Proper Orthogonal Decomposition Based Feedback Optimal Control Synthesis of Distributed Parameter Systems Using Neural Networks

Radhakant Padhi; S. N. Balakrishnan

doi:10.1109/ACC.2002.1025337

Proper Orthogonal Decomposition Based Feedback Optimal Control Synthesis of Distributed Parameter Systems Using Neural Networks

Radhakant Padhi
, S. N. Balakrishnan

Missouri University of Science and Technology

Research output: Contribution to journal › Article › peer-review

Abstract

A new method for optimal control design of distributed parameter systems is presented in this paper. The concept of proper orthogonal decomposition is used for the model reduction of distributed parameter systems to form a reduced order lumped parameter problem. The optimal control problem is then solved in the time domain, in a state feedback sense, following the philosophy of ''adaptive critic'' neural networks. The control solution is then mapped back to the spatial domain using the same basis functions. Numerical simulation results are presented for a linear and nonlinear one-dimensional heat equation problem in an infinite time regulator framework.

Original language	American English
Journal	Proceedings of the 2002 American Control Conference
DOIs	https://doi.org/10.1109/ACC.2002.1025337
State	Published - Jan 1 2002

Keywords

1D Heat Equation Problem
Distributed Parameter Systems
Heat Conduction
Model Reduction
Neural Nets
Neural Networks
Optimal Control
Orthogonal Decomposition
Reduced Order Lumped Parameter
Reduced Order Systems
State Feedback
Time Domain Analysis

Disciplines

Aerospace Engineering
Mechanical Engineering

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title = "Proper Orthogonal Decomposition Based Feedback Optimal Control Synthesis of Distributed Parameter Systems Using Neural Networks",

abstract = " A new method for optimal control design of distributed parameter systems is presented in this paper. The concept of proper orthogonal decomposition is used for the model reduction of distributed parameter systems to form a reduced order lumped parameter problem. The optimal control problem is then solved in the time domain, in a state feedback sense, following the philosophy of ''adaptive critic'' neural networks. The control solution is then mapped back to the spatial domain using the same basis functions. Numerical simulation results are presented for a linear and nonlinear one-dimensional heat equation problem in an infinite time regulator framework.",

keywords = "1D Heat Equation Problem, Distributed Parameter Systems, Heat Conduction, Model Reduction, Neural Nets, Neural Networks, Optimal Control, Orthogonal Decomposition, Reduced Order Lumped Parameter, Reduced Order Systems, State Feedback, Time Domain Analysis",

author = "Radhakant Padhi and Balakrishnan, \{S. N.\}",

year = "2002",

month = jan,

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doi = "10.1109/ACC.2002.1025337",

language = "American English",

journal = "Proceedings of the 2002 American Control Conference",

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T1 - Proper Orthogonal Decomposition Based Feedback Optimal Control Synthesis of Distributed Parameter Systems Using Neural Networks

AU - Padhi, Radhakant

AU - Balakrishnan, S. N.

PY - 2002/1/1

Y1 - 2002/1/1

N2 - A new method for optimal control design of distributed parameter systems is presented in this paper. The concept of proper orthogonal decomposition is used for the model reduction of distributed parameter systems to form a reduced order lumped parameter problem. The optimal control problem is then solved in the time domain, in a state feedback sense, following the philosophy of ''adaptive critic'' neural networks. The control solution is then mapped back to the spatial domain using the same basis functions. Numerical simulation results are presented for a linear and nonlinear one-dimensional heat equation problem in an infinite time regulator framework.

AB - A new method for optimal control design of distributed parameter systems is presented in this paper. The concept of proper orthogonal decomposition is used for the model reduction of distributed parameter systems to form a reduced order lumped parameter problem. The optimal control problem is then solved in the time domain, in a state feedback sense, following the philosophy of ''adaptive critic'' neural networks. The control solution is then mapped back to the spatial domain using the same basis functions. Numerical simulation results are presented for a linear and nonlinear one-dimensional heat equation problem in an infinite time regulator framework.

KW - 1D Heat Equation Problem

KW - Distributed Parameter Systems

KW - Heat Conduction

KW - Model Reduction

KW - Neural Nets

KW - Neural Networks

KW - Optimal Control

KW - Orthogonal Decomposition

KW - Reduced Order Lumped Parameter

KW - Reduced Order Systems

KW - State Feedback

KW - Time Domain Analysis

UR - https://scholarsmine.mst.edu/mec_aereng_facwork/3464

U2 - 10.1109/ACC.2002.1025337

DO - 10.1109/ACC.2002.1025337

M3 - Article

JO - Proceedings of the 2002 American Control Conference

JF - Proceedings of the 2002 American Control Conference

ER -

Proper Orthogonal Decomposition Based Feedback Optimal Control Synthesis of Distributed Parameter Systems Using Neural Networks

Abstract

Keywords

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