Stability margins of singularly perturbed discrete-time systems based on state feedback and linear quadratic optimal control

1992 ◽  
Vol 13 (3) ◽  
pp. 227-245 ◽  
Author(s):  
Chiu-Pin Cheng ◽  
Tzuu-Hseng S. Li ◽  
York-Yih Sun
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
State Feedback ◽  
Singularly Perturbed ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Stability Margins ◽  
Discrete Time Systems ◽  
Quadratic Optimal Control ◽  
Time Systems

scholarly journals Stochastic Linear Quadratic Optimal Control with Indefinite Control Weights and Constraint for Discrete-Time Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Xikui Liu ◽  
Guiling Li ◽  
Yan Li
Keyword(s):  
Optimal Control ◽  
Riccati Equation ◽  
Discrete Time ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Discrete Time Systems ◽  
Quadratic Optimal Control ◽  
The Cost ◽  
Time Systems ◽  
Difference Riccati Equation

The Karush-Kuhn-Tucker (KKT) theorem is used to study stochastic linear quadratic optimal control with terminal constraint for discrete-time systems, allowing the control weighting matrices in the cost to be indefinite. A generalized difference Riccati equation is derived, which is different from those without constraint case. It is proved that the well-posedness and the attainability of stochastic linear quadratic optimal control problem are equivalent. Moreover, an optimal control can be denoted by the solution of the generalized difference Riccati equation.

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.

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