Infinite-horizon linear-quadratic optimal control

Описание: Summary: In this video we study infinite-horizon linear-quadratic optimal control problems using the dynamic programming approach and exploiting the monotonicity property of the DP operator. We state Bellman’s equation and give conditions under which the DP iterates converge to the infinite-horizon value function. We also introduce the linear quadratic regulartor (LQR), which is a stabilising linear controller. Unlike finite-horizon optimal control problems, infinite-horizon ones yield stabilising controllers. Later we will see that MPC is intended to be an approximation of an infinite-horizon formulation. We conclude this video lecture with two examples, one of which is the design of an LQR controller for the control of the pitch angle of an aeroplane.


▬ Errata ▬▬▬▬▬▬▬▬▬▬▬

Slide 13: There is a typo on slide 13: a star is missing from kappa_infinity (in yellow)



▬ Contents ▬▬▬▬▬▬▬▬▬▬

00:00 - Introduction
02:00 - DP recursion
04:26 - Bellman's Equation
06:23 - Convergence of DP
10:46 - LQR
14:04 - Examples
16:49 - Outro



▬ About ▬▬▬▬▬▬▬▬▬▬▬

This video is part of a series of video lectures for the module "Control Estimation Theory," which is taught in the MSc in Electronics, at the School of Electronics, Electrical Engineering and Computer Science (EEECS) at Queen's University Belfast (see https://www.qub.ac.uk/courses/postgra.... The module is taught by Dr Pantelis Sopasakis.