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Lecture

Multivariable Control

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 concept of multivariable control, focusing on Gaussian random variables, marginal and conditional densities, affine transformations, linear systems driven by Gaussian noise, and the Lyapunov equation. The instructor explains how to characterize the steady-state process and the convergence of the variance. Examples illustrate the application of these concepts in unstable and stable systems.

Instructor

Giancarlo Ferrari Trecate

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Information engineering

Control theory and engineering: Control theory

Related concepts (32)

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.

Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.

Affine transformation

In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles. More generally, an affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space onto itself while preserving both the dimension of any affine subspaces (meaning that it sends points to points, lines to lines, planes to planes, and so on) and the ratios of the lengths of parallel line segments.

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.

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.

Related lectures (57)

Multivariable Control: Gaussian Processes and Linear Systems

Explores Gaussian processes, linear systems, transformations, and noise properties in multivariable control applications.

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Probability and Statistics: Fundamental Theorems

Explores fundamental theorems in probability and statistics, joint probability laws, and marginal distributions.

Conditional Density and Expectation

Covers conditional density, independence of random variables, expectation, and variance calculation.

Advanced Probabilities: Random Variables & Expected Values