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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)

- James C Spall
- 2004

This paper extends results presented in preliminary form at the 2003 ACC to provide more theoretical justification for the Monte Carlo method (Sect. 4), to introduce the use of antithetic random numbers (Sect. 5), and to carry out a new numerical study (Sect. 6). A more complete version of this paper is available upon request. Abstract: The Fisher… (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)

—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)

We present a stochastic approximation algorithm based on penalty function method and a simultaneous perturbation gradient estimate for solving stochastic optimisation problems with general inequality constraints. We present a general convergence result that applies to a class of penalty functions including the quadratic penalty function, the augmented… (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)