Optimal Distributed Control: Projected GD for Locally Optimal Controllers

This lecture covers optimal distributed control, focusing on the challenges of implementing LQR controllers in large-scale systems due to measurement limitations. The instructor introduces the concept of using Gradient Descent (GD) to overcome these limitations and achieve locally optimal distributed controllers. The lecture delves into the theoretical foundations of GD, including the computation of the cost function and the convergence results. Additionally, the instructor discusses the application of GD in Stochastic LQR systems and the computation of the optimal policy. The lecture concludes with a detailed explanation of improving the controller through GD and the sparsity requirements for achieving optimal distributed control.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related lectures (37)

Related concepts (32)

ME-422: Multivariable control

This course covers methods for the analysis and control of systems with multiple inputs and outputs, which are ubiquitous in modern technology and industry. Special emphasis will be given to discrete-

Model predictive control

Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification.

Adaptive control

Adaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain.cite journal|author=Chengyu Cao, Lili Ma, Yunjun Xu|title="Adaptive Control Theory and Applications", Journal of Control Science and Engineering'|volume=2012|issue=1|year=2012|doi=10.1155/2012/827353|pages=1,2|doi-access=free For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing conditions.

Control theory

Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required.

H-infinity methods in control theory

H∞ (i.e. "H-infinity") methods are used in control theory to synthesize controllers to achieve stabilization with guaranteed performance. To use H∞ methods, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this optimization. H∞ techniques have the advantage over classical control techniques in that H∞ techniques are readily applicable to problems involving multivariate systems with cross-coupling between channels; disadvantages of H∞ techniques include the level of mathematical understanding needed to apply them successfully and the need for a reasonably good model of the system to be controlled.

Stochastic differential equation

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.

Infinite-Horizon LQ Control: Solution & Example ME-422: Multivariable control

Explores Infinite-Horizon Linear Quadratic (LQ) optimal control, emphasizing solution methods and practical examples.

Multivariable Control: State Estimation and Disturbance Rejection ME-422: Multivariable control

Covers the design of estimators and controllers for multivariable systems, focusing on state estimation and disturbance rejection.

Gradient Descent for LQR Controllers ME-422: Multivariable control

Covers the computation of cost function for multivariable control systems using the LQR framework and applying gradient descent for controller improvement.

Sparse Matrices in Multivariable Control ME-422: Multivariable control

Explores sparse matrices in multivariable control, emphasizing projection computation and PGD convergence.

Kalman Filter: Channel Estimation and Control ME-422: Multivariable control

Explores Kalman Filter for estimating channel coefficients in communication systems and its performance in noisy environments.