Control theory | Stochastic control

Separation principle

In control theory, a separation principle, more formally known as a principle of separation of estimation and control, states that under some assumptions the problem of designing an optimal feedback controller for a stochastic system can be solved by designing an optimal observer for the state of the system, which feeds into an optimal deterministic controller for the system. Thus the problem can be broken into two separate parts, which facilitates the design. The first instance of such a principle is in the setting of deterministic linear systems, namely that if a stable observer and a stable state feedback are designed for a linear time-invariant system (LTI system hereafter), then the combined observer and feedback is stable. The separation principle does not hold in general for nonlinear systems. Another instance of the separation principle arises in the setting of linear stochastic systems, namely that state estimation (possibly nonlinear) together with an optimal state feedback controller designed to minimize a quadratic cost, is optimal for the stochastic control problem with output measurements. When process and observation noise are Gaussian, the optimal solution separates into a Kalman filter and a linear-quadratic regulator. This is known as linear-quadratic-Gaussian control. More generally, under suitable conditions and when the noise is a martingale (with possible jumps), again a separation principle applies and is known as the separation principle in stochastic control. The separation principle also holds for high gain observers used for state estimation of a class of nonlinear systems and control of quantum systems. (Wikipedia).

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

(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

Video thumbnail

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

Video thumbnail

Ex 1: 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

Video thumbnail

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

Video thumbnail

Oxford 3a Hume's Theory of General or Abstract Ideas

A course by Peter Millican from Oxford University. Course Description: Dr Peter Millican gives a series of lectures looking at Scottish 18th Century Philosopher David Hume and the first book of his Treatise of Human Nature. Taken from: https://podcasts.ox.ac.uk/series/introduction-david

From playlist Oxford: Introduction to David Hume's Treatise of Human Nature Book One | CosmoLearning Philosophy

Video thumbnail

A non-linear spinor theory of elementary particles

This presentation is about a non-linear spinor theory of elementary particles developed by Norbert Winter, an elementary particle physicist and former employee of the Max-Planck Institute for Physics in Munich, Germany. The idea of a non-linear theory of elementary particles dates back to

From playlist Summer of Math Exposition Youtube Videos

Video thumbnail

What is Gel Electrophoresis | Don't Memorise

How do we separate the desired DNA fragment from a complete mixture of several DNA fragments? The job sounds almost impossible! But there is a technique that comes to our rescue! Gel Electrophoresis is a separation technique which separates DNA fragments based on their Length or Size. Want

From playlist Biology

Video thumbnail

Bitcoin Q&A: Layered Scaling and Privacy

How should Bitcoin, as a network protocol, be scaled through a layered architecture? One of the fundamental principles of network protocol design is to have separation between the layers so they don't bleed into each other with unintended side-effects. These are the same principles in soft

From playlist Privacy and Surveillance

Video thumbnail

M1E MoDRN Introduction: The 12 Principles of Green Chemistry

Module 1: Introduction M1E MoDRN Introduction: The 12 Principles of Green Chemistry In this module, Prof. Anastas introduces the concept of green chemistry, its principles and explains why using green chemistry can lead to fundamental changes and a sustainable world. In this video, Prof. A

From playlist Introduction to Green Chemistry with Paul Anastas, Module 1

Video thumbnail

M1E MoDRN Introduction: "The 12 Principles of Green Chemistry"

In this module, Prof. Anastas introduces The 12 Principles of Green Chemistry. Prof. Anastas introduces the concept of green chemistry, its principles and explains why using green chemistry can lead to fundamental changes and a sustainable world.

From playlist Introduction to Green Chemistry

Video thumbnail

PRINCE2® Foundation Training Videos | PRINCE2® Tailoring | PRINCE2® Certification | Simplilearn

This PRINCE2® Foundation Training Video will explain Tailoring PRINCE2® to project environment, explain embedding and tailoring, PRINCE2® approach to tailoring and PRINCE2® application in a project. 🔥Explore Our Free Courses: https://www.simplilearn.com/skillup-free-online-courses?utm_camp

From playlist PRINCE2 Foundation Training Videos

Video thumbnail

Towards superresolution surface metrology: Quantum (...) - G. Adesso - Workshop 1 - CEB T2 2018

Gerardo Adesso (Univ. Nottingham) / 15.05.2018 Towards superresolution surface metrology: Quantum estimation of angular and axial separations We investigate localization of two incoherent point sources with arbitrary angular and axial separations in the paraxial approximation. By using q

From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments

Video thumbnail

Separation of variables and the Schrodinger equation

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

Video thumbnail

David Deutsch - Do General Principles Govern All Science?

Are there 'general principles' that encompass all sciences, which have explanatory strength from physics to biology? Could such general principles even explain actions and activities beyond the physical and biological sciences, such as in psychology, sociology and economics? For more vide

From playlist Closer To Truth - David Deutsch Interviews

Video thumbnail

Limits & Continuity (2 of 3: Limits that exists when functions don't)

More resources available at www.misterwootube.com

From playlist Introduction to Differentiation

Related pages

Feedback | Separation principle in stochastic control | Linear independence | Control theory | Triangular matrix | Kalman filter | State observer | BIBO stability