Learning control for polynomial systems using sum of squares relaxations

Guo, Meichen; Persis, Claudio De; Tesi, Pietro

doi:10.48550/arxiv.2004.00850

Cited by 5 publications

(9 citation statements)

References 24 publications

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“…dissipativity properties using noisy data. Similarly, the recent papers Guo et al (2020a) and Guo et al (2020b) extend the results in De Persis and Tesi (2019); van Waarde et al (2020) to design stabilizing controllers for unknown polynomial systems based on noisy data. Notably, these papers consider continuous-time systems and develop SOS feasibility criteria for controller design.…”

Section: Introductionmentioning

confidence: 61%

Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics

Strässer,

Berberich,

Allgöwer

2020

Preprint

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In this paper, we present a data-driven controller design method for continuous-time nonlinear systems with rational system dynamics, using no model knowledge but only measured data affected by noise. We first extend recent results on data-driven control for linear time-invariant systems by presenting a purely data-driven representation of unknown nonlinear systems with rational dynamics. By applying robust control techniques to this parametrization, we obtain sum-of-squares based criteria for designing controllers with closed-loop robust stability guarantees for all continuoustime systems with rational system dynamics which are consistent with the measured data and the assumed noise bound. Finally, we apply the developed approach to a numerical example.

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Section: Introductionmentioning

confidence: 61%

Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics

Strässer,

Berberich,

Allgöwer

2020

Preprint

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“…and let us show that such E satisfies (23) to complete the proof. Since α ≥ 0 and E j ≥ 0 for each j ∈ N V S by ( 18), we have from ( 29)…”

Section: A Proof Of Theoremmentioning

confidence: 95%

“…The =⇒ -direction is trivial by using Lemma 2 for x = x j ∈ S with j ∈ N V S . The ⇐=-direction is proven if for E j with j ∈ N V S satisfying (18) and an arbitrary x ∈ S, we find E that can depend on x and satisfies (23). This is done by exploiting that for a bounded S as in (17), an arbitrary x ∈ S can always be written in terms of a convex combination of the vertices of S as x = V S j=1 α j x j through coefficients α j (j ∈ N V S ) that satisfy 1 α = 1 and α ≥ 0.…”

Section: A Proof Of Theoremmentioning

confidence: 99%

“…While early use of this insight in the context of data-driven control has appeared, e.g., in [31], [33], recent contributions have emphasized its role in the constrained optimal control of unknown stochastic linear systems [13], [14] and in the derivation of explicit formulas for data-driven control with optimal and robust performance [19]. Since then, many very recent works in data-driven control have appeared, among which [4], [35], [5], [32], [36], [3], [23], [6]. In the context of stabilization or H 2 , H ∞ control (instead of robust invariance), data-driven approaches with noisy data were considered in [19], [36], [4].…”

Section: Introductionmentioning

confidence: 99%

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Controller design for robust invariance from noisy data

Bisoffi,

De Persis,

Tesi

2020

Preprint

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For an unknown linear system, starting from noisy open-loop input-state data collected during a finite-length experiment, we directly design a linear feedback controller that guarantees robust invariance of a given polyhedral set of the state in the presence of disturbances. The main result is a necessary and sufficient condition for the existence of such a controller, and amounts to the solution of a linear program. The benefits of large and rich data sets for the solution of the problem are discussed.A numerical example about a simplified platoon of two vehicles illustrates the method.

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“…time horizon of unknown nonlinear systems with polynomial dynamics. Contrary to [12], we consider polynomial systems in discrete time and measurements in presence of noise. By characterizing this noise by two distinct descriptions, we propose two data-based set-membership representations of the ground-truth system which constitute two frameworks to deduce computationally attractive conditions for verifying dissipativity properties using SOS optimization.…”

Section: Introductionmentioning

confidence: 99%

Dissipativity verification with guarantees for polynomial systems from noisy input-state data

Martin¹,

Allgöwer²

2020

Preprint

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In this paper, we investigate the verification of dissipativity properties for polynomial systems without explicit knowledge of a model but directly from noise-corrupted measurements. Contrary to most data-driven approaches for nonlinear systems, we determine dissipativity properties over infinite time horizon using input-state data. To this end, we propose two characterizations of the noise that affects the system and deduce from each characterization a data-based set-membership representation of the ground-truth system. Each representation then serves as a framework to derive computationally attractive conditions to verify dissipativity properties with rigorous guarantees from noise-corrupted data using SOS optimization.

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Learning control for polynomial systems using sum of squares relaxations

Cited by 5 publications

References 24 publications

Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics

Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics

Controller design for robust invariance from noisy data

Dissipativity verification with guarantees for polynomial systems from noisy input-state data

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