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Reference dependent invariant sets: Sum of squares based computation and applications in constrained control
- Source :
- Automatica. 129:109614
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- Article number 109614 The goal of this paper is to present a systematic method to compute reference dependent positively in- variant sets for systems subject to constraints. To this end, we first characterize these sets as level sets of reference dependent Lyapunov functions. Based on this characterization and using Sum of Squares theory, we provide a polynomial certificate for the existence of such sets. Subsequently, through some algebraic manipulations, we express this certificate in terms of a Semi-Definite Programming problem which maximizes the size of the resulting reference dependent invariant sets. We then present some results implementing the proposed method to an example and propose some variants that may help in reducing possible numerical issues. Finally, the proposed approach is employed in the Model Predictive Control for Tracking scheme to compute the terminal set, and in the Explicit Reference Governor framework to compute the so-called Dynamic Safety Margin. The effectiveness of the proposed method in each of the schemes is demonstrated through simulation studies. Ministerio de Economía y Competitividad de España DPI2016-76493-C3-1-R Ministerio de Ciencia e Innovación (España) PID2019-106212RB-C41
- Subjects :
- Lyapunov function
0209 industrial biotechnology
Polynomial
Control of Constrained Systems
Sum of Squares
Computer science
Computation
Systems and Control (eess.SY)
02 engineering and technology
Electrical Engineering and Systems Science - Systems and Control
Reference Dependence
Set (abstract data type)
symbols.namesake
020901 industrial engineering & automation
FOS: Electrical engineering, electronic engineering, information engineering
0202 electrical engineering, electronic engineering, information engineering
Electrical and Electronic Engineering
Algebraic number
Invariant (mathematics)
Tracking
Invariance
020208 electrical & electronic engineering
Explained sum of squares
Model predictive control
Control and Systems Engineering
symbols
Algorithm
Subjects
Details
- ISSN :
- 00051098
- Volume :
- 129
- Database :
- OpenAIRE
- Journal :
- Automatica
- Accession number :
- edsair.doi.dedup.....6733344782661f279faae7bee657fbec