Control theory | Stochastic control
The separation principle is one of the fundamental principles of stochastic control theory, which states that the problems of optimal control and state estimation can be decoupled under certain conditions. In its most basic formulation it deals with a linear stochastic system with a state process , an output process and a control , where is a vector-valued Wiener process, is a zero-mean Gaussian random vector independent of , , and , , , , are matrix-valued functions which generally are taken to be continuous of bounded variation. Moreover, is nonsingular on some interval . The problem is to design an output feedback law which maps the observed process to the control input in a nonanticipatory manner so as to minimize the functional where denotes expected value, prime denotes transpose. and and are continuous matrix functions of bounded variation, is positive semi-definite and is positive definite for all . Under suitable conditions, which need to be properly stated, the optimal policy can be chosen in the form where is the linear least-squares estimate of the state vector obtained from the Kalman filter where is the gain of the optimal linear-quadratic regulator obtained by taking and deterministic, and where is the Kalman gain. There is also a non-Gaussian version of this problem (to be discussed below) where the Wiener process is replaced by a more general square-integrable martingale with possible jumps. In this case, the Kalman filter needs to be replaced by a nonlinear filter providing an estimate of the (strict sense) conditional mean where is the filtration generated by the output process; i.e., the family of increasing sigma fields representing the data as it is produced. In the early literature on the separation principle it was common to allow as admissible controls all processes that are adapted to the filtration . This is equivalent to allowing all non-anticipatory Borel functions as feedback laws, which raises the question of existence of a unique solution to the equations of the feedback loop. Moreover, one needs to exclude the possibility that a nonlinear controller extracts more information from the data than what is possible with a linear control law. (Wikipedia).
Differential Equations: Separation of Variables
This video provides several examples of how to solve a DE using the technique of separation of variables. website: http://mathispower4u.com blog: http://mathispower4u.wordpress.com
From playlist First Order Differential Equations: Separation of Variables
A02 Independence of the solution set
The independence of a linear system. How to make sure that a set of solutions are not constant multiples of each other.
From playlist A Second Course in Differential Equations
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A brief explanation of separation of variables, application to the time-dependent Schrodinger equation, and the solution to the time part. (This lecture is part of a series for a course based on Griffiths' Introduction to Quantum Mechanics. The Full playlist is at http://www.youtube.com/
From playlist Mathematical Physics II - Youtube
Ex 2: Differential Equations: Separation of Variables
This video solves a differential equation using separation of variables. Video Library: http://mathispower4u.com Search by Topic: http://mathispower4u.wordress.com
From playlist First Order Differential Equations: Separation of Variables
Solving Differential Equations by Separation of Variables
This video introduces the technique of separation of variables to solve differential equations.
From playlist First Order Differential Equations: Separation of Variables
B01 An introduction to separable variables
In this first lecture I explain the concept of using the separation of variables to solve a differential equation.
From playlist Differential Equations
Ex 1: Initial Value Problem - Separation of Variables
This video provides an example of how to solve an initial value problem that requires the technique of separation of variables. Video Library: http://mathispower4u.com Search by Topic: http://mathispower4u.wordpress.com
From playlist First Order Differential Equations: Separation of Variables
Chain Rule for Several Variable Functions
How to apply the chain rule for partial deriviatves. An example is discussed. Free ebook tinyurl.com/EngMathYT
From playlist Several Variable Calculus / Vector Calculus
Tenth SIAM Activity Group on FME Virtual Talk
Speaker: Rene Carmona, Paul M. Wythes '55 Professor of Engineering and Finance, ORFE & PACM, Princeton University, Title: Contract theory and mean field games to inform epidemic models. Abstract: After a short introduction to contract theory, we review recent results on models involving
From playlist SIAM Activity Group on FME Virtual Talk Series
Paolo Guasoni, Lesson II - 19 december 2017
QUANTITATIVE FINANCE SEMINARS @ SNS PROF. PAOLO GUASONI TOPICS IN PORTFOLIO CHOICE
From playlist Quantitative Finance Seminar @ SNS
Dylan Possamaï: Principal Agent Modelling - lecture 1
CIRM HYBRID EVENT These lectures will consist in an overview of recent progresses made in contracting theory, using the so-called dynamic programming approach. The basic situation is that of a Principal wanting to hire an Agent to do a task on his behalf, and who has to be properly incenti
From playlist Probability and Statistics
Dylan Possamaï: Principal Agent Modelling - lecture 2
CIRM HYBRID EVENT These lectures will consist in an overview of recent progresses made in contracting theory, using the so-called dynamic programming approach. The basic situation is that of a Principal wanting to hire an Agent to do a task on his behalf, and who has to be properly incenti
From playlist Probability and Statistics
Sanjoy Mitter - Overview of variational approach to nonlinear filtering
PROGRAM: Nonlinear filtering and data assimilation DATES: Wednesday 08 Jan, 2014 - Saturday 11 Jan, 2014 VENUE: ICTS-TIFR, IISc Campus, Bangalore LINK:http://www.icts.res.in/discussion_meeting/NFDA2014/ The applications of the framework of filtering theory to the problem of data assimi
From playlist Nonlinear filtering and data assimilation
Benjamin Gess: "Large deviations for conservative, stochastic PDE and non-equilibrium fluctuations"
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop IV: Stochastic Analysis Related to Hamilton-Jacobi PDEs "Large deviations for conservative, stochastic PDE and non-equilibrium fluctuations" Benjamin Gess - Universität Leipzig Abstract: Macroscopic fluctuation theory provides a general
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
Learning Optimal Control with Stochastic Models of Hamiltonian Dynamics for Shape & Function Optim.
Speaker: Chandrajit Bajaj (7/25/22) Abstract: Shape and Function Optimization can be achieved through Optimal Control over infinite-dimensional search space. All optimal control problems can be solved by first applying the Pontryagin maximum principle, and then computing a solution to the
From playlist Applied Geometry for Data Sciences 2022
Stefano Soatto: "Invariance and disentanglement in deep representations"
New Deep Learning Techniques 2018 "Invariance and disentanglement in deep representations" Stefano Soatto, University of California, Los Angeles (UCLA) Abstract: Theories of Deep Learning are like anatomical parts best not named explicitly in an abstract: Everyone seems to have one. That
From playlist New Deep Learning Techniques 2018
3 Nandakumaran - An Introduction to deterministic optimal control and controllability
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow
From playlist Introduction to Differentiation
(ML 13.11) D-separation (part 2)
Definition of d-separation, and statement of the d-separation theorem for "reading off" conditional independence properties from directed graphical models.
From playlist Machine Learning
Duality between estimation and control - Sanjoy Mitter
PROGRAM: Data Assimilation Research Program Venue: Centre for Applicable Mathematics-TIFR and Indian Institute of Science Dates: 04 - 23 July, 2011 DESCRIPTION: Data assimilation (DA) is a powerful and versatile method for combining observational data of a system with its dynamical mod
From playlist Data Assimilation Research Program