The recursive least square is widely used in parameter identification. But it is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm- recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. It is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.

Abstract-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 Li and Yorke. 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.

This paper focuses on a problem of sliding mode output tracking for non-minimum-phase nonlinear systems whose zero dynamics is not stable. Sliding mode consists of continuous power functions instead of switch functions, and the power of the function has the term of fraction whose denominator and numerator are all positive odd numbers, so the chattering phenomenon can be avoided. The method of the design is based on the centre manifold theory, and a sliding manifold can be constructed by the combination of the polynomial of tracing error and internal dynamics variable.

Proportion integral differential generalized predictive control(PID-GPC), a new type of generalized predictive control (GPC) is introduced, and its quality is analyzed with internal model control (IMC). A very important characteristic, which distinguishes CPC from ordinary IMC, and the robust effect are found. At the same time, a robust region is obtained according to the control laws, so that the defect that the robust analysis could be carried out only with stable models is overcome. It is verified that the robustness of PID-GPC is stronger than general GPC.

This paper reports a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz, R