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—Stochastic approximation (SA) has long been applied for problems of minimizing loss functions or root finding with noisy input information. As with all stochastic search algorithms , there are adjustable algorithm coefficients that must be specified, and that can have a profound effect on algorithm performance. It is known that choosing these coefficients… (More)

—It is known that a stochastic approximation (SA) analogue of the deterministic Newton-Raphson algorithm provides an asymptotically optimal or near-optimal form of stochastic search. However, directly determining the required Jacobian matrix (or Hessian matrix for optimization) has often been difficult or impossible in practice. This paper presents a… (More)

This paper considers the use of neural networks (NN's) in controlling a nonlinear, stochastic system with unknown process equations. The approach here is based on using the output error of the system to train the NN controller without the need to assume or construct a separate model (NN or other type) for the unknown process dynamics. To implement such a… (More)

Covariance calculations and confidence intervals for maximum likelihood estimates (MLEs) are commonly used in identification and statistical inference. To accurately construct such confidence intervals, one typically needs to know the covariance of the MLE. Standard statistical theory shows that the normalized MLE is asymptotically normally distributed with… (More)

This paper considers the design of robust neural network tracking controllers for nonlinear systems. The neural network is used in the closed-loop system to estimate the nonlinear system function. We introduce the conic sector theory to establish a robust neural control system, with guaranteed boundedness for both the input/output (I/O) signals and the… (More)

Multivariate stochastic optimization plays a major role in the analysis and control of many real-world systems. In almost all large-scale practical optimization problems, it is necessary to use a mathematical algorithm that iteratively seeks out the solution because an analytical (closed-form) solution is rarely available. In the above spirit, the "… (More)