Koopman System Approximation-Based Optimal Control of Multiple Mobile Robots

This article presents a study of the Koopman operator theory and its application to optimal control of a multiple-mobile-robot system. The operator, while operating on a set of observation functions of the state vector of a nonlinear system, produces a set of dynamic equations that, through a dynami...

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Veröffentlicht in:IEEE transactions on control systems technology Jg. 33; H. 3; S. 963 - 979
Hauptverfasser: Zhao, Qianhong, Tao, Gang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.05.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Adaptation models
Analytical models
Approximation
Control systems
Control theory
Dynamical systems
Feedback control
Heuristic algorithms
Iterative algorithms
Koopman operator
Linear programming
Mathematical models
Nonlinear dynamical systems
Nonlinear programming
Nonlinear systems
online learning
Optimal control
Optimization
Parameters
Programming
Real time
Robot control
Robot learning
robot system
Simulation
State variable
State vectors
Utility functions
Vectors
ISSN:1063-6536, 1558-0865
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Abstract This article presents a study of the Koopman operator theory and its application to optimal control of a multiple-mobile-robot system. The operator, while operating on a set of observation functions of the state vector of a nonlinear system, produces a set of dynamic equations that, through a dynamic transformation, form a new dynamic system. The Koopman system technique is then applied to the development of a linear or bilinear model approximation of nonlinear utility functions for optimal control of a system of multiple (mobile) robots, by selecting the utility functions as the Koopman system state variables and expressing the set of Koopman variables as the state variables of a linear or bilinear system whose parameters are determined through optimization. An iterative algorithm is developed to estimate the parameters adaptively. Finally, the optimal control problems based on a linear or bilinear approximation model are formulated, by transforming the nonlinear programming problem to a linear programming problem. The above models are simulated on a three-mobile-robot system to verify their performance in both centralized and decentralized versions. From the simulation results, the bilinear model has more capacity to approximate the nonlinear utility functions. Both the centralized and decentralized bilinear approximation model-based control signals can achieve the control objective and are generated fast enough for real-time control.
AbstractList This article presents a study of the Koopman operator theory and its application to optimal control of a multiple-mobile-robot system. The operator, while operating on a set of observation functions of the state vector of a nonlinear system, produces a set of dynamic equations that, through a dynamic transformation, form a new dynamic system. The Koopman system technique is then applied to the development of a linear or bilinear model approximation of nonlinear utility functions for optimal control of a system of multiple (mobile) robots, by selecting the utility functions as the Koopman system state variables and expressing the set of Koopman variables as the state variables of a linear or bilinear system whose parameters are determined through optimization. An iterative algorithm is developed to estimate the parameters adaptively. Finally, the optimal control problems based on a linear or bilinear approximation model are formulated, by transforming the nonlinear programming problem to a linear programming problem. The above models are simulated on a three-mobile-robot system to verify their performance in both centralized and decentralized versions. From the simulation results, the bilinear model has more capacity to approximate the nonlinear utility functions. Both the centralized and decentralized bilinear approximation model-based control signals can achieve the control objective and are generated fast enough for real-time control.
Author Zhao, Qianhong
Tao, Gang
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SubjectTerms Adaptation models
Analytical models
Approximation
Control systems
Control theory
Dynamical systems
Feedback control
Heuristic algorithms
Iterative algorithms
Koopman operator
Linear programming
Mathematical models
Nonlinear dynamical systems
Nonlinear programming
Nonlinear systems
online learning
Optimal control
Optimization
Parameters
Programming
Real time
Robot control
Robot learning
robot system
Simulation
State variable
State vectors
Utility functions
Vectors
Title Koopman System Approximation-Based Optimal Control of Multiple Mobile Robots
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