In this letter, a novel nonlinear neural network (NN) predictive control strategy based on the new tent-map chaotic particle swarm optimization (TCPSO) is presented. The TCPSO incorporating tent-map chaos, which can avoid trapping to local minima and improve the searching performance of standard particle swarm optimization (PSO), is applied to perform the nonlinear optimization to enhance the convergence and accuracy. Numerical simulations of two benchmark functions are used to test the performance of TCPSO. Furthermore, simulation on a nonlinear plant is given to illustrate the effectiveness of the proposed control scheme.

Original Hebbian encoding scheme of bidirectional associative memory (BAM) provides a poor pattern capacity and recall performance. Based on Rosenblatt's perceptron learning algorithm, the pattern capacity of BAM is enlarged, and perfect recall of all training pattern pairs is guaranteed. However, these methods put their emphases on pattern capacity, rather than error correction capability which is another critical point of BAM. This paper analyzes the sensitivity to noise in BAM and obtains an interesting idea to improve noise immunity of BAM. Some researchers have found that the noise sensitivity of BAM relates to the minimum absolute value of net inputs (MAV). However, in this paper, the analysis on failure association shows that it is related not only to MAV but also to the variance of weights associated with synapse connections. In fact, it is a positive monotone increasing function of the quotient of MAV divided by the variance of weights. This idea provides an useful principle of improving error correction capability of BAM. Some revised encoding schemes, such as small variance learning for BAM (SVBAM), evolutionary pseudorelaxation learning for BAM (EPRLAB) and evolutionary bidirectional learning (EBL), have been introduced to illustrate the performance of this principle. All these methods perform better than their original versions in noise immunity. Moreover, these methods have no negative effect on the pattern capacity of BAM. The convergence of these methods is also discussed in this paper. If there exist solutions, EPRLAB and EBL always converge to a global optimal solution in the senses of both pattern capacity and noise immunity. However, the convergence of SVBAM may be affected by a preset function.

A linear model of recurrent neural networks, called the Elman networks, is combined with the simple nonlinear modulo (mod) operation on its linear activated function so as to generate chaos purposely. Conditions on the weight matrix are obtained, under which the generated chaos satisfies the mathematical definition of chaos in the sense of T.Y. Li and J.A. Yorke (1975). Some simple and representative weight matrices are constructed for designing such Elman networks that can generate Li-Yorke chaos. Several numerical simulations are shown to verify and visualize the design.