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Linear-Quadratic Controls in Risk-Averse Decision Making
Performance-Measure Statistics and Control Decision Optimization
Khanh D. Pham
The Air Force Research Laboratory
Space Vehicles Directorate
3550 Aberdeen Ave. S.E.
Kirtland Air Force Base
New Mexico, USA
ISSN 2190-8354 ISSN 2191-575X (electronic)
ISBN 978-1-4614-5078-8 ISBN 978-1-4614-5079-5 (eBook)
DOI 10.1007/978-1-4614-5079-5
Springer New York Heidelberg Dordrecht London
Library of Congress Control Number: 2012949189
Mathematics Subject Classification (2010): 60-00, 93cxx, 62-xx, 65k10
© Khanh D. Pham 2013
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Contents
1 Introduction .................................................................. 1
1.1 Risk Assessment and Management .................................... 1
1.2 Monograph Ideas and Contributions ................................... 2
1.3 Methodology ............................................................ 2
1.4 Chapter Organization ................................................... 3
References ..................................................................... 5
2 Risk-Averse Control of Linear-Quadratic Tracking Problems ......... 7
2.1 Introduction ............................................................. 7
2.2 The Problem............................................................. 8
2.3 The Value of Performance-MeasureStatistics......................... 9
2.4 Statements of Mayer Problem with Performance Risk Aversion ..... 16
2.5 Risk-Averse Control of Adaptive Behavior............................ 21
2.6 Chapter Summary ....................................................... 28
References ..................................................................... 29
3 Overtaking Tracking Problems in Risk-Averse Control................. 31
3.1 Introduction ............................................................. 31
3.2 Problem Description .................................................... 32
3.3 A Framework for Performance-MeasureStatistics.................... 34
3.4 Statements of the Risk-Averse Control Problem ...................... 38
3.5 Optimal Risk-Averse Tracking Solution ............................... 42
3.6 Chapter Summary ....................................................... 46
References ..................................................................... 47
4 Performance Risk Management in Servo Systems ...................... 49
4.1 Introduction ............................................................. 49
4.2 The Performance Information Process ................................. 50
4.3 The System Control Problem........................................... 54
4.4 Statistical Optimal Control Solution ................................... 59
4.5 Chapter Summary ....................................................... 65
References ..................................................................... 66
5 Risk-Averse Control Problems in Model-Following Systems ........... 67
5.1 Introduction ............................................................. 67
5.2 Performance Information in Control with Risk Consequences ....... 68
5.3 Formulation of the Control Problem ................................... 75
5.4 Existence of Risk-Averse Control Solution............................ 80
5.5 Chapter Summary ....................................................... 85
References ..................................................................... 85
6 Incomplete Feedback Design in Model-Following Systems ............. 87
6.1 Introduction ............................................................. 87
6.2 Backward Differential Equations for Performance-Measure
Statistics ................................................................. 88
6.3 Performance-Measure Statistics for Risk-Averse Control ............ 95
6.4 Output-Feedback Control Solution..................................... 100
6.5 Chapter Summary ....................................................... 104
References ..................................................................... 104
7 Reliable Control for Stochastic Systems with Low Sensitivity .......... 107
7.1 Introduction ............................................................. 107
7.2 The Problem and Representations for Performance Robustness...... 108
7.3 Problem Statements with the Maximum Principle .................... 114
7.4 Low Sensitivity Control with Risk Aversion .......................... 118
7.5 Chapter Summary ....................................................... 122
References ..................................................................... 123
8 Output-Feedback Control for Stochastic Systems with Low
Sensitivity ..................................................................... 125
8.1 Introduction ............................................................. 125
8.2 Linking Performance-MeasureStatistics and Risk Perceptions ...... 126
8.3 Statements Toward the Optimal Decision Problem.................... 136
8.4 Risk-Averse Control Solution in the Closed-Loop System ........... 141
8.5 Chapter Summary ....................................................... 144
References ..................................................................... 144
9 Epilogue....................................................................... 145
9.1 The Aspect of Performance-InformationAnalysis .................... 145
9.2 The Aspect of Risk-Averse Decision Making ......................... 146
9.3 What Will Be?........................................................... 146
Index............................................................................... 149