We study the complexity of approximating monotone Boolean functions with disjunctive normal form (DNF) formulas, exploring two main directions. First, we construct DNF approximators for arbitrary monotone functions achieving one-sided error: we show that every monotone f can be ε-approximated by a DNF g of size 2n−Ωε( √ n) satisfying g(x) ≤ f(x) for all x ∈ {0, 1}. This is the first non-trivial...

Uncertainty and unknown nonlinearity are often inevitable in the suspension systems, which were solved using fuzzy logic system or neural networks. However, these methods restricted by structural complexity of controller huge computing cost. Meanwhile, estimation error such approximators is affected adopted adaptive laws learning gains. Thus, view above problem, this paper proposes approximatio...

Berg and Ulfberg and Amano and Maruoka have used CNF-DNF-approximators to prove exponential lower bounds for the monotone network complexity of the clique function and of Andreev's function. We show that these approximators can be used to prove the same lower bound for their non-monotone network complexity. This implies P not equal NP.

This paper presents a Neural Network (NN) based tool for the modeling, simulation and analysis of aircraft Sensor Failure, Detection, Identification and Accommodation (SFDIA) problems. The SFDIA scheme exploits the analytical redundancy of the system to provide validation capability to measurement devices by employing Neural Networks as on-line non-linear approximators. The tool allows evaluati...

In direct adaptive control, the adaptation mechanism attempts to adjust a parameterized nonlinear controller to approximate an ideal controller. In the indirect case, however, we approximate parts of the plant dynamics that are used by a feedback controller to cancel the system nonlinearities. In both cases, ‘‘approximators’’ such as linear mappings, polynomials, fuzzy systems, or neural networ...

This report proofs that discriminative Restricted Boltzmann Machines (RBMs) are universal approximators for discrete data by adapting existing universal approximation proofs for generative RBMs. Discriminative Restricted Boltzmann Machines are Universal Approximators for Discrete Data Laurens van der Maaten Pattern Recognition & Bioinformatics Laboratory Delft University of Technology

Exponentially stable trajectory following of robotic manipulators under a class of adaptive controls. In this paper we investigate the problem of fault diagnosis in rigid-link robotic manipulators. A learning architecture, with neural networks as on-line approximators of the oo-nominal system behavior, is used for monitoring the robotic system for faults. The approximation of the oo-nominal beh...

Adaptive control for nonlinear time-varying systems is of both theoretical and practical importance. In this paper, we propose an adaptive control methodology for a class of nonlinear systems with a time-varying structure. This class of systems is composed of interpolations of nonlinear subsystems which are input–output feedback linearizable. Both indirect and direct adaptive control methods ar...

We establish a scale separation of Kolmogorov width type between subspaces given Banach space under the condition that sequence linear maps converges much faster on one subspaces. The general technique is then applied to show reproducing kernel Hilbert spaces are poor $$L^{2}$$ -approximators for class two-layer neural networks in high dimension, and multi-layer with small path norm approximato...