Linear-quadratic-Gaussian problem for a new class of singularly perturbed stochastic systems

2016 ◽  
Author(s):  
Kliti Kodra ◽  
Zoran Gajic
Keyword(s):  
Stochastic Systems ◽  
Singularly Perturbed ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
New Class

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.

Design of a performance-adaptive proportional—integral—derivative controller for stochastic systems

2008 ◽  
Vol 222 (7) ◽  
pp. 691-700 ◽  
Author(s):  
T Yamamoto ◽  
Y Ohnishi ◽  
S L Shah
Keyword(s):  
Process Model ◽  
Stochastic Systems ◽  
Proportional Integral Derivative ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Adaptive Controllers ◽  
Proportional Integral Derivative Controller ◽  
Control Loops ◽  
Proportional Integral ◽  
Control Scheme

In order to manufacture high-quality products it is necessary to regularly monitor the performance of the control loops that regulate the quality variables of interest. This paper describes a design scheme of performance-adaptive controllers which are based on the above control strategy. According to the proposed control scheme, the output prediction error is monitored regularly and system identification is initiated if this error exceeds a user-defined threshold. Subsequently proportional—integral—derivative (PID) parameters are updated for the new model. Optimal PID parameters are calculated based on the linear quadratic Gaussian (LQG) trade-off curve obtained for the reidentified process model. The behaviour of the proposed control scheme is numerically evaluated by some simulation examples.

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