Abstract
The aim of the given paper is development of a parametric identification approach for a closedloop system when the parameters of a discrete-time linear time-invariant (LTI) dynamic system as well as that of LQG (Linear Quadratic Gaussian) controller are not known and ought to be calculated. The recursive techniques based on an the maximum likelihood(M) and generalized maximum likelihood(GM) estimator algorithms are applied here in the calculation of the system as well as noise filter parameters. Afterwards, the recursive parameter estimates are used in each current iteration to determine unknown parameters of the LQG-controller, too. The results of numerical simulation by computer are discussed.
Highlights
The stochastic optimal control of a discrete-time linear time-invariant (LTI) dynamic system is performed using the LQG approach [1]
In designing a robust control system, one ought to determine the type of uncertainties appearing in the system to be controlled [6]
Nonnormal noise, and the presence of outliers, degrades the performance of a system acting in a closed-loop
Summary
The stochastic optimal control of a discrete-time LTI dynamic system is performed using the LQG approach [1]. Ordinary recursive techniques used for a parametric identification of LQG control systems, as a rule, are inefficient In such a case, robust recursive techniques ought to be applied here. We introduce the robust recursive GM- and M- procedures for calculating robust estimates of the parameters of LTI dynamic systems, acting in a closed-loop in the case of correlated noise with outliers in it. The ordinary least-squares estimator could be obtained as a special case of (1) by setting in it the function τ (x(t), r) = r2/2 with ∂τ (x(t), r)/∂r = ζ {x(t), r}, where r is a short form of the standardized residual.
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