Abstract
In the utilization of C language, it often appears that the function calls itself directly or indirectly, that is, the function calls itself recursively. The recursive solution of the same ...kind of problem can be expressed by recursion, and the specific problem can be reduced by recursion. Based on this, this paper first analyses the concept and function of C language recursion, then studies the process description of recursion algorithm, and finally gives the implementation strategy of C language recursion algorithm.
This paper is concerned with the polynomial filtering problem for a class of nonlinear systems with quantisations and missing measurements. The nonlinear functions are approximated with polynomials ...of a chosen degree and the approximation errors are described as low-order polynomial terms with norm-bounded coefficients. The transmitted outputs are quantised by a logarithmic quantiser and are also subject to randomly missing measurements governed by a Bernoulli distributed sequence taking values on 0 or 1. Dedicated efforts are made to derive an upper bound of the filtering error covariance in the simultaneous presence of the polynomial approximation errors, the quantisations as well as the missing measurements at each time instant. Such an upper bound is then minimised through designing a suitable filter gain by solving a set of matrix equations. The filter design algorithm is recursive and therefore applicable for online computation. An illustrative example is exploited to show the effectiveness of the proposed algorithm.
The active noise control (ANC) based on the principle of superposition is an attractive method to attenuate the noise signals. However, the impulsive noise in the ANC systems will degrade the ...performance of the controller. In this paper, a filtered-x recursive maximum correntropy (FxRMC) algorithm is proposed based on the maximum correntropy criterion (MCC) to reduce the effect of outliers. The proposed FxRMC algorithm does not requires any priori information of the noise characteristics and outperforms the filtered-x least mean square (FxLMS) algorithm for impulsive noise. Meanwhile, in order to adjust the kernel size of FxRMC algorithm online, a recursive approach is proposed through taking into account the past estimates of error signals over a sliding window. Simulation and experimental results in the context of active impulsive noise control demonstrate that the proposed algorithms achieve much better performance than the existing algorithms in various noise environments.
•A FxRMC algorithm based on the maximum correntropy is proposed.•An adaptive kernel size scheme is developed.•Simulation and experiment results demonstrate the improved performance.
In this research, the issue of parameter estimation for control systems is considered to develop a highly efficient estimation approach for the purpose of satisfying the need of industrial process ...modelling. For dynamical production processes, an error objective function in accordance with the dynamically sampled data is constructed for on-line identification. In order to simulate the instantaneous response of dynamical processes, the experimental scheme of impulse responses is adopted, and the observational data of impulse responses are used as the identification experimental data. In order to acquire high accuracy and stable performance, a hierarchical least mean square method is designed by means of the decomposition technique and the hierarchical principle. Finally, the superiority of the hierarchical least mean square approach is verified by the comparison simulation experiment and the effectiveness of the hierarchical least mean square method is proved by the detailed numerical examples.
In this paper, we focus on the modeling problem of the multi-frequency signals which contain many different frequency components. Based on the Newton search and the measured data, a Newton recursive ...parameter estimation algorithm is developed to estimate the amplitude, the angular frequency and the phase of a multi-frequency signal. In order to improve the performance of the identification algorithm, a convergence factor is introduced in the Hessian matrix of the developed Newton recursive method. The numerical examples verify that the proposed algorithm is effective for modeling the multi-frequency sine signals.
Big multi-step wind speed forecasting is hard to be realized due to the high -requirement of the built forecasting models. However, the big multi-step forecasting is expected in the wind power ...systems, which can provide sufficient time for the wind grids to be operated in the emergency cases. In the study, a new hybrid computational framework for the big multi-step wind speed forecasting is proposed, consisting of Wavelet Packet Decomposition (WPD), Elman Neural Networks (ENN), boosting algorithms and Wavelet Packet Filter (WPF). The novelty of the study is to investigate the big multi-step wind speed forecasting performance using various computing strategies in the proposed new hybrid WPD-Boost-ENN-WPF framework. Four different wind speed time series data are provided to complete the real forecasting experiments. The experimental results indicate that: (a) all of the proposed hybrid models have better performance than the corresponding single forecasting models in the big multi-step predictions. The 9 step MAE errors for the experimental data #1 from the proposed four hybrid forecasting models are only 1.2821 m/s, 1.1276 m/s, 1.1718 m/s and 1.2684 m/s, respectively; (b) the proposed four hybrid forecasting models have no significant forecasting difference; and (c) all of them are suitable for the big multi-step wind speed forecasting.
•Four new smart forecasting models are proposed for the wind speed forecasting.•Two new data computing strategies and two boosting algorithms are adopted.•Multi-step forecasting performance of the proposed hybrid models is investigated thoroughly.
Aiming at the problem of quantitative inertia evaluation of a new energy electric power system, the system inertia constant tracking method based on system identification is studied. The method is ...divided into two categories: non-recursive algorithm and recursive algorithm. The non-recursive algorithm uses a batch of data for batch processing to obtain the estimated value of the identification model parameters. The recursive algorithm is based on the estimated value of the model parameter at the previous moment and corrects the estimated value based on the new data currently obtained. From the perspective of the identification principle, the difference and internal relationship between the two in terms of calculation storage and identification speed are analyzed. The IEEE typical system is used to compare and verify the experimental examples. Theoretical analysis and experimental results show that the recursive algorithm has high identification accuracy, stable identification results and fast identification speed. It is suitable for the identification of objects with large numbers of nodes and complex structures, which is conducive to real-time monitoring and fast perception of the inertia constant of the new energy power system.
•Dynamic modeling of multiple impact-contacts in open kinematic chains has been studied.•Recursive Gibbs–Appell formulation has been used to derive the motion equations.•In order to model the impact ...phenomenon, the regularized method has been utilized.•Detecting the impact moments and solving the stiff differential equations are investigated.•Nine of the famous contact force models have been compared to select a more suitable one.
In this paper, the phenomenon of multiple impact-contacts has been dynamically modeled for an open kinematic chain with rigid links and revolute joints. The dynamic equations of the mentioned system have been extracted based on the recursive Gibbs–Appell formulation. The impact-contact phenomenon has been formulated by the regularized method in which the force of impact is a continuous function of the relative penetration and relative velocity of two colliding surfaces with respect to each other. The geometrical specifications and the mechanical properties of colliding surfaces are the two main parameters used in the modeling of viscoelastic contact force models. In this work, a recursive algorithm, which has been developed based on 3 × 3 rotation matrices to reduce the computational load, symbolically derives the motion equations of a multibody system that collides with surrounding surfaces at several points. The system under study includes the non-impact (flight) phase and the impact phase. Going from the flight phase to the impact phase and back, detecting the exact moment of impact, and also solving the differential equations of motion during a very short impact time have their particular challenges and complexities, which are dealt with in this work. In the next step, nine famous contact force models have been compared in order to select the most suitable model for simulation work. Finally, to show the accuracy and the capability of the presented algorithm, the dynamic behavior of an open-chain robotic mechanism consisting of 4 rigid links connected by revolute joints has been simulated and analyzed.
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