Optimal Feedback Controls for Parameter Identification
Optimal Feedback Controls for Parameter Identification

Author: David N. Olmstead

Publisher:

Published: 1979

Total Pages: 177

ISBN-13:

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This dissertation investigates improving the estimates of unknown constant parameters in the plant and control matrices of a linear discrete system from noisy measurements by the use of a control consisting of a feedback term and open-loop term. The feedback term allows one to move the poles of the system to location which improve the information in the output about the parameters beyond that attainable with only open-loop control inputs. An energy constraint is placed on the open-loop term of the control and the closed-loop poles are required to remain within a predetermined constraint space. Output feedback is used and for the cases where the dimension of the output is less than the dimension of the system states, an additional consistency constraint on the closed-loop poles is required. The criterion that has been used is the maximization of the trace or weighted trace of the Fisher information matrix. A graident projection algorithm has been developed that maximizes this scalar function while maintaining the poles within the constraint space. This procedure results in maximizing the sum of a maximum eigenvalue of a positive semi-definite matrix and a term resulting from the feedback of measurement noise into the process equations. The variable in this maximizaton procedure is the feedback matrix. The optimal open-loop control sequence is a scaled eigenvector corresponding to the maximum eigenvalue. The procedure is developed for the multiple parameter and multiple input control cases. Examples are used to demonstrate the enhancement of parameter identification gained by adding feedback control to an open-loop control input. (Author).

Identification and System Parameter Estimation 1982
Identification and System Parameter Estimation 1982

Author: G. A. Bekey

Publisher: Elsevier

Published: 2016-06-06

Total Pages: 869

ISBN-13: 1483165787

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Identification and System Parameter Estimation 1982 covers the proceedings of the Sixth International Federation of Automatic Control (IFAC) Symposium. The book also serves as a tribute to Dr. Naum S. Rajbman. The text covers issues concerning identification and estimation, such as increasing interrelationships between identification/estimation and other aspects of system theory, including control theory, signal processing, experimental design, numerical mathematics, pattern recognition, and information theory. The book also provides coverage regarding the application and problems faced by several engineering and scientific fields that use identification and estimation, such as biological systems, traffic control, geophysics, aeronautics, robotics, economics, and power systems. Researchers from all scientific fields will find this book a great reference material, since it presents topics that concern various disciplines.

Online Parameter Identification for Optimal Feedback Control of Nonlinear Dynamical Systems
Online Parameter Identification for Optimal Feedback Control of Nonlinear Dynamical Systems

Author: Margareta Runge

Publisher:

Published: 2024

Total Pages: 0

ISBN-13:

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This research aims to enhance current methods for the optimal feedback control of complex nonlinear dynamical systems via online parameter identifications. Accurate knowledge of the system parameters is essential in numerous practical applications to ensure effective control. A considerable number of advanced control algorithms use model-based approaches. However, the model parameters may often be unknown or subject to change over time. This could result in deviations from the feedback control objective, increased expected costs, and even divergence of the controller. The main objective of this thesis is to develop a combined online parameter identification and model-based controller approach that allows continuously estimating the model parameters of a nonlinear system. The available real-time measurements of the system are used to compute an approximation of the searched parameters. This repeated parameter estimation enables the control algorithm to adapt to the changing system dynamics and maintain optimal control accuracy. This study investigates three approaches. First, a coupled algorithm is developed that employs parameter identifications during operation to adapt a linear quadratic regulator using techniques from parametric sensitivity analysis. Additionally, an approach is presented that also examines the information quality in the data used to predict the probability of success of the parameter estimation. An adaptive control algorithm using nonlinear model predictive control (NMPC) and online parameter identification is proposed as a third alternative. All proposed techniques rely on highly efficient numerical methods for solving nonlinear optimization problems (NLP) and the potential to transfer related problems from optimal control into an NLP by discretization. The proposed approaches are extensively evaluated by conducting simulations and comparing them to the existing standard control methods.

Stochastic Models, Estimation, and Control
Stochastic Models, Estimation, and Control

Author: Peter S. Maybeck

Publisher: Academic Press

Published: 1982-08-25

Total Pages: 311

ISBN-13: 0080960030

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This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.

Applied Optimal Estimation
Applied Optimal Estimation

Author: The Analytic Sciences Corporation

Publisher: MIT Press

Published: 1974-05-15

Total Pages: 388

ISBN-13: 9780262570480

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This is the first book on the optimal estimation that places its major emphasis on practical applications, treating the subject more from an engineering than a mathematical orientation. Even so, theoretical and mathematical concepts are introduced and developed sufficiently to make the book a self-contained source of instruction for readers without prior knowledge of the basic principles of the field. The work is the product of the technical staff of The Analytic Sciences Corporation (TASC), an organization whose success has resulted largely from its applications of optimal estimation techniques to a wide variety of real situations involving large-scale systems. Arthur Gelb writes in the Foreword that "It is our intent throughout to provide a simple and interesting picture of the central issues underlying modern estimation theory and practice. Heuristic, rather than theoretically elegant, arguments are used extensively, with emphasis on physical insights and key questions of practical importance." Numerous illustrative examples, many based on actual applications, have been interspersed throughout the text to lead the student to a concrete understanding of the theoretical material. The inclusion of problems with "built-in" answers at the end of each of the nine chapters further enhances the self-study potential of the text. After a brief historical prelude, the book introduces the mathematics underlying random process theory and state-space characterization of linear dynamic systems. The theory and practice of optimal estimation is them presented, including filtering, smoothing, and prediction. Both linear and non-linear systems, and continuous- and discrete-time cases, are covered in considerable detail. New results are described concerning the application of covariance analysis to non-linear systems and the connection between observers and optimal estimators. The final chapters treat such practical and often pivotal issues as suboptimal structure, and computer loading considerations. This book is an outgrowth of a course given by TASC at a number of US Government facilities. Virtually all of the members of the TASC technical staff have, at one time and in one way or another, contributed to the material contained in the work.