ℓ1-regularization methodologies have appeared recently in many pattern recognition and image processing tasks frequently connected to ℓ1-optimization in the control theory. We consider the problem of optimal stabilizing controller synthesis for a discrete non-minimum phase dynamic plant described by a linear difference equation with an additive unknown-but-bounded noise. Under considering the “worst” case of noise, the solving of these optimization problem has a combinatorial complexity. The choosing of an appropriate sufficiently high sampling rate allows to achieve an arbitrarily small level of suboptimality using a noncombinatorial algorithm. In this paper, we suggest to use fractional delays to achieve a small level of suboptimality without increasing the sampling rate so much. We propose an approximation of the fractional lag with a combination of rounding and a first-order fractional lag filter. The suggested approximation of the fractional delay is illustrated via a simulation example with a non-minimum phase second-order plant. The proposed methodology appears to be suitable to be used in various pattern recognition approaches.

History matching is the process of integrating dynamic production data in the reservoir model. It consists in estimation of uncertain model parameters such that oil or water production data from flow simulation become close to observed dynamic data. Various optimization methods can be used to estimate the model parameters. Simultaneous perturbation stochastic approximation (SPSA) is one of the stochastic approximation algorithms. It requires only two objective function measurements for gradient approximation per iteration. Also parameters estimated by this algorithm might converge to their true values under arbitrary bounded additive noise, while many other optimization algorithms require the noise to have zero mean. SPSA algorithm has not been well explored for history matching problems and has been applied only to simple Gaussian models. In this paper, we applied SPSA to history matching of binary channelized reservoir models. We also used SPSA in combination with parameterization method CNN-PCA. And we considered the case of complex noise in observed production data and with objective function that does not require assumptions of normality of the observations, which is common in history matching literature. We experimentally showed that SPSA method can be successfully used for history matching of non-Gaussian geological models with different types of noise in observations and outperforms Particle Swarm Optimization by convergence speed.