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linear quadratic gaussian control with quantised innovations Kalman filter over a symmetric channel

IET control THEORY AND APPLICATIONS 2011年第3期5卷 437-446页

作者： You, K. Xie, L. Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

This study discusses the quantised linear quadratic gaussian (LQG) control problem for linear stochastic systems. A symmetric channel that connects the sensor and the controller is considered. Given a quantiser that is applied on the most recent innovation of the measurement, it is shown that the well-known separation principle remains valid. Based on a quantised innovations Kalman filter, a suboptimal LQG controller is given in terms of the solutions of two Riccati difference equations associated, respectively, with the state estimation and the standard linear quadratic regulator control. The corresponding approximate suboptimal cost is also derived. An illustrative example is included to demonstrate the effectiveness of the proposed controller.

关键词： Signal processing theory Optimisation techniques Riccati difference equations stochastic systems Kalman filters symmetric channel Time-varying control systems state estimation quantiser LQG control problem suboptimal LQG controller linear systems linear quadratic gaussian control Algebra standard linear quadratic regulator control quantised innovations Kalman filter Mathematical analysis Optimal control quantised linear quadratic gaussian control difference equations quantisation (signal) optimal control Simulation, modelling and identification Riccati equations linear stochastic systems separation principle corresponding approximate suboptimal cost

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linear quadratic gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2009年第6期26卷 1307-1325页

作者： Petit, Cyril Conan, Jean-Marc Kulcsar, Caroline Raynaud, Henri-Francois PHASE ONERA F-92322 Chatillon France Univ Paris 13 Inst Galilee L2TI F-93430 Villetaneuse France

We present a comprehensive analysis of the linear quadratic gaussian control approach applied to adaptive optics (AO) and multiconjugated AO (MCAO) based on numerical and experimental validations. The structure of the control law is presented and its main properties discussed. We then propose an extended experimental validation of this control law in AO and a simplified MCAO configuration. Performance is compared with end-to-end numerical simulations. Sensitivity of the performance regarding tuning parameters is tested. Finally, extension to full MCAO and laser tomographic AO (LTAO) through numerical simulation is presented and analyzed. (C) 2009 Optical Society of America

关键词： comprehensive analysis Numerical AUXILIARY ORIFICES linear quadratic gaussian control numerical simulation control law

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Lack of Separation Principle for Quantized linear quadratic gaussian control

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IEEE TRANSACTIONS ON AUTOMATIC control 2012年第9期57卷 2385-2390页

作者： Fu, Minyue Zhejiang Univ Sch Control Sci & Engn Hangzhou Zhejiang Peoples R China

This technical note studies the quantized linear quadratic gaussian (LQG) control problem which is generalized from the classical LQG control but with the constraint that the feedback signal is quantized with a fixed bit rate. We show that state feedback control, state estimation and quantization can not be fully separated in general. Only a weak separation principle holds which converts the quantized LQG control problem into a quantized state estimation problem. Further separation of estimation and quantization is not possible in general. A concrete example is provided to demonstrate this fact. It is also shown that the so-called "whitening" approach to quantized state estimation is not optimal.

关键词： Certainty equivalence linear quadratic gaussian control networked control quantized estimation quantized feedback control separation principle

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Investigation on linear quadratic gaussian control of semi-active suspension for three-axle vehicle

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JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE control 2021年第3期40卷 1633-1648页

作者： Li, Shaohua Zhao, Junwu Zhang, Zhida Shijiazhuang Tiedao Univ State Key Lab Mech Behav & Syst Safety Traff Engn Shijiazhuang Hebei Peoples R China Jilin Univ Coll Automot Engn Changchun Peoples R China Chongqing Univ State Key Lab Mech Transmiss Chongqing 400044 Peoples R China

An 8-DOF three-axle vehicle model with semi-active suspension is built in this paper, of which the accuracy is verified through simulations and experiments. Based on the optimal control theory, the linear quadratic gaussian controller for semi-active suspension is designed with 10 evaluation indicators. Considering the deficiency of linear quadratic gaussian control weight coefficients based on experience, analytic hierarchy process is employed to determine the weight coefficients of each indicator. The control effect is analyzed through MATLAB/Simulink. The adaptability of proposed control strategy under 25 driving conditions is analyzed with different road grades and speeds. The driving condition of "70 km/h travel speed on the road of grade B" is selected, under which the comparison of vehicle responses between semi-active suspension and passive suspension is made. Results show that the vertical vibration is effectively diminished by using semi-active suspension with linear quadratic gaussian controller. Compared with passive suspension, the riding comfort is improved and the adverse effect on handling stability is eliminated. The three-axle vehicle with semi-active suspension has good adaptability to various working conditions.

关键词： Three-axle vehicle semi-active suspension linear quadratic gaussian control analytic hierarchy process riding comfort

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ROBUST linear quadratic gaussian control FOR FLEXIBLE STRUCTURES

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JOURNAL OF GUIDANCE control AND DYNAMICS 1990年第1期13卷 66-72页

作者： BLELLOCH, PA MINGORI, DL UNIV CALIF LOS ANGELES DEPT MECH AEROSP & NUCL ENGNLOS ANGELESCA 90024

A procedure is developed to deal with performance and robustness issues in the design of multiple-input multiple-output compensators for lightly damped flexible structures. The procedure is based upon representing errors in the plant design model as structured uncertainties, and applying a modified linear quadratic gaussian design method. The cost function in the regulator problem and the process noise model in the estimator problem are varied in a manner that reflects specific parameter uncertainty including frequency, damping, or modal displacement errors. Numerical examples dealing with the control of a large flexible space antenna with uncertain frequencies demonstrate the application of the method.

关键词： Flexible Structures linear quadratic gaussian control Multiple Input Multiple Output Space Antenna linear quadratic Regulator Finite Element Modeling gaussian White Noise Full State Feedback Viscoelastic Damping Spectral Density

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Active linear quadratic gaussian control of the vibration of a flexible beam with a time-varying mass

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND control ENGINEERING 2015年第6期229卷 475-484页

作者： Ma, Chicheng Zhang, Xinong Xie, Shilin Luo, Yajun Xi An Jiao Tong Univ State Key Lab Mech Struct Strength & Vibrat Xian 710049 Peoples R China

A linear quadratic gaussian method for active vibration control of a flexible beam with a time-varying mass is studied in this article. As the time-varying mass can change the resonance frequencies of system and induce instability of system, the vibration control of time-varying mass systems using piezoelectric actuators has been the subject of recent interest. The equation of motion of a beam with a time-varying concentrated mass is obtained by using admissible functions and the principle of separation of variables. Then, active control using piezoelectric actuators is simulated for the time-varying mass system. The linear quadratic gaussian control strategy is employed for the suppression of transverse vibration of the beam with time-varying mass under different conditions. The numerical results show that the proposed scheme can attenuate the vibration of the variable mass system effectively in the interested frequency range. The control method can be used for the beam with constant mass or time-varying mass.

关键词： Active vibration control piezoelectric actuator linear quadratic gaussian control time-varying mass

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linear quadratic gaussian control with advanced continuous-time disturbance models for building thermal regulation

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APPLIED ENERGY 2022年 327卷

作者： Thilker, Christian Ankerstjerne Jorgensen, John Bagterp Madsen, Henrik Tech Univ Denmark Dept Appl Math & Comp Sci Asmussens AlleBldg 303B DK-2800 Lyngby Denmark

This paper introduces a linear quadratic control scheme for a continuous-time system with observations taken at discrete times. Particular attention is given to the derivation of the disturbance terms in the model. control performance may depend critical on accurate disturbance forecasts. This is the case for building climate control, where solar rays pass through e.g. windows and deliver significant amounts of energy and the dynamics can be very fast, fluctuating, and spontaneous. We thus argue that it is critical for control performance to sufficiently describe and include disturbances in the control description to obtain satisfactory control accuracy. We suggest and derive in details a control framework based on continuous-time stochastic differential equations (SDEs) and linear quadratic gaussian control using an advanced continuous-time disturbance model to supply disturbance forecasts. The numerical simulation results suggest that control with embedded forecasts handles uncertainties well and provides up to 26% performance improvements compared to standard disturbance mitigation techniques. Furthermore, we demonstrate that the quadratic controller has a useful trade-off between variability in the control signal, economic cost, and variability around the reference point.

关键词： linear quadratic gaussian control Stochastic differential equations Non-linear disturbance models Continuous-time Smart energy systems

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Tip-tilt disturbance model identification based on non-linear least squares fitting for linear quadratic gaussian control

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OPTICS COMMUNICATIONS 2018年 415卷 31-38页

作者： Yang, Kangjian Yang, Ping Wang, Shuai Dong, Lizhi Xu, Bing Chinese Acad Sci Key Lab Adapt Opt Chengdu 610209 Sichuan Peoples R China Chinese Acad Sci Inst Opt & Elect Chengdu 610209 Sichuan Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China

We propose a method to identify tip-tilt disturbance model for linear quadratic gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that linear quadratic gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the linear quadratic gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Adaptive optics linear quadratic gaussian control Vibration control Model identification

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Discounted cost linear quadratic gaussian control for descriptor systems

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INTERNATIONAL JOURNAL OF control 2022年第5期95卷 1349-1362页

作者： Mena, Hermann Pfurtscheller, Lena-Maria Voigt, Matthias Univ Yachay Tech Dept Math San Miguel De Urcuqui Ecuador Univ Innsbruck Inst Math Innsbruck Austria Univ Hamburg Fachbereich Math Hamburg Germany Tech Univ Berlin Inst Math Berlin Germany

We consider the linear quadratic gaussian control problem with a discounted cost functional for descriptor systems on the infinite time horizon. Based on recent results from the deterministic framework, we characterise the feasibility of this problem using a linear matrix inequality. In particular, conditions for existence and uniqueness of optimal controls are derived, which are weaker compared to the standard approaches in the literature. We further show that also for the stochastic problem, the optimal control is given in terms of the stabilising solution of the Lur'e equation, which generalises the algebraic Riccati equation. We conclude our paper by examining an application of our theory to fluid dynamics problems.

关键词： Descriptor systems linear quadratic gaussian control Kalman– Yakubovich– Popov inequality dissipation inequality Navier– Stokes equation

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Adaptive linear quadratic gaussian control: The cost-biased approach revisited

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SIAM JOURNAL ON control AND OPTIMIZATION 1998年第6期36卷 1890-1907页

作者： Campi, MC Kumar, PR Univ Brescia Dept Elect Engn & Automat I-25123 Brescia Italy Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA

In adaptive control, a standard approach is to resort to the so-called certainty equivalence principle which consists of generating some standard parameter estimate and then using it in the control law as if it were the true parameter. As a consequence of this philosophy, the estimation problem is decoupled from the control problem and this substantially simplifies the corresponding adaptive control scheme. On the other hand, the complete absence of dual properties makes certainty equivalent controllers run into an identifiability problem which generally leads to a strictly suboptimal performance. In this paper, we introduce a cost-biased parameter estimator to overcome this difficulty. This estimator is applied to a linear quadratic gaussian controller. The corresponding adaptive scheme is proven to be stable and optimal when the unknown system parameter lies in an infinite, yet compact, parameter set.

关键词： adaptive control linear quadratic gaussian control self-optimizing control cost-biased approach certainty equivalence

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