Guarantees for data-driven control of nonlinear systems using semidefinite programming: A survey

Martin, Tim; Schön, Thomas B.; Allgöwer, Frank

doi:10.1016/j.arcontrol.2023.100911

Cited by 7 publications

(3 citation statements)

References 69 publications

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“…These studies collectively underscore the shift towards leveraging real-time data for control purposes, reflecting a broader trend in automation and control engineering. Other papers in the field [19][20][21][22][23][24][25][26] corroborated these findings, showcasing data-driven control's adaptability to different system types and its capability to enhance system responsiveness and efficiency.…”

Section: Data-driven Controlmentioning

confidence: 69%

Enhancing Industrial Process Control: Integrating Intelligent Digital Twin Technology with Proportional-Integral-Derivative Regulators

Dapkute,

Siozinys,

Jonaitis

et al. 2024

Machines

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This paper explores the integration of intelligent digital twin technology with PID regulators in industrial process control utilizing smart meter data. It presents a novel approach involving the creation of mathematical models to simulate real-time system behavior, thereby enhancing the PID control loop. The focus is on the development of specialized IT infrastructure to support this integration, which includes data acquisition, processing, and control optimization. This integration aims to not only improve control system efficiency but also introduce a robust predictive maintenance framework, offering significant benefits across a wide range of industrial applications.

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Section: Data-driven Controlmentioning

confidence: 69%

Enhancing Industrial Process Control: Integrating Intelligent Digital Twin Technology with Proportional-Integral-Derivative Regulators

Dapkute,

Siozinys,

Jonaitis

et al. 2024

Machines

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“…The inverted pendulum is a classical example for dynamical systems, which is often used as a benchmark in nonlinear data-driven control, cf. [38]- [42]. This dynamical system can be modeled by…”

Section: Nonlinear Inverted Pendulummentioning

confidence: 99%

Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics

Strässer

Berberich

Allgöwer

2021

2021 60th IEEE Conference on Decision and Control (CDC)

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Data-driven analysis and control of dynamical systems have gained a lot of interest in recent years. While the class of linear systems is well studied, theoretical results for nonlinear systems are still rare. In this paper, we present a data-driven controller design method for discretetime control-affine nonlinear systems. Our approach relies on the Koopman operator, which is a linear but infinite-dimensional operator lifting the nonlinear system to a higher-dimensional space. Particularly, we derive a linear fractional representation of a lifted bilinear system representation based on measured data. Further, we restrict the lifting to finite dimensions, but account for the truncation error using a finite-gain argument. We derive a linear matrix inequality based design procedure to guarantee robust local stability for the resulting bilinear system for all error terms satisfying the finite-gain bound and, thus, also for the underlying nonlinear system. Finally, we apply the developed design method to the nonlinear Van der Pol oscillator.

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“…In direct DDC, a control policy is formed from the collected data and modeling assumptions without first performing system identification (and synthesizing a controller for the identified system) [4]. Set-membership DDC has three main ingredients: the set of data-consistent plants (given a noise model), the set of commonly stabilized plants by a designed controller, and the certificate of set-containment that the stabilized-set contains the consistent-set [5]. The Matrix S-Lemma can be used to provide proofs of quadratic and worst-case H 2 or H ∞ robust control when the noise model is defined by a matrix ellipsoid (quadratic matrix inequality) [6], [7].…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Superstabilizing Control of Error-in-Variables Discrete-Time Linear Systems

Miller

Dai

Sznaier

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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This paper presents a linear-programming based algorithm to perform data-driven stabilizing control of linear positive systems. A set of state-input-transition observations is collected up to magnitudebounded noise. A state feedback controller and dual linear copositive Lyapunov function are created such that the set of all data-consistent plants is contained within the set of all stabilized systems. This containment is certified through the use of the Extended Farkas Lemma and solved via Linear Programming. Sign patterns and sparsity structure for the controller may be imposed using linear constraints. The complexity of this algorithm scales in a polynomial manner with the number of states and inputs. The Linear-Programming based algorithm is extended to positive-stabilization of switched linear systems and Linear Parameter-Varying systems. Effectiveness is demonstrated on example systems.

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Guarantees for data-driven control of nonlinear systems using semidefinite programming: A survey

Cited by 7 publications

References 69 publications

Enhancing Industrial Process Control: Integrating Intelligent Digital Twin Technology with Proportional-Integral-Derivative Regulators

Enhancing Industrial Process Control: Integrating Intelligent Digital Twin Technology with Proportional-Integral-Derivative Regulators

Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics

Data-Driven Superstabilizing Control of Error-in-Variables Discrete-Time Linear Systems

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