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1.
The main goal of this study is to develop an efficient matrix approach for a new class of nonlinear 2D optimal control problems (OCPs) affected by variable-order fractional dynamical systems. The offered approach is established upon the shifted Chebyshev polynomials (SCPs) and their operational matrices. Through the way, a new operational matrix (OM) of variable-order fractional derivative is derived for the mentioned polynomials.The necessary optimality conditions are reduced to algebraic systems of equations by using the SCPs expansions of the state and control variables, and applying the method of constrained extrema. More precisely, the state and control variables are expanded in components of the SCPs with undetermined coefficients. Then these expansions are substituted in the cost functional and the 2D Gauss-Legendre quadrature rule is utilized to compute the double integral and consequently achieve a nonlinear algebraic equation.After that, the generated OM is employed to extract some algebraic equations from the approximated fractional dynamical system. Finally, the procedure of the constrained extremum is used by coupling the algebraic constraints yielded from the dynamical system and the initial and boundary conditions with the algebraic equation extracted from the cost functional by a set of unknown Lagrange multipliers. The method is established for three various types of boundary conditions.The precision of the proposed approach is examined through various types of test examples.Numerical simulations confirm the suggested approach is very accurate to provide satisfactory results.  相似文献   

2.
Identification of autoregressive models with exogenous input (ARX) is a classical problem in system identification. This article considers the errors-in-variables (EIV) ARX model identification problem, where input measurements are also corrupted with noise. The recently proposed Dynamic Iterative Principal Components Analysis (DIPCA) technique solves the EIV identification problem but is only applicable to white measurement errors. We propose a novel identification algorithm based on a modified DIPCA approach for identifying the EIV-ARX model for single-input, single-output (SISO) systems where the output measurements are corrupted with coloured noise consistent with the ARX model. Most of the existing methods assume important parameters like input-output orders, delay, or noise-variances to be known. This work’s novelty lies in the joint estimation of error variances, process order, delay, and model parameters. The central idea used to obtain all these parameters in a theoretically rigorous manner is based on transforming the lagged measurements using the appropriate error covariance matrix, which is obtained using estimated error variances and model parameters. Simulation studies on two systems are presented to demonstrate the efficacy of the proposed algorithm.  相似文献   

3.
In this paper, a new direct method based on the Chebyshev cardinal functions is proposed to solve a class of variable-order fractional optimal control problems (V-OFOCPs). To this end, a new operational matrix (OM) of variable-order (V-O) fractional derivative in the Caputo sense is derived for these basis functions and is used to obtain an approximate solution for the problem under study. In the proposed method, the state and the control variables are expanded in terms of the Chebyshev cardinal functions with unknown coefficients, at first. Then, the OM of V-O fractional derivative and some properties of the Chebyshev cardinal functions are employed to achieve a nonlinear algebraic equation corresponding to the performance index and a nonlinear system of algebraic equations corresponding to the dynamical system in terms of the unknown coefficients. Finally, the method of constrained extremum is applied, which consists of adjoining the constraint equations derived from the given dynamical system and the initial conditions to the performance index by a set of undetermined Lagrange multipliers. As a result, the necessary conditions of optimality are derived as a system of algebraic equations in the unknown coefficients of the state variable, control variable, and Lagrange multipliers. Furthermore, some numerical examples of different types are demonstrated with their approximate solutions for confirming the high accuracy and applicability of the proposed method.  相似文献   

4.
This paper considers a class of nonlinear fractional-order multi-agent systems (FOMASs) with time-varying delay and unknown dynamics, and a new robust adaptive control technique is proposed for cooperative control. The unknown nonlinearities of the systems are online approximated by the introduced recurrent general type-2 fuzzy neural network (RGT2FNN). The unknown nonlinear functions are estimated, simultaneously with the control process. In other words, at each sample time the parameters of the proposed RGT2FNNs are updated and then the control signals are generated. In addition to the unknown dynamics, the orders of the fractional systems are also supposed to be unknown. The biogeography-based optimization algorithm (BBO) is extended to estimate the unknown parameters of RGT2FNN and fractional-orders. A LMI based compensator is introduced to guarantee the robustness of the proposed control system. The excellent performance and effectiveness of the suggested method is verified by several simulation examples and it is compared with the other methods. It is confirmed that the introduced cooperative controller results in a desirable performance in the presence of time-varying delay, unknown dynamics, and unknown fractional-orders.  相似文献   

5.
The identification of linear, discrete time, scalar output systems which are driven exclusively by white, zero mean, inaccessible noise sequences is discussed. Two principal results are presented. First, two methods (least squares and an autocorrelation technique) for identifying the system characteristic equation coefficients are compared. The least squares approach is shown to be biased except for special cases. In general, the bias cannot be removed. If the state transition matrix is of the phase variable form, bias removal requires a knowledge of the measurement noise variance and all but one of the state driving noise variances. The autocorrelation technique is not biased asymptotically and does not require a knowledge of the noise variances.Secondly, it is shown that the m2 elements of the state transition matrix cannot be identified uniquely from the scalar output sequence autocorrelation coefficients if the system order is higher than one. The implication of this uncertainty in the state transition matrix on optimal filtering of the output sequence is briefly discussed.  相似文献   

6.
For state estimation of high accuracy, prior knowledge of measurement noise is necessary. In this paper, a method for solving the joint state estimation problem of jump Markov nonlinear systems (JMNSs) without knowing the measurement noise covariance is developed. By using the Inverse-Gamma distribution to describe the dynamics of measurement noise covariance, the joint conditional posterior distribution of the state variable and measurement noise covariance is approximated by a product of separable variational Bayesian (VB) marginals. In the newly constructed approach, the interacting multiple model (IMM) algorithm, as well as the particle-based approximation strategy, is employed to handle the computationally intractable problem and the nonlinear characteristics of systems, respectively. An interesting feature of the proposed method is that the distribution of states is spanned by a set of particles with weights, while the counterpart of measurement noise covariance is obtained analytically. Moreover, the number of particles is fixed under each mode, indicating a reasonable computational cost. Simulation results based on a numerical example and a tunnel diode circuit (TDC) system are presented to demonstrate that the proposed method can estimate the measurement noise covariance well and provide satisfied state estimation when the statistics of the measurement are unavailable.  相似文献   

7.
An approximate method is proposed for the determination of the output sensitivity function of linear time-varying systems using polynomial series expansions. The novelities of the proposed method are the use of the operational matrix of differentiation for the derivation of the algebraic equations approximating the differential equation, and the use of the operational matrix of polynomial series transformation for the simplification of the algorithm required for the application of the method using any type of polynomial series.  相似文献   

8.
This paper considers the parameter and order estimation for multiple-input single-output nonlinear systems. Since the orders of the system are unknown, a high-dimensional identification model and a sparse parameter vector are established to include all the valid inputs and basic parameters. Applying the data filtering technique, the input-output data are filtered and the original identification model with autoregressive noise is changed into the identification model with white noise. Based on the compressed sensing recovery theory, a data filtering-based orthogonal matching pursuit algorithm is presented for estimating the system parameters and the orders. The presented method can obtain highly accurate estimates from a small number of measurements by finding the highest absolute inner product. The simulation results confirm that the proposed algorithm is effective for recovering the model of the multiple-input single-output Hammerstein finite impulse response systems.  相似文献   

9.
In this paper we consider a class of fractional order linear time invariant (FO-LTI) interval systems with linear coupling relationships among the fractional order, the system matrix and the input matrix. We present the sufficient conditions for the robust stability and stabilization of such coupling FO-LTI interval systems with the fractional order α satisfying 0<α<1. All the results are proposed in terms of linear matrix inequalities (LMI). Two numerical examples show that our results are effective for checking the robust asymptotical stability and designing the stabilizing controller for FO-LTI interval systems.  相似文献   

10.
This paper studies the problem of output feedback sliding mode control (OFSMC) for fractional order nonlinear systems. A necessary and sufficient condition for the existence of a sliding surface is obtained by a new singular system approach and a linear matrix equality (LMI), which reduces the conservativeness of the system. Then an OFSMC law is designed based on a fractional order Lyapunov method, which ensures that the resulting fractional closed-loop system is asymptotically stable and the states of the fractional closed-loop system converge to the sliding surface in finite time. A fractional electrical circuit is discussed to illustrate the effectiveness of the proposed approach.  相似文献   

11.
This paper considers the distributed adaptive fault-tolerant control problem for linear multi-agent systems with matched unknown nonlinear functions and actuator bias faults. By using fuzzy logic systems to approximate the unknown nonlinear function and constructing a local observer to estimate the states, an effective distributed adaptive fault-tolerant controller is developed. Furthermore, different from the traditional method to estimate the weight matrix, only the weight vector needs to be estimated by exchanging the order of weight vectors and fuzzy basis functions in the fuzzy logic systems. In contrast to the existing results, the assumption that the dimensions of input vector and output vector are equal is removed. In addition, it is proved that the proposed control protocol guarantees all signals in the closed-loop systems are bounded and all agents converge to the leader with bounded residual errors. Finally, simulation examples are given to illustrate the effectiveness of the proposed method.  相似文献   

12.
Based on the idea of tracking control and stability theory of fractional-order systems, a novel synchronization approach for fractional order chaotic systems is proposed. We prove that the synchronization between drive system and response system with different fractional order q can be achieved, and the synchronization between different fractional-order chaotic systems with different fractional order q can be achieved. Two examples are used to illustrate the effectiveness of the proposed synchronization method. Numerical simulations coincide with the theoretical analysis.  相似文献   

13.
In this study, an adaptive fractional order sliding mode controller with a neural estimator is proposed for a class of systems with nonlinear disturbances. Compared with traditional sliding mode controller, the new proposed fractional order sliding mode controller contains a fractional order term in the sliding surface. The fractional order sliding surface is used in adaptive laws which are derived in the framework of Lyapunov stability theory. The bound of the disturbances is estimated by a radial basis function neural network to relax the requirement of disturbance bound. To investigate the effectiveness of the proposed adaptive neural fractional order sliding mode controller, the methodology is applied to a Z-axis Micro-Electro-Mechanical System (MEMS) gyroscope to control the vibrating dynamics of the proof mass. Simulation results demonstrate that the proposed control system can improve tracking performance as well as parameter identification performance.  相似文献   

14.
In this paper, we propose a method to estimate the asymptotic stability region (ASR) of uncertain variable structure systems with bounded controllers. Using linear matrix inequalities (LMIs) we estimate the ASR and we show the exponential stability of the closed-loop control system in the estimated ASR. We also give simple LMI-based algorithms for estimating the ASR and designing a switching surface which will make the estimated ASR big. Finally, we give numerical examples in order to show that our method can be better than the previous results for a certain class of uncertain variable structure systems with bounded controllers.  相似文献   

15.
This study proposes fractional-order Kalman filers using Tustin generating function and the average value of fractional-order derivative to estimate the state of fractional-order systems involving colored process and measurement noises. By Tustin generating function, a fractional-order differential equation is provided to approximate the dynamics of a continuous-time fractional-order system and colored process and measurement noises. By constructing an augmented system with respect to state, the process noise and the measurement noise to deal with colored noises, the fractional-order Kalman filter using Tustin generating function is proposed to improve the estimation accuracy. Besides, the average value of fractional-order derivative is proposed, and the corresponding fractional-order Kalman filter by the augmented system method is presented to reduce estimation error. Finally, three illustrative examples are given to illustrate that the proposed two kinds of Kalman filters are more effective than fractional-order Kalman filter based on Gru¨nwald–Letnikov definition.  相似文献   

16.
The performance of the current state estimation will degrade in the existence of slow-varying noise statistics. To solve the aforementioned issues, an improved strong tracking maximum correntropy criterion variational-Bayesian adaptive Kalman filter is presented in this paper. First of all, the inverse-Wishart distribution, as the conjugate-prior, is adopted to model the unknown and time-varying measurement and process noise covariances, then the noise covariances and system state are estimated via the variational Bayesian method. Secondly, the multiple fading-factors are obtained and evaluated to modify the prediction error covariance matrix to address the problems associated with inaccurate error estimation. Finally, the maximum correntropy criterion is employed to correct the filtering gain, which improves the filtering performance of the proposed algorithm. Simulation results show that the proposed filter exhibits better accuracy and convergence performance compared to other existing algorithms.  相似文献   

17.
Gas flow has fractional order dynamics; therefore, it is reasonable to assume that the pneumatic systems with a proportional valve to regulate gas flow have fractional order dynamics as well. There is a hypothesis that the fractional order control has better control performance for this inherent fractional order system, although the model used for fractional controller design is integer order. To test this hypothesis, a fractional order sliding mode controller is proposed to control the pneumatic position servo system, which is based on the exponential reaching law. In this method, the fractional order derivative is introduced into the sliding mode surface. The stability of the controller is proven using Lyapunov theorem. Since the pressure sensor is not required, the control system configuration is simple and inexpensive. The experimental results presented indicate the proposed method has better control performance than the fractional order proportional integral derivative (FPID) controller and some conventional integral order control methods. Points to be noticed here are that the fractional order sliding mode control is superior to the integral order sliding mode counterpart, and the FPID is superior to the corresponding integral order PID, both with optimal parameters. Among all the methods compared, the proposed method achieves the highest tracking accuracy. Moreover, the proposed controller has less chattering in the manipulated variable, the energy consumption of the controller is therefore substantially reduced.  相似文献   

18.
This paper concentrates on computing the stabilizing region of PDμ controller for fractional order system with general interval uncertainties and an interval delay. The stabilizing region means the complete/approximate set of PDμ controllers that stabilize the given closed-loop control system. General interval uncertainties refer to both coefficients and orders of the fractional system suffer from interval uncertainties. Interval delay indicates that the delay also vary in a specified interval.Firstly, a method is presented to calculate the stabilizing region for general interval fractional system with an interval time-constant delay. Based on a novel mapping function and the concept of critical controller parameters, the stabilizing region can be determined numerically. Secondly, the stabilizing region computation problem for general interval fractional system with an interval time-varyingdelay is considered. By applying a revised small-gain theorem, the stabilizing region can be calculated like the time-constant delay case. Thirdly, two alternative methods are proposed to improve the computational efficiency of stabilizing region calculation. Both methods can reduce the number of polynomials which are used to determine the stabilizing region. Examples are followed to illustrate the proposed results.  相似文献   

19.
本文基于传统多普勒系数估计方法,提出一种基于分数阶Fourier变换的多普勒系数估计方法,该方法利用分数阶Fourier变换估计得到经过信道后LFM信号调频斜率的变化量值,进而得到多普勒系数的估计。通过计算机仿真研究验证了该方法的有效性与稳健性。  相似文献   

20.
A Chebyshev collocation method, an expansion method, has been proposed in order to solve the systems of higher-order linear integro-differential equations. This method transforms the IDE system and the given conditions into the matrix equations via Chebyshev collocation points. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Chebyshev coefficients of the solution function. Some numerical results are also given to illustrate the efficiency of the method. Moreover, this method is valid for the systems of differential and integral equations.  相似文献   

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