## Linear-Quadratic Controls in Risk-Averse Decision Making: Performance-Measure Statistics and Control Decision OptimizationLinear-Quadratic Controls in Risk-Averse Decision Making cuts across control engineering (control feedback and decision optimization) and statistics (post-design performance analysis) with a common theme: reliability increase seen from the responsive angle of incorporating and engineering multi-level performance robustness beyond the long-run average performance into control feedback design and decision making and complex dynamic systems from the start. This monograph provides a complete description of statistical optimal control (also known as cost-cumulant control) theory. In control problems and topics, emphasis is primarily placed on major developments attained and explicit connections between mathematical statistics of performance appraisals and decision and control optimization. Chapter summaries shed light on the relevance of developed results, which makes this monograph suitable for graduate-level lectures in applied mathematics and electrical engineering with systems-theoretic concentration, elective study or a reference for interested readers, researchers, and graduate students who are interested in theoretical constructs and design principles for stochastic controlled systems. |

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### Contents

Chapter 1 Introduction
| 1 |

Chapter 2 RiskAverse Control of LinearQuadratic Tracking Problems
| 7 |

Chapter 3 Overtaking Tracking Problems in RiskAverse Control
| 31 |

Chapter 4 Performance Risk Management in Servo Systems
| 48 |

Chapter 5 RiskAverse Control Problems in ModelFollowing Systems
| 67 |

Chapter 6 Incomplete Feedback Design in ModelFollowing Systems
| 87 |

### Other editions - View all

Linear-Quadratic Controls in Risk-Averse Decision Making: Performance ... Khanh D. Pham Limited preview - 2012 |

Linear-Quadratic Controls in Risk-Averse Decision Making: Performance ... Khanh D. Pham No preview available - 2012 |

### Common terms and phrases

admissible feedback gain afﬁne input aversion aware performance index chapter coefﬁcients continuous-time control design control solutions cost cumulants cumulant-generating function deﬁned Deﬁnition dynamic programming dynamical equations feedback control feedforward feedforward gain ﬁnite horizon Fix k G follows g r g k G t0,tf G Z+ given higher-order characteristics HJB equation initial condition Lipschitz continuous low sensitivity Maclaurin series mathematical statistics matrix matrix-valued Mayer type model-following control moment-generating function monograph optimal control problem optimization problem output parameter performance appraisal performance information performance measure performance reliability performance risk performance robustness performance uncertainty performance variations performance-measure statistics Proof quadratic random variable reachable set rIl k d rIl rIl risk-averse control Risk-Averse Decision risk-value aware performance Sain satisﬁed state-feedback statistical optimal control stochastic control stochastic differential equation Stochastic Optimal stochastic systems terminal-value conditions time-backward tracking problem value function variables veriﬁcation theorem Wiener process