A Nonlinear System Identification Method Based on Adaptive Neural Network

Nonlinear system identification (NSI) is of great significance to modern scientific engineering and control engineering. Despite their identification ability, the existing analysis methods for nonlinear systems have several limitations. The neural network (NN) can overcome some of these limitations in NSI, but fail to achieve desirable accuracy or training speed. This paper puts forward an NSI method based on adaptive NN, with the aim to further improve the convergence speed and accuracy of NN-based NSI. Specifically, a generic model-based nonlinear system identifier was constructed, which integrates the error feedback and correction of predictive control with the generic model theory. Next, the radial basis function (RBF) NN was optimized by adaptive particle swarm optimization (PSO), and used to build an NSI model. The effectiveness and speed of our model were verified through experiments. The research results provide a reference for applying the adaptive PSO-optimized RBFNN in other fields

What do we pay for asymmetric information? The evolution of mechanisms in online markets

The appearance of the Internet reduces transaction costs greatly, and brings the boom of online markets. While we are trying to regard it as the most realistic approximation of perfect competition market, the asymmetric information and a series of problems caused by it stop us from dreaming. As the old saying goes, there is no free lunch. This summer witnessed the collapse of the reputation system in Taobao, the biggest online transaction website in China. In fact, during the evolution of mechanisms in online markets, reputation, punishment and barriers to entry have been established in turn. What do we pay for maintaining these mechanisms? In which circumstance will they be effective? In this paper I try to build a series of models within the principal-agent frame- work and repeated games to explain why and what we should pay for asymmetric information while enjoying shopping online. Specifically, these mechanisms are considered step by step and their boundary validation conditions are discussed. Finally, as the conclusion indicates, the more range that a mechanism is effective, the more opportunity cost should be paid as a rent for information.online market; mechanism design; reputation;

Smaller SDP for SOS Decomposition

A popular numerical method to compute SOS (sum of squares of polynomials) decompositions for polynomials is to transform the problem into semi-definite programming (SDP) problems and then solve them by SDP solvers. In this paper, we focus on reducing the sizes of inputs to SDP solvers to improve the efficiency and reliability of those SDP based methods. Two types of polynomials, convex cover polynomials and split polynomials, are defined. A convex cover polynomial or a split polynomial can be decomposed into several smaller sub-polynomials such that the original polynomial is SOS if and only if the sub-polynomials are all SOS. Thus the original SOS problem can be decomposed equivalently into smaller sub-problems. It is proved that convex cover polynomials are split polynomials and it is quite possible that sparse polynomials with many variables are split polynomials, which can be efficiently detected in practice. Some necessary conditions for polynomials to be SOS are also given, which can help refute quickly those polynomials which have no SOS representations so that SDP solvers are not called in this case. All the new results lead to a new SDP based method to compute SOS decompositions, which improves this kind of methods by passing smaller inputs to SDP solvers in some cases. Experiments show that the number of monomials obtained by our program is often smaller than that by other SDP based software, especially for polynomials with many variables and high degrees. Numerical results on various tests are reported to show the performance of our program.Comment: 18 page