Lecture

Extended Kalman Predictor: Linearized KF

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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 Extended Kalman Predictor (EKF) algorithm, focusing on the linearized Kalman Filter (KF) for multivariable control systems. The instructor explains the idea behind using the EKF with linearized KF, the formulae involved, and the reasons for choosing Xkk-1 over kk in computing Ĉk. The lecture also discusses the challenges of estimating unknown parameters with the EKF and provides examples of predator-prey systems. Various concepts such as the optimal distributed control, stochastic LQR, and evaluating control policies are explored in detail.

Instructor

Giancarlo Ferrari Trecate

Expertise Automatic control, Dependable control, Neural-network Control, Machine learning, Microgrids, Hybrid systems Mission See the webpage of the DECODE (Dependable Control and Decision) group. Teaching & PhD PhD Students Laura Meroi, Julien Pallage, Nicolas Léo Pierre Kirsch, Simone Baratto, Daniele Martinelli, Riccardo Cescon, Jakob Nylöf, Sabri El Amrani Past EPFL PhD Students Pulkit Nahata, Mustafa Sahin Turan, Baiwei Guo, Jean-Sébastien Brouillon, Clara Galimberti, Andrea Martin, Muhammad Zakwan,

Official source

Related concepts (25)

Ensemble Kalman filter

The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnKF originated as a version of the Kalman filter for large problems (essentially, the covariance matrix is replaced by the sample covariance), and it is now an important data assimilation component of ensemble forecasting.

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.

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.

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

Estimation theory

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.

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