Risk-sensitive linear/quadratic/gaussian control

1981 ◽  
Vol 13 (4) ◽  
pp. 764-777 ◽  
Author(s):  
P. Whittle
Keyword(s):  
Optimal Control ◽  
Kalman Filter ◽  
Risk Aversion ◽  
Separation Theorem ◽  
Linear Quadratic ◽  
Criterion Function ◽  
Linear Quadratic Gaussian ◽  
State Estimate ◽  
Certainty Equivalence ◽  
Risk Sensitive

The conventional linear/quadratic/Gaussian assumptions are modified in that minimisation of the expectation of cost G defined by (2) is replaced by minimisation of the criterion function (5). The scalar –θ is a measure of risk-aversion. It is shown that modified versions of certainty equivalence and the separation theorem still hold, that optimal control is still linear Markov, and state estimate generated by a version of the Kalman filter. There are also various new features, remarked upon in Sections 5 and 7. The paper generalises earlier work of Jacobson.

Risk-sensitive linear/quadratic/gaussian control

1981 ◽  
Vol 13 (04) ◽  
pp. 764-777 ◽  
Author(s):  
P. Whittle
Keyword(s):  
Optimal Control ◽  
Kalman Filter ◽  
Risk Aversion ◽  
Separation Theorem ◽  
Linear Quadratic ◽  
Criterion Function ◽  
Linear Quadratic Gaussian ◽  
State Estimate ◽  
Certainty Equivalence ◽  
Risk Sensitive

The conventional linear/quadratic/Gaussian assumptions are modified in that minimisation of the expectation of cost G defined by (2) is replaced by minimisation of the criterion function (5). The scalar –θ is a measure of risk-aversion. It is shown that modified versions of certainty equivalence and the separation theorem still hold, that optimal control is still linear Markov, and state estimate generated by a version of the Kalman filter. There are also various new features, remarked upon in Sections 5 and 7. The paper generalises earlier work of Jacobson.

scholarly journals Route Planning: B

2021 ◽  
pp. 259-269
Author(s):  
Jean Walrand
Keyword(s):  
Route Planning ◽  
The State ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Certainty Equivalence ◽  
Markov Decision Problems ◽  
Markov Decision ◽  
The Cost ◽  
Elegant Solution

AbstractThere is a class of control problems that admit a particularly elegant solution: the linear quadratic Gaussian (LQG) problems. In these problems, the state dynamics and observations are linear, the cost is quadratic, and the noise is Gaussian. Section 14.1 explains the theory of LQG problems when one observes the state. Section 14.2 discusses the situation when the observations are noisy and shows the remarkable certainty equivalence property of the solution. Section 14.3 explains how noisy observations affect Markov decision problems.

Linear Quadratic Gaussian Optimal Control for Human Eye Aberration Correction

2014 ◽  
Vol 51 (4) ◽  
pp. 041102
Author(s):  
王波 Wang Bo ◽  
钮赛赛 Niu Saisai ◽  
吴卫明 Wu Weiming
Keyword(s):  
Optimal Control ◽  
Aberration Correction ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Human Eye

Kalman Filter Control Embedded into the Reinforcement Learning Framework

2004 ◽  
Vol 16 (3) ◽  
pp. 491-499 ◽  
Author(s):  
István Szita ◽  
András Lőrincz
Keyword(s):  
Optimal Control ◽  
Kalman Filter ◽  
Reinforcement Learning ◽  
Learning Rule ◽  
Slight Modification ◽  
Linear Quadratic ◽  
Filter Model ◽  
Learning Framework ◽  
Value Estimation ◽  
On Line

There is a growing interest in using Kalman filter models in brain modeling. The question arises whether Kalman filter models can be used on-line not only for estimation but for control. The usual method of optimal control of Kalman filter makes use of off-line backward recursion, which is not satisfactory for this purpose. Here, it is shown that a slight modification of the linear-quadratic-gaussian Kalman filter model allows the on-line estimation of optimal control by using reinforcement learning and overcomes this difficulty. Moreover, the emerging learning rule for value estimation exhibits a Hebbian form, which is weighted by the error of the value estimation.

Microclimate control of a greenhouse by adaptive Generalized Linear Quadratic strategy

2018 ◽  
Vol 11 (1) ◽  
pp. 377 ◽  
Author(s):  
Mohamed Essahafi ◽  
Mustapha Ait Lafkih
Keyword(s):  
Optimal Control ◽  
Least Squares ◽  
Recursive Least Squares ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Advanced Technique ◽  
Online Identification ◽  
State Models ◽  
The Cost ◽  
And Control

<p>To highlight the conceptual aspects related to the implementation of techniques optimal control in the form state, we present in this paper, the identification and control of the temperature and humidity of the air inside a greenhouse. Using respectively an online identification based on the recursive least squares with forgotten Factor method and the multivariable adaptive linear quadratic Gaussian approach which the advanced technique (LQG) is presented.  The design of this controller parameters is based on state models identified directly from measured greenhouse data. hence the performances of the controller developed are illustrated by different tests and simulations on identified models of a greenhouse. Discussions on the results obtained are then processed in the paper to show the effectiveness of the controller in terms of stability and optimization of the cost of control.</p>

LQG Control for Nonstandard Singularly Perturbed Discrete-Time Systems

2004 ◽  
Vol 126 (4) ◽  
pp. 860-864 ◽  
Author(s):  
Beom-Soo Kim ◽  
Young-Joong Kim ◽  
Myo-Taeg Lim
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Discrete Time ◽  
Singularly Perturbed ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Reduced Order ◽  
Discrete Time Systems ◽  
Time Systems

In this paper we present a control method and a high accuracy solution technique in solving the linear quadratic Gaussian problems for nonstandard singularly perturbed discrete time systems. The methodology that exists in the literature for the solution of the standard singularly perturbed discrete time linear quadratic Gaussian optimal control problem cannot be extended to the corresponding nonstandard counterpart. The solution of the linear quadratic Gaussian optimal control problem is obtained by solving the pure-slow and pure-fast reduced-order continuous-time algebraic Riccati equations and by implementing the pure-slow and pure-fast reduced-order Kalman filters. In order to show the effectiveness of the proposed method, we present the numerical result for a one-link flexible robot arm.

scholarly journals Temperature Control of Stirred Tank Heater using Optimal Control Technique

2020 ◽  
Author(s):  
Mustefa Jibril ◽  
Messay Tadese ◽  
Eliyas Alemayehu
Keyword(s):  
Optimal Control ◽  
Temperature Control ◽  
Open Loop ◽  
Loop System ◽  
Stirred Tank ◽  
Control Technique ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Quadratic Integral

This paper presents the application of optimal control problem in modeling of stirred tank heater temperature control. The analysis of the open loop system shows that the system is not efficient without a controller. Linear Quadratic Gaussian (LQG) and Linear Quadratic Integral (LQI) controllers are used to increase the performance of the system. Comparison of the closed loop system with the proposed controllers have been done with Matlab/Simulink Toolbox and a promising results have been analyzed.

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