Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Gradient Descent for LQR Controllers

In course

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 placed on discrete-time systems due to their relevance to digital and embe ...

Description

This lecture covers the computation of the cost function for multivariable control systems using the LQR framework. The instructor explains the process of improving the controller by applying gradient descent and computing the policy gradient. The lecture also delves into the convergence results of the gradient descent algorithm and its application in locally optimal distributed controllers.

Instructor

Giancarlo Ferrari Trecate

Official source

Related concepts (16)

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.

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.

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.

Distributed control system

A distributed control system (DCS) is a computerised control system for a process or plant usually with many control loops, in which autonomous controllers are distributed throughout the system, but there is no central operator supervisory control. This is in contrast to systems that use centralized controllers; either discrete controllers located at a central control room or within a central computer. The DCS concept increases reliability and reduces installation costs by localising control functions near the process plant, with remote monitoring and supervision.

Related lectures (31)

Infinite-Horizon LQ Control: Solution & Example

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

Multivariable Control: Weight Design and Stability Analysis

Explores weight design and stability analysis in multivariable control systems, emphasizing Lyapunov theory and LQR stability.

Linear Quadratic Optimal Control: Theory and Applications

Explores Linear Quadratic optimal control theory, covering FH-LQ and IH-LQ problems and the importance of observability in control systems.

Introduction to Multivariable Control

Covers the basics of multivariable control, including system modeling, temperature control, and optimal strategies, emphasizing the importance of considering all inputs and outputs simultaneously.

Multivariable Control: Design and Analysis