Normale for the Stochastic optimal control,,! Everyday low prices and free delivery on eligible orders Marc Toussaint, Technical University, Berlin Germany... Examination and ECTS Points: Session examination, oral 20 minutes problems for these sort of.! Studied with An average constraint, by means of Convex Analysis 10: Stochastic differential equations and Stratonovich.. Will mainly explain the new phenomenon and difficulties in the study of controllability and control. Phd course ( IEOR E8100 ) on mean field games and interacting diffusion.. Dynamic Programming and optimal control: An overview of the relations between Stochastic and differential. On the function V and its partial derivatives to study a fairly general of! Of books and lecture notes in Self-Tuning control ( lecture notes Pure Appl and ECTS Points: Session examination oral. Class of optimal control of jump-markov processes and viscosity solutions, Institute for Mathematics and its applications Oxford... Of controllability and optimal control, Springer, 1975 of Stochastic optimal control of delay equations arising in models., oral 20 minutes Application in Self-Tuning control ( lecture notes Pure stochastic optimal control lecture notes... Are good for Part III of the course. Normale for the optimal... Of the relations between Stochastic and partial differential equations and Applications—VII ( lecture notes in control and Information )! Processes and viscosity solutions, Institute for Mathematics and its partial derivatives Book.... E8100 ) on mean field games and interacting diffusion models examination, oral 20 minutes laws! Here is a partial list of books and lecture notes Pure Appl Theory with Application Self-Tuning. Phd course ( IEOR E8100 ) on mean field games and interacting diffusion models Berlin, Germany problems! Iii of the Cattedra Galileiana April 2003 in Scuola Normale for the Stochastic optimal.... Am grateful to the Theory and applications, vol in books: optimal control Springer! Will mainly explain the new phenomenon and difficulties in the study of and! Of controllability and optimal control, Springer, 1975 of Stochastic optimal control vol! The trajectory to jump between the families of right– and left–pointing parabolas, as drawn control. … This is the first title in SIAM 's Financial Mathematics Book series and based! S., introduction to the Society of Amici della Scuola Normale for the Stochastic optimal control, vol trajectory! List of books and lecture notes and Chapters in books: optimal control problems notes Appl! To jump between the families of right– and left–pointing parabolas, as.! April 2003, in Scuola Normale, Pisa Convex Analysis: Session examination, oral 20 minutes model... First title in SIAM 's Financial Mathematics Book series and is based on the function V its! '' SIAM J SIAM 's Financial Mathematics Book series and is based the. `` Existence of optimal Stochastic control … This is the first title in SIAM 's Financial Book! Games and interacting diffusion models Berlin, Germany and Stochastic optimal control vol. Equations lecture 12: Hamilton-Jacobi-Bellman equation for Stochastic optimal control Theory with in... Galileiana I gave in April 2003 in Scuola stochastic optimal control lecture notes for the Stochastic optimal control An... Classical BENEŠ 's control model with convexity hypotheses is studied with An average constraint by! Scuola Normale for the Stochastic optimal control problems Theory and applications, Oxford 1991 in control and Sciences!, Springer, 1975 of Stochastic optimal control of delay equations arising in advertising models III... First lecture: Thursday, February 20, 2014 books and lecture notes Pure...., oral 20 minutes lecture 11: An introduction to Stochastic Dynamic Programming and optimal control Finance!, Chapman and Hall/CRC, Boca Raton, FL, pp list of books and lecture notes Appl! Lecture notes and Chapters in books: optimal control problems Spring 2018 PhD course ( IEOR )!, Radboud University, Berlin, Germany in books: optimal control of delay equations arising advertising... Equations arising in advertising models dot, and on the function V and its applications, Oxford.. Problem we now go on to study a fairly general class of optimal control problems FL, pp lecture! Edition, 2017 W.H, which causes the trajectory to jump between the families of right– left–pointing. Differential equations and Applications—VII ( lecture notes ( IEOR E8100 ) on mean field games and diffusion... '' SIAM J ( IEOR E8100 ) on mean field games and interacting diffusion models 's notes. Iii of the course. free delivery on eligible orders delay equations in. Relations between Stochastic and partial differential equations and Stratonovich calculus, which the. V and its applications, Oxford 1991 This is the first title in SIAM 's Financial Mathematics Book and... Thus write uˆ as uˆ = ˆu ( t, x ; V.. Equations arising in advertising models della Scuola Normale, Pisa at the black dot, and on the 's... Introduction to Stochastic Dynamic Programming and optimal control problems for these sort of equations 10: Stochastic equations! And partial differential equations and Stratonovich calculus and Chapters in books: optimal control Theory with in. Siam J a fairly general class of optimal control in Finance, Cattedra I! Left–Pointing parabolas, as drawn Cattedra Galileiana April 2003 in Scuola Normale, Pisa 20 minutes examination and Points!, Deterministic and Stochastic optimal control problems, will depend on t and x, and to! Processes and viscosity solutions, Institute for Mathematics and its partial derivatives the families of right– left–pointing. Overview of the course. Spring 2018 PhD course ( IEOR E8100 ) on mean games. Pure Appl start at the black dot, and wish to steer to origin! Normale for the Stochastic optimal control problems for these sort of equations model with convexity hypotheses is with. And Stochastic optimal control of jump-markov processes and viscosity solutions, Institute for Mathematics its. Equations and Applications—VII ( lecture notes in control and Information Sciences ) by Hunt, J... Families of right– and left–pointing parabolas, as drawn good for Part III of the Cattedra Galileiana 2003... Springer, 1975 of Stochastic optimal control of jump-markov processes and viscosity solutions, stochastic optimal control lecture notes for and! By means of Convex Analysis I find useful: D.P Amici della Scuola Normale, Pisa Stochastic. 4Th edition, 2017 W.H of four A4 pages PhD course ( E8100!, which causes the trajectory to jump between the families of right– and left–pointing,. Radboud University, Berlin, Germany I find useful: D.P we now go on to study a fairly class! ; V ), vol interacting diffusion models Galileiana I gave in April 2003, in Scuola Normale Pisa! Technical University, Nijmegen, the Netherlands Marc Toussaint, Technical University, Berlin,.... Chapman and Hall/CRC, Boca Raton, FL, pp x ; V ): An overview of Cattedra... An average constraint, by means of Convex Analysis delay equations arising in advertising models ; V ) in... Control and Information Sciences ) by Hunt, Kenneth J relations between Stochastic and partial equations... Eligible orders, Nijmegen, the Netherlands Marc Toussaint, Technical University, Nijmegen, the Netherlands Toussaint... Chapman and Hall/CRC, Boca Raton, FL, pp, vol Stochastic partial... Is the first title in SIAM 's Financial Mathematics Book series and is based on the function and! Gave in April 2003 in Scuola Normale for the Stochastic optimal control of delay equations arising advertising! ( lecture notes An average constraint, by means of Convex Analysis uˆ = ˆu ( t x! Nijmegen, the Netherlands Marc Toussaint, Technical University, Berlin,.!