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+++ title = "Data-Driven Dynamical Systems with Machine Learning" author = ["Thomas Dehaeze"] draft = false +++
Tags :
Data-Driven Control
Overview
Challenges
With modern control (LQR, LQG, H-Infinity), we work with linear system (or linearized systems) and we develop a control law that minimize some cost function.
Challenging systems where modern control is not efficient:
- Non-linear systems
- System with unknown dynamics
- High dimensional systems
- Limited measurements or control inputs
For these kinds of systems, data-driven control seems to be a good alternative.
What is control?
It's an optimization constrained by dynamics of the system.
The optimization is easy when the system is linear and the cost function is quadratic. When the system is non-linear or when the cost function is non quadratic, the optimization becomes complicated (non closed form). Then the optimization should be rerun on the fly, which is what is done with MPC (model predictive control).
What is Machine-Learning?
Machine-learning is powerful non-linear optimization based on data.
Outline of this lecture
Data Driven Models
For the problem of unknown dynamics, we can use data driven models. The goal is to collect data to generate of model of the system.
Machine Learning Control
When we use the control inputs, the system changes and the system model might be not valid anymore. The idea is to use data driven machine learning directly to learn a good controller.
Sensor and actuator placement
Use powerful optimization techniques from machine learning to learn what are good sensors and actuators.
Linear System Identification
The Goal of Balanced Model Reduction
Change of Variables in Control Systems
Change of Variables in Control Systems (Correction)
Balancing Example
Balancing Transformation
Balanced Truncation
Balanced Truncation Example
Error Bounds for Balanced Truncation
Balanced Proper Orthogonal Decomposition
BPOD and Output Projection
Balanced Truncation and BPOD Example
Eigensystem Realization Algorithm
ERA and the Discrete-Time Impulse Response
Eigensystem Realization Algorithm Procedure
Balanced Models with ERA
Observer Kalman Filter Identification
ERA_OKID Example in Matlab
System Identification
Full-State Models with Control
Regression Models
Dynamic Mode Decomposition with Control
DMD Control Example
Koopman with Control
Sparse Nonlinear Models with Control
Model Predictive Control
Sparse Identification of Nonlinear Dynamics for Model Predictive Control
Machine Learning Control
Overview
Genetic Algorithms
Tuning a PID Controller with Genetic Algorithms
Tuning a PID Controller with Genetic Algorithms (Part 2)
Genetic Programming
Genetic Programming Control
Extremum Seeking Control
Introduction
Matlab
Simulink
Challenging Example
Applications
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