Further studies on stability analysis of nonlinear Roesser-type two-dimensional systems

This paper is concerned with further relaxations of the stability analysis of nonlinear Roesser-type two-dimensional （2D） systems in the Takagi-Sugeno fuzzy form. To achieve the goal, a novel slack matrix variable technique, which is homogenous polynomially parameter-dependent on the normalized fuzzy weighting functions with arbitrary degree, is developed and the algebraic properties of the normalized fuzzy weighting functions are collected into a set of augmented matrices. Consequently, more information about the normalized fuzzy weighting functions is involved and the relaxation quality of the stability analysis is significantly improved. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed result.

Short-term Wind Power Prediction Based on Soft Margin Multiple Kernel Learning Method

For short-term wind power prediction,a soft margin multiple kernel learning(MKL)method is proposed.In order to improve the predictive effect of the MKL method for wind power,a kernel slack variable is introduced into each base kernel to solve the objective function.Two kinds of soft margin MKL methods based on hinge loss function and square hinge loss function can be obtained when hinge loss functions and square hinge loss functions are selected.The improved methods demonstrate good robustness and avoid the disadvantage of the hard margin MKL method which only selects a few base kernels and discards other useful kernels when solving the objective function,thereby achieving an effective yet sparse solution for the MKL method.In order to verify the effectiveness of the proposed method,the soft margin MKL method was applied to the second wind farm of Tianfeng from Xinjiang for short-term wind power single-step prediction,and the single-step and multi-step predictions of short-term wind power was also carried out using measured data provided by alberta electric system operator(AESO).Compared with the support vector machine(SVM),extreme learning machine(ELM),kernel based extreme learning machine(KELM)methods as well as the SimpleMKL method under the same conditions,the experimental results demonstrate that the soft margin MKL method with different loss functions can efficiently achieve higher prediction accuracy and good generalization performance for short-term wind power prediction,which confirms the effectiveness of the method.

Optimal two-impulse space interception with multiple constraints

We consider optimal two-impulse space interception problems with multiple constraints.The multiple constraints are imposed on the terminal position of a space interceptor,impulse and impact instants,and the component-wise magnitudes of velocity impulses.These optimization problems are formulated as multi-point boundary value problems and solved by the calculus of variations.Slackness variable methods are used to convert all inequality constraints into equality constraints so that the Lagrange multiplier method can be used.A new dynamic slackness variable method is presented.As a result,an indirect optimization method is developed.Subsequently,our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles.A number of conclusions for local optimal solutions have been drawn based on highly accurate numerical solutions.Specifically,by numerical examples,we show that when time and velocity impulse constraints are imposed,optimal two-impulse solutions may occur;if two-impulse instants are free,then a two-impulse space interception problem with velocity impulse constraints may degenerate to a one-impulse case.