Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator

Sootla, Aivar; Mauroy, Alexandre; Gonçalves, Jorge

doi:10.1016/j.ifacol.2016.10.247

Cited by 8 publications

(21 citation statements)

References 23 publications

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“…4.3). Optimal control formulations have also been considered for switching problems [166,165,136]. Based on a global bilinearization, the underlying dynamical system can be stabilized using feedback linearization [65].…”

Section: Control Designmentioning

confidence: 99%

Data-Driven Approximations of Dynamical Systems Operators for Control

Kaiser

Kutz

Brunton

2020

Lecture Notes in Control and Information Sciences

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The Koopman and Perron Frobenius transport operators are fundamentally changing how we approach dynamical systems, providing linear representations for even strongly nonlinear dynamics. Although there is tremendous potential benefit of such a linear representation for estimation and control, transport operators are infinite-dimensional, making them difficult to work with numerically. Obtaining low-dimensional matrix approximations of these operators is paramount for applications, and the dynamic mode decomposition has quickly become a standard numerical algorithm to approximate the Koopman operator. Related methods have seen rapid development, due to a combination of an increasing abundance of data and the extensibility of DMD based on its simple framing in terms of linear algebra. In this chapter, we review key innovations in the data-driven characterization of transport operators for control, providing a high-level and unified perspective. We emphasize important recent developments around sparsity and control, and discuss emerging methods in big data and machine learning.

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Section: Control Designmentioning

confidence: 99%

Data-Driven Approximations of Dynamical Systems Operators for Control

Kaiser

Kutz

Brunton

2020

Lecture Notes in Control and Information Sciences

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“…In [4], [5], it has been proposed to solve the switching problem using temporal pulses of a fixed length τ and a fixed magnitude µ for monotone systems (cf. [6]).…”

Section: Introductionmentioning

confidence: 99%

Pulse-Based Control Using Koopman Operator Under Parametric Uncertainty

Sootla

Ernst

2018

IEEE Trans. Automat. Contr.

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Abstract-In applications, such as biomedicine and systems/synthetic biology, technical limitations in actuation complicate implementation of time-varying control signals. In order to alleviate some of these limitations, it may be desirable to derive simple control policies, such as step functions with fixed magnitude and length (or temporal pulses). In this technical note, we further develop a recently proposed pulse-based solution to the convergence problem, i.e., minimizing the convergence time to the target exponentially stable equilibrium, for monotone systems. In particular, we extend this solution to monotone systems with parametric uncertainty. Our solutions also provide worst-case estimates on convergence times. Furthermore, we indicate how our tools can be used for a class of non-monotone systems, and more importantly how these tools can be extended to other control problems. We illustrate our approach on switching under parametric uncertainty and regulation around a saddle point problems in a genetic toggle switch system.

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“…Applying linear stability analysis to establish global stability is one example (Mauroy and Mezic, 2013). Sootla et al (2016) leverage the Koopman operator in the design of temporal pulse control of bistable monotone systems. Brunton et al (2016) demonstrated the potential use of these operators to design optimal control laws for fully nonlinear systems using techniques from linear optimal control.…”

Section: Literature Review On the System Identification And Finite LImentioning

confidence: 99%

“…Sootla et al. () leverage the Koopman operator in the design of temporal pulse control of bistable monotone systems. Brunton et al.…”

Section: Introductionmentioning

confidence: 99%

Efficient Infrastructure Restoration Strategies Using the Recovery Operator

González

Chapman

Dueñas‐Osorio

et al. 2017

Computer aided Civil Eng

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Infrastructure systems are critical for society's resilience, government operation, and overall defense. Thereby, it is imperative to develop informative and computationally efficient analysis methods for infrastructure systems, which reveal system vulnerabilities and recoverability. To capture practical constraints in systems analyses, various layers of complexity play a role, including limited element capacities, restoration resources, and the presence of interdependence among systems. High‐fidelity modeling such as mixed integer programming and physics‐based modeling can often be computationally expensive, making time‐sensitive analyses challenging. Furthermore, the complexity of recovery solutions can reduce analysis transparency. An alternative, presented in this work, is a reduced‐order representation, dubbed a recovery operator, of a high‐fidelity time‐dependent recovery model of a system of interdependent networks. The form of the operator is assumed to be a time‐invariant linear dynamic model apt for infrastructure restoration. The recovery operator is generated by applying system identification techniques to numerous disaster and recovery scenarios. The proposed compact representation provides simple yet powerful information regarding systemic recovery dynamics, and enables generating fast suboptimal recovery policies in time‐critical applications.

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Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator

Cited by 8 publications

References 23 publications

Data-Driven Approximations of Dynamical Systems Operators for Control

Data-Driven Approximations of Dynamical Systems Operators for Control

Pulse-Based Control Using Koopman Operator Under Parametric Uncertainty

Efficient Infrastructure Restoration Strategies Using the Recovery Operator

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