Search

An approach is proposed to avoid model structure determination in system identification using NARMAX (nonlinear auto-regressive moving average with exogenous inputs) model. Identification procedure is formulated as an optimization procedure of a special class of Hopfield network in the proposed approach. The particular structure of these Hopfield networks can avoid the local optimum problem. Training of these Hopfield network achieves model structure determination and parameter estimation. Convergence of Hopfield networks guarantees that a NARMAX model of random initial state will approach a valid identification model with accurate state parameters. Results of two simulation examples illustrate that this approach is efficient and simple.

A popular version of optimal control problems is discussed and a nonlinear two point boundary value problem embedded in the optimal control problem is then converted into an initial-value problem according to the boundary value sensitivity differential equations. An integration method for matrix differential equations is also presented. In this novel way, the exact solutions are obtained for the linear optimal control problems. Two illustrative numerical examples are given to show the power and efficiency.

Fuzzy disturbance observer and feedback linearization method are adopted to solve the attitude control problem for the rigid spacecraft driven by three orthogonal reaction flywheels. Since the spacecraft model is nonlinear and strongly coupled, it is difficult to design the controller directly. Differential geometry theory based feedback linearization technique is used to convert the original model to the linear decoupled SISO system models, which greatly simplifies the controller design. The fuzzy disturbance observer based on fuzzy basis function vector is used to observe the disturbance torque. The estimated value of disturbance torque is converted to equivalent control by the gain adjustment part. The equivalent control along with the control obtained by feedback linearization are then used as the input to the reaction flywheels. Simulation results show that the proposed method can counteract the effect of the disturbance torque, and achieve accurate tracking of attitude.

Support vector regression (SVR) is an effective method for the predication of chaotic time-series, which is a fundamental topic of nonlinear dynamics. Through analyzing the possible variation of support vector sets after new samples are inserted to the training set, a novel SVR algorithm is proposed; thus an online learning algorithm is set up. In connection with the specific characteristics of chaotic signals, a wavelet kernel satisfying wavelet frames is also presented. The wavelet kernel can approximate arbitrary functions, and is especially suitable for local processing; hence the generalization ability of SVR is improved. To illustrate the good performance of the online wavelet SVR, a benchmark problem, i.e. the online prediction of chaotic Mackey-Glass time-series, is considered. The simulation results indicate that the online wavelet SVR algorithm outperforms the existing algorithms in higher efficiency of learning as well as better accuracy of prediction.

Based on the property that the wavelet can approximate any nonlinear continuous function in the compact supporting set,a new method is presented to control chaos.By this method the trajectories of some typical chaotic systems,such as Duffing equation,Lorenz model,etc.,are controlled to the target orbits or points.It is proved that the wavelet base control algorithm is feasible and control effect is better.