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The purpose of this paper is to deal with the anomaly detection problem in multi-unmanned aerial vehicles (UAVs) formation that can be transformed to identify some unknown parameters; a more general nonlinear dynamical model for each UAV is considered to include two terms. Due to an unknown parameter corresponding to the normal or abnormal state for each UAV, the bias-compensated approach is proposed to obtain the unbiased parameter estimation. Meanwhile, the biased error and accuracy analysis are also given in case of strict statistical description of the uncertainty or white noise. To relax this strict statistical description on external noise, an analytic center approach is proposed to identify the unknown parameters in presence of bounded noise, such that two inner and outer ellipsoidal approximations are constructed to include the membership set. To be precise, this paper is regarded as one extension and summary for the author’s previous research on the anomaly detection in multi-UAV formation. Finally, one simulation example is given to confirm the theoretical results.

Firstly, one extended nonlinear relation is constructed to embody the mutual relationship of UAVs. Secondly, to obtain the unbiased parameter estimations, the bias-compensated approach is applied to achieve it under the condition of white noise. Thirdly, in case of unknown but bounded noise, an analytic center approach is proposed to deal with this special case. Without loss of generality, the author thinks this paper can be used as one extension and summary for research on multi-UAVs formation anomaly detection.

An anomaly detection problem in multi-UAVs formation can be transformed into a problem of nonlinear system identification, and in modeling the nonlinear dynamical model for each UAV, two terms are considered simultaneously to embody the mutual relationships with other nearest UAV.

To the best knowledge of the authors, this problem of the anomaly detection problem in multi-UAVs formation is proposed by the authors’ previous work, and the problem of multi-UAVs formation anomaly detection can be transferred into one problem of parameter identification. In case of unknown but bounded noise, an analytic center approach is proposed to identify the unknown parameters, which correspond to achieve the goal of the anomaly detection.

The purpose of this paper is to extend the authors’ previous contributions on aircraft flutter model parameters identification. Because closed-loop condition is more widely used in today’s practice, a closed-loop stochastic model of the aircraft flutter test is constructed to model the aircraft flutter process, whose input–output signals are all corrupted by the observed noises. Through using a rational transfer function, the equivalent property between the aircraft flutter model parameters and polynomial coefficients is established, and then the problem of aircraft flutter model parameters identification is turned to one closed-loop identification problem. An iterative identification algorithm is proposed to identify the unknown polynomial coefficients, being benefit for the latter flutter model parameter identification. Furthermore, as the closed-loop output corresponds to the flutter amplitude, so from the point of the minimization with respect to the variance of the closed-loop output, the optimal input signal and optimal feedback controller are all derived to achieve the zero flutter, respectively, for example, the optimal input spectrum and the detailed form for optimal feedback controller.

First, model parameter identification for aircraft flutter is reviewed as one problem of parameter identification and this aircraft flutter model corresponds to one closed-loop stochastic model, whose input signal and output are corrupted by external noises. Second, for aircraft flutter closed-loop statistical model with statistical noise, an iterative identification algorithm is proposed to identify the unknown model parameters. Third, from the point of minimizing with respect to the variance of the closed-loop output, the optimal input signal and optimal feedback controller are all derived to achieve the zero flutter, respectively, for example, the optimal input spectrum and the detailed form for optimal feedback controller.

This aircraft flutter model corresponds to one closed-loop stochastic model, whose input signal and output are corrupted by external noises. Then, identification algorithm and optimal input signal design are studied for aircraft flutter model parameter identification with statistical noise, respectively. It means the optimal input signal and optimal feedback controller are useful for the aircraft flutter model parameter identification within the constructed new closed-loop stochastic model.

To the best of the authors’ knowledge, this problem of the model parameter identification for aircraft flutter is proposed by their previous work, and they proposed many identification strategies to identify these model parameters. This paper proposes a new closed-loop stochastic model to construct the aircraft flutter test, and some related topics are considered about this closed-loop identification for aircraft flutter model parameter identification in the framework of closed-loop condition.

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.

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.

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.

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.

This new paper aims to extend the authors’ previous contributions about open-loop aircraft flutter test to closed-loop aircraft flutter test by virtue of the proposed direct data–driven strategy. After feeding back the output signal to the input and introducing one feedback controller in the adding feedback loop, two parts, i.e. unknown aircraft flutter model and unknown feedback controller, exist in this closed-loop aircraft flutter system, simultaneously, whose input and output are all corrupted with external noise. Because of the relations between aircraft flutter model parameters and the unknown aircraft model, direct data–driven identification is proposed to identify that aircraft flutter model, then some identification algorithms and their statistical analysis are given through the authors’ own derivations. As the feedback controller can suppress the aircraft flutter or guarantee the flutter response converge to one desired constant value, the direct data–driven control is applied to design that feedback controller only through the observed data sequence directly. Numerical simulation results have demonstrated the efficiency of the proposed direct data–driven strategy. Generally, during our new information age, direct data–driven strategy is widely applied around our living life.

First, consider one more complex closed loop stochastic aircraft flutter model, whose input–output are all corrupted with external noise. Second, for the identification problem of closed-loop aircraft flutter model parameters, new identification algorithm and some considerations are given to the corresponding direct data–driven identification. Third, to design that feedback controller, existing in that closed-loop aircraft flutter model, direct data–driven control is proposed to design the feedback controller, which suppresses the flutter response actively.

A novel direct data–driven strategy is proposed to achieve the dual missions, i.e. identification and control for closed-loop aircraft flutter test. First, direct data–driven identification is applied to identify that unknown aircraft flutter model being related with aircraft flutter model parameters identification. Second, direct data–driven control is proposed to design that feedback controller.

To the best of the authors’ knowledge, this new paper extends the authors’ previous contributions about open-loop aircraft flutter test to closed-loop aircraft flutter test by virtue of the proposed direct data–driven strategy. Consider the identification problem of aircraft flutter model parameters within the presented closed loop environment, direct data–driven identification algorithm is proposed to achieve the identification goal. Direct data–driven control is proposed to design the feedback controller, i.e. only using the observed data to design the feedback controller.

The purpose of this paper considers optimal input signal design for flutter model parameters identification, as input signal is the first step during the whole identification process. According to the constructed flutter stochastic model with observed noises, separable least squares identification and set membership identification are proposed to identify those unknown model parameters for statistical noise and unknown but bounded noise, respectively. The common trace operation with respect to the asymptotic variance matrix is minimized to solve the power spectral for the optimal input signal in the framework of statistical noise. Moreover, for the unknown bout bounded noise, the radius of information, corresponding to the established parameter uncertainty interval, is minimized to give the optimal input signal.

First, model identification for aircraft flutter is reviewed as one problem of parameter identification and this aircraft flutter model corresponds to one stochastic model, whose input signal and output are corrupted by external noises. Second, for aircraft flutter statistical model with statistical noise, separable least squares identification is proposed to identify the unknown model parameters, then the optimal input signal is designed to satisfy one given performance function. Third, for aircraft flutter model with unknown but bounded noise, set membership identification is proposed to solve the parameter set for each unknown model parameter. Then, the optimal input signal is designed by applying the idea of the radius of information with unknown but bounded noise.

This aircraft flutter model corresponds to one stochastic model, whose input signal and output are corrupted by external noises. Then identification strategy and optimal input signal design are studied for aircraft flutter model parameter identification with statistical noise and unknown but bounded noise, respectively.

To the best knowledge of the authors, this problem of the model parameter identification for aircraft flutter was proposed by their previous work, and they proposed many identification strategies to identify these model parameters. This paper proposes two novel identification strategies and opens a new subject about optimal input signal design for statistical noise and unknown noise, respectively.

Based on dual information asymmetry, the two-stage segmented compensation mechanism for technological innovation of civilian enterprises’ participation in military (CEPIM) has been discussed.

On the basis of the traditional principal-agent problems, the incentive compatibility condition is introduced as well as the hybrid incentive compensation model is established, to solve optimal solution of the compensation parameters under the dynamic contract condition and the validity is verified by numerical simulation.

The results show that: (1) The two-stage segmented compensation mechanism has the functions of “self-selection” and “stimulus to the strong”, (2) It promotes the civilian enterprises to obtain more innovation benefit compensation through the second stage, (3) There is an inverted U-shaped relationship between government compensation effectiveness and the innovation ability of compensation objects and (4) The “compensable threshold” and “optimal compensation threshold” should be set, respectively, to assess the applicability and priority of compensation.

In this paper, through numerical simulation, the optimal solution for two-stage segmented compensation, segmented compensation coefficient, expected returns for all parties and excess expected returns have been verified under various information asymmetry. The results show that the mechanism of two-stage segmented compensation can improve the expected returns for both civilian enterprises and the government. However, under dual information asymmetry, for innovation ability of the intended compensation candidates, a “compensation threshold” should be set to determine whether the compensation should be carried out, furthermore an “optimal compensation threshold” should be set to determine the compensation priority.