A Convex Approach to Data-Driven Optimal Control via Perron-Frobenius and Koopman Operators

This article is about the data-driven computation of optimal control for a class of control affine deterministic nonlinear systems. We assume that the control dynamical system model is not available, and the only information about the system dynamics is available in the form of time-series data. We...

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Published in:IEEE transactions on automatic control Vol. 67; no. 9; pp. 4778 - 4785
Main Authors: Huang, Bowen, Vaidya, Umesh
Format: Journal Article
Language:English
Published: New York IEEE 01.09.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Approximation algorithms
Computational geometry
Control systems
Convex optimization
Convexity
data-driven control
Dynamic stability
Dynamical systems
Heuristic algorithms
linear operator approach
Markov processes
Nonlinear control
Nonlinear systems
Numerical stability
Optimal control
Optimization
Stability criteria
System dynamics
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Abstract This article is about the data-driven computation of optimal control for a class of control affine deterministic nonlinear systems. We assume that the control dynamical system model is not available, and the only information about the system dynamics is available in the form of time-series data. We provide a convex formulation for the optimal control problem (OCP) of the nonlinear system. The convex formulation relies on the duality result in the dynamical system's stability theory involving density function and Perron-Frobenius operator. We formulate the OCP as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the Koopman operator's data-driven computation, which is dual to the Perron-Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.
AbstractList This article is about the data-driven computation of optimal control for a class of control affine deterministic nonlinear systems. We assume that the control dynamical system model is not available, and the only information about the system dynamics is available in the form of time-series data. We provide a convex formulation for the optimal control problem (OCP) of the nonlinear system. The convex formulation relies on the duality result in the dynamical system’s stability theory involving density function and Perron–Frobenius operator. We formulate the OCP as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the Koopman operator’s data-driven computation, which is dual to the Perron–Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.
Author Vaidya, Umesh
Huang, Bowen
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SubjectTerms Approximation algorithms
Computational geometry
Control systems
Convex optimization
Convexity
data-driven control
Dynamic stability
Dynamical systems
Heuristic algorithms
linear operator approach
Markov processes
Nonlinear control
Nonlinear systems
Numerical stability
Optimal control
Optimization
Stability criteria
System dynamics
Title A Convex Approach to Data-Driven Optimal Control via Perron-Frobenius and Koopman Operators
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https://www.proquest.com/docview/2708651831
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