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Purpose The purpose of this paper is to probe the recursive identification of piecewise affine Hammerstein models directly by using input-output data. To explain the identification process of a parametric piecewise affine nonlinear function, the authors prove that the inverse function corresponding to the given piecewise affine nonlinear function is also an equivalent piecewise affine form. Based on this equivalent property, during the detailed identification process with respect to piecewise affine function and linear dynamical system, three recursive least squares methods are proposed to identify those unknown parameters under the probabilistic description or bounded property of noise. Design/methodology/approach First, the basic recursive least squares method is used to identify those unknown parameters under the probabilistic description of noise. Second, multi-innovation recursive least squares method is proposed to improve the efficiency lacked in basic recursive least squares method. Third, to relax the strict probabilistic description on noise, the authors provide a projection algorithm with a dead zone in the presence of bounded noise and analyze its two properties. Findings Based on complex mathematical derivation, the inverse function of a given piecewise affine nonlinear function is also an equivalent piecewise affine form. As the least squares method is suited under one condition that the considered noise may be a zero mean random signal, a projection algorithm with a dead zone in the presence of bounded noise can enhance the robustness in the parameter update equation. Originality/value To the best knowledge of the authors, this is the first attempt at identifying piecewise affine Hammerstein models, which combine a piecewise affine function and a linear dynamical system. In the presence of bounded noise, the modified recursive least squares methods are efficient in identifying two kinds of unknown parameters, so that the common set membership method can be replaced by the proposed methods.

To provide a reasonable design scheme to improve the performance of composite wax powder, the ternary complex Na+···graphene oxide (GO)···CH4 was selected as a model system to evaluate the cooperativity effect between the Na+···σ/π and H-bonding interactions in the composite wax powder doped with GO at the M06-2X/6-311++G(2d,p) and MP2/6-311++G(2d,p) levels. The cooperativities in GO···(CH4)n (n = 1∼10) and thermodynamic cooperativity effects in Na+···GO···CH4 were also investigated. Although the changes of the absolute values of H-bonding interactions were slight, from those of relative values, the influence of the Na+···π or Na+···O interaction on the C–H···π, O–H···C or C–H···O interaction was notable upon the formation of ternary systems. The anti-cooperativity effect was found in the cyclic structure, while the cooperativity effect appeared in the linear conformation. The Na+···σ/π and H-bonding interactions as well as cooperativities in Na+···GO···CH4 were stronger than those in Na+···coronene···CH4. The formation of Na+···GO···CH4 is a thermodynamic cooperativity process driven by the enthalpy change. Therefore, it could be inferred that, when graphite powder or carbon black was replaced by GO, the compatibilities could be strengthened among various components, and thus the performance of casting moulds could be improved. Atoms-in-molecules (AIM) and reduced density gradient (RDG) analyses confirmed the cooperativity effect and revealed the nature of the improved performance of composite wax powder with GO. The GO···(CH4)n (n = 1∼3) are positively cooperative, while the negative cooperativity is shown when n = 4∼10.

Here the problem of designing multi-UAVs formation autonomous reconfiguration is considered. Combined with three kinds of cost functions, nonlinear dynamic equations, and four inequality constraints, one nonlinear multiobjective optimization problem is constructed. After applying weighted sum method and separating all equality or inequality constraints, the former nonlinear multiobjective optimization problem can be converted into a standard nonlinear single objective optimization problem. Then the interior point algorithm is applied to solve it. Further some improvements are proposed to avoid rank deficiency of some matrices. The equivalence property between multiobjective optimization and single objective optimization through weighted sum method is proved. Finally the efficiency of the proposed strategy can be confirmed by the simulation example results.

To the direct weight optimization identification of the nonlinear system, we add some linear terms about input sequences in the former linear affine function so as to approximate the nonlinear property. To choose the two classes of unknown weights in the more linear terms, this paper derives the detailed process on how to choose these unknown weights from theoretical analysis and engineering practice, respectively, and makes sure of their key roles between the unknown weights. From the theoretical analysis, the added unknown weights’ auxiliary role can be known in the whole process of approximating the nonlinear system. From the practical analysis, we learn how to transform one complex optimization problem to its corresponding common quadratic program problem. Then, the common quadratic program problem can be solved by the basic interior point method. Finally, the efficiency and possibility of the proposed strategies can be confirmed by the simulation results.

The experimental infrared (IR) spectrum of composite wax powder was investigated. The frequency shifts of the C=C anti-symmetrical stretching mode were observed and the experimental cooperativity effect involving Na+···π interaction was suggested. In order to further reveal the nature of cooperativity effect, the interaction energies in Mn+···coronene···CH4 (Mn+ = Li+, Na+, K+, Be2+, Mg2+ or Ca2+) as the model systems of composite wax powder were calculated by using the B3LYP, M06-2X and MP2 methods with 6-311++G** basis set. The results show that the Mn+···π interactions were strengthened upon the formation of ternary complexes. Although the changes of absolute values of the interactions between CH4 and coronene were not obvious, the relative values were considerably significant upon the formation of ternary complexes. The cooperativity effect was perhaps the reason for the formation of notable advantage of composite wax powder upon the introduction of surfactant with cation into wax powder. Reduced density gradient and atoms-in-molecules analysis confirm the cooperativity effect in Mn+···coronene···CH4, and reveal the nature of the formation of the predominant advantage of composite wax powder.

The interaction of morphine and cholinergic system was shown in previous studies. In the present study, we investigated whether morphine would interact with the cholinergic antagonists, scopolamine and atropine in a Y-maze spatial recognition memory. Pre-test treatments of morphine (5, 1.5, 0.5 mg/kg), scopolamine (1, 0.1 mg/kg), atropine (0.5, 0.1 mg/kg) were used in the experiments, relatively high or low doses were paired respectively as co-administration measures. The results showed that co-administration of morphine 0.5 mg/kg + scopolamine 0.1 mg/kg and morphine 0.5 mg/kg + atropine 0.1 mg/kg disturbed the inspective exploratory behavior (percent of arm duration) but not the inquisitive behavior (percent of arm visits) of the spatial memory retrieval, while the drugs didn’t cause amnesia when single administered of the concerned low doses. Distinct interaction was found between scopolamine and morphine on increasing locomotor activity.

When considering the problem of how to design multi UAV formation keeping optimization model, we combine the kinematic equation of multi UAV, performance index and constrained condition to construct a constrained optimization problem. After some transformation is used in the performance function to decompose the optimization problem, we introduce the Lagrange multiplier vector to construct a Lagrange function of this constrained optimization problem. To obtain the two classes of optimization variables-primal variable and dual variable, we find that all primal variables and dual variables can be formulated to the expressions about one dual variable. Then the gradient projection method from the convex optimization theory is proposed to obtain this dual variable. When this dual variable is solved, all the other optimization variables can also be obtained through simple substitution Finally, the efficiency of the proposed strategy can be confirmed by the simulation results.

In this paper, subspace predictive control strategy is applied to design predictive controller. Given the state space model, the output estimations corresponding to the predictive output is derived to be one explicit function of the measured input-output data. Then using these output estimations, the problem of designing predictive controller is formulated as one optimization problem with equality and inequality conditions. In order to solve this constrain optimization problem, we use dual decomposition idea to change the original constrain optimization problem into an unconstrain optimization problem. So the classical gradient algorithm is put forth to solve the primal dual optimization problem. The problem of designing dual decomposition controller is studied for subspace predictive control strategy under fault condition. For state space equation with fault condition, we establish one function form between fault and residual using only input-output measured data sequence, and construct one least squares optimization problem to obtain fault estimation. The statistical property about residual is analyzed based on our derived output prediction, then the Kronecker product is used to derive the detailed structure corresponding to residual vector at every time instant. After substituting our output prediction into objective function of predictive control, one quadratic programming problem with equality and inequality constraints is considered. For solving this constrained optimization problem, fast gradient method is not suited for this complex optimization problem, as one regularization term is added in our objective function. So in order to solve this complex quadratic optimization problem, we propose a dual decomposition idea so that this dual decomposition idea can convert the former constrained optimization into unconstrained optimization, then one nearest neighbor gradient algorithm is given to solve its optimal value.

The nonlinear model has a linear dynamic system following some static nonlinearity. The dominating approach to estimate the components of this model has been to minimize the error between the simulated and the measured outputs. For the special case of Gaussian input signals, we estimate the linear part of the Hammerstein model using the Bussgang’s classic theorem. For the case with general disturbances, we derive the Maximum Likelihood method. Finally one simulation example is used to prove the efficiency of our theory.

This paper studies the guaranteed state estimation in terms of zonotope, and does some improvements for nonlinear discrete time system with a bounded description of noise and parameters. Firstly we extend the Taylor series with respect to two variables so that the mean value extension which is used to compute an interval enclosure can be improved and extended. Secondly based on the improved mean value extension, a generalization of classical method is proposed as it considers uncertainty in the model of system. Thirdly we give one iterative process in one algorithm to obtain a bound of the exact uncertain state set. Finally the simulation example results confirm the identification theoretical results.

Organizational commitment reflects the members of the college student community recognition and involvement, which affects the normal operation of organization enormously and is also determining the rise and fall of this student organization. In this paper, a random sample of 300 student leaders for trial, using interviews and questionnaires to collect relevant data through the data processing SPSS13.0 focus on: The dimension structure of college community are affective commitment and growing commitment.

The transmittance curves of ZnWO4 single crystals grown by Czochralski method have been measured. We suggest that the existense of oxygen vacancy is the basic reason for the rosy color of the crystal. The position of the optical indicatrix, the refractive indices in the visible wavelength region and the Sellmeier's equations have been determined more accurately.