A general transfer-function approach to the discrete-time steady-state linear quadratic Gaussian stochastic control problem

1979 ◽  
Vol 29 (3) ◽  
pp. 361-386 ◽  
Author(s):  
U. SHAKED
Keyword(s):  
Steady State ◽  
Transfer Function ◽  
Control Problem ◽  
Stochastic Control ◽  
Discrete Time ◽  
Function Approach ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Stochastic Control Problem

Explicit Solution of LQG Compensator Design Problem for Flexible Structures With Collocated Rate Sensors

1993 ◽  
Author(s):  
A. V. Balakrishnan
Keyword(s):  
Transfer Function ◽  
Stochastic Control ◽  
Explicit Solution ◽  
Design Problem ◽  
Flexible Structures ◽  
Continuum Models ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Compensator Design ◽  
Positive Realness

Abstract We present an explicit solution to a stochastic control problem generally referred to as the LQG (Linear Quadratic Gaussian) or Stochastic Regulator problem for continuum models of flexible structures with collocated rate sensors, which holds a fortiori for FEM or truncated modal models. Robustness properties accruing from the positive realness of the optimal compensator transfer function are described, and convergence of modal approximations is proved. Preliminary experimental results on the NASA LaRC SCOLE testbed are included.

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.

Sign in / Sign up

Export Citation Format

Share Document