Trade-offs in learning controllers from noisy data

Autor: Andrea Bisoffi, Pietro Tesi, Claudio De Persis
Přispěvatelé: Discrete Technology and Production Automation, Smart Manufacturing Systems
Jazyk: angličtina
Rok vydání: 2021
Předmět:
0209 industrial biotechnology
Mathematical optimization
General Computer Science
Computer science
Linear matrix inequalities
Robust control
Systems and Control (eess.SY)
Dynamical Systems (math.DS)
02 engineering and technology
Electrical Engineering and Systems Science - Systems and Control
Set (abstract data type)
020901 industrial engineering & automation
Simple (abstract algebra)
FOS: Electrical engineering
electronic engineering
information engineering
FOS: Mathematics
0202 electrical engineering
electronic engineering
information engineering
Electrical and Electronic Engineering
Mathematics - Dynamical Systems
Uncertainty reduction
Finite set
Mathematics - Optimization and Control
Uncertainty reduction theory
Data-driven control
Mechanical Engineering
020208 electrical & electronic engineering
Linear system
Feasible region
Data affected by disturbance with energy or instantaneous bounds
Controller learning
Data point
Optimization and Control (math.OC)
Control and Systems Engineering
Data-driven control
Controller learning
Data affected by disturbance with energy or instantaneous bounds
Linear matrix inequalities
Uncertainty reduction
Robust control
Zdroj: Systems & Control Letters, 154:104985. ELSEVIER SCIENCE BV
ISSN: 0167-6911
DOI: 10.1016/j.sysconle.2021.104985
Popis: In data-driven control, a central question is how to handle noisy data. In this work, we consider the problem of designing a stabilizing controller for an unknown linear system using only a finite set of noisy data collected from the system. For this problem, many recent works have considered a disturbance model based on energy-type bounds. Here, we consider an alternative more natural model where the disturbance obeys instantaneous bounds. In this case, the existing approaches, which would convert instantaneous bounds into energy-type bounds, can be overly conservative. In contrast, without any conversion step, simple arguments based on the S-procedure lead to a very effective controller design through a convex program. Specifically, the feasible set of the latter design problem is always larger, and the set of system matrices consistent with data is always smaller and decreases significantly with the number of data points. These findings and some computational aspects are examined in a number of numerical examples.
Databáze: OpenAIRE
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