On the Optimal Control of Relaxation Systems

Pates, Richard; Bergeling, Carolina; Rantzer, Anders

doi:10.48550/arxiv.1909.07219

Cited by 2 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Positivity provides computational scaleability in many standard control problems such as Lyapunov analysis [27], optimal control design [6,34], or system gain computation [8]. Specific types of positive systems such as the parallel interconnection of first order lags have already been studied in the context of relaxation systems and passivity [23,36].…”

Section: Introductionmentioning

confidence: 99%

Variation diminishing linear time-invariant systems

Grussler,

Sepulchre

2020

Preprint

View full text Add to dashboard Cite

This paper studies the variation diminishing property of k-positive systems, which map inputs with k − 1 sign changes to outputs with at most the same variation. We characterize this property for the Toeplitz and Hankel operators of finite-dimensional linear time invariant systems. Our main result is that these operators have a dominant approximation in the form of series or parallel interconnections of k first order positive systems. This is shown by expressing the k-positivity of a LTI system as the external positivity (that is, 1-positivity) of k compound LTI systems. Our characterization generalizes well known properties of externally positive systems (k = 1) and totally positive systems (k = ∞).

show abstract

Section: Introductionmentioning

confidence: 99%

Variation diminishing linear time-invariant systems

Grussler,

Sepulchre

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Such approximations, known as relaxation or state-space symmetric systems, are of considerable practical interest as they are passive, externally (input-output) positive and can be solely implemented by capacitors and resistors [34]. Further, it has been shown recently that these systems are a source for sparse, scaleable optimal controller design [23]. Approximations with this property are therefore highly desirable.…”

Section: Introductionmentioning

confidence: 99%

Balanced truncation of $k$-positive systems

Grussler,

Damm,

Sepulchre

2020

Preprint

View full text Add to dashboard Cite

This papers shows that balanced truncation of single-input-single-output systems with k-positive Hankel operators is totally positive for any approximation of order up to k. The results generalize the fact that balanced truncation of a relaxation system are known to be totally positive for any order (k = ∞) and extends our preliminary work on first order approximation of internally positive systems to externally (input-output) positive systems (k = 1).

show abstract

On the Optimal Control of Relaxation Systems

Cited by 2 publications

References 0 publications

Variation diminishing linear time-invariant systems

Variation diminishing linear time-invariant systems

Balanced truncation of $k$-positive systems

Contact Info

Product

Resources

About