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1.
In this paper, a composite Chebyshev finite difference method for solving linear quadratic optimal control problems with inequality constraints on state and control variables is introduced. This method is an extension of Chebyshev finite difference scheme and is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well known Chebyshev–Gauss–Lobatto nodes. The excellent properties of hybrid functions are used to convert optimal control problem into a mathematical programming problem whose solution is much more easier than the original one. Various types of optimal control problems are investigated to demonstrate the effectiveness of the proposed approximation scheme. The method is simple, easy to implement and provides very accurate results.  相似文献   

2.
Using block-pulse functions (BPFs)/shifted Legendre polynomials (SLPs) a unified approach for computing optimal control law of linear time-varying time-delay systems with reverse time terms and quadratic performance index is discussed in this paper. The governing delay-differential equations of dynamical systems are converted into linear algebraic equations by using operational matrices of orthogonal functions (BPFs and SLPs). The problem of finding optimal control law is thus reduced to the problem of solving algebraic equations. One example is included to demonstrate the applicability of the proposed approach.  相似文献   

3.
For the approximation of real functions in L2(0, ∞) that are frequently encountered in signal analysis and parameter identification, analytical and computer studies suggest the use of Laguerre functions. Such functions can form at least locally optimal or near-optimal sets. The results are shown for continuous systems to be encouragingly flat, indicating low sensitivity to the position of the Laguerre multiple pole. Relationships to linear time-invariant discrete systems are given, using discrete Laguerre functions.  相似文献   

4.
A new time-domain approach to the derivation of a Chebyshev scale matrix is presented. The derived Chebyshev scale matrix, together with the Chebyshev integration matrix, is used to analyze differential equations containing terms with a scaled argument. The results are expressed in terms of Chebyshev series. As illustrated in the included examples, the Chebyshev series solution converges faster than that represented in Laguerre series.  相似文献   

5.
By applying hybrid functions of general block-pulse functions and Legendre polynomials, the linear-quadratic problem of linear time-varying systems with delays are transformed into the optimization problem of multivariate functions. The approximate solutions of the optimal control and state as well as the optimal value of the objective functional are derived. The numerical examples illustrate that the algorithms are valid.  相似文献   

6.
Piecewise constant orthogonal functions over triangular domains play an important role in many applications. In the present paper, some Haar and Walsh functions over triangular domains are constructed. Compared with the previously proposed Haar functions in [5], the new Haar functions take only integer. For any continuous function, the uniform convergence of the new Haar-Fourier series is proved. Moreover, based on the relation between the new Haar and Walsh functions, the uniform convergence of the Walsh-Fourier series is studied. Additionally, we obtain the relation between the Walsh functions in the two different orders, Paley order and Hadamard order, which have not been discussed previously.  相似文献   

7.
A method for finding the optimal control of a linear time varying delay system with quadratic performance index is discussed. The properties of the hybrid functions which consists of block-pulse functions plus Legendre polynomials are presented. The operational matrices of integration, delay and product are utilized to reduce the solution of optimal control to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.  相似文献   

8.
This paper establishes a clear procedure for the variational problem solution via the Walsh functions.technique. First the Walsh functions are introduced and their properties briefly summarized. Then an operational matrix is derived for integration use. The variational problems are solved by means of the direct method using the Walsh series. An illustrative example and a practical application to a heat conduction problem are included.  相似文献   

9.
By applying hybrid functions of general block-pulse functions and Legendre polynomials, linear Volterra integrodifferential systems are converted into a system of algebraic equations. The approximate solutions of linear Volterra integrodifferential systems are derived. Using the results we obtain the optimal control and state as well as the optimal value of the objective functional. The numerical examples illustrate that the algorithms are valid.  相似文献   

10.
This paper introduces an efficient direct approach for solving delay fractional optimal control problems. The concepts of the fractional integral and the fractional derivative are considered in the Riemann–Liouville sense and the Caputo sense, respectively. The suggested framework is based on a hybrid of block-pulse functions and orthonormal Taylor polynomials. The convergence of the proposed hybrid functions with respect to the L2-norm is demonstrated. The operational matrix of fractional integration associated with the hybrid functions is constructed by using the Laplace transform method. The problem under consideration is transformed into a mathematical programming one. The method of Lagrange multipliers is then implemented for solving the resulting optimization problem. The performance and computational efficiency of the developed numerical scheme are assessed through various types of delay fractional optimal control problems. Our numerical findings are compared with either exact solutions or the existing results in the literature.  相似文献   

11.
The Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems. A new set of orthogonal functions is derived from Walsh functions. By using the new functions, the generalized Walsh operational matrices corresponding to √s, √(s2+ 1), e-s and e-√s etc. are established. Several distributed parameter problems are solved by the new approach.  相似文献   

12.
In this paper, a numerical method to solve nonlinear optimal control problems with terminal state constraints, control inequality constraints and simple bounds on the state variables, is presented. The method converts the optimal control problem into a sequence of quadratic programming problems. To this end, the quasilinearization method is used to replace the nonlinear optimal control problem with a sequence of constrained linear-quadratic optimal control problems, then each of the state variables is approximated by a finite length Chebyshev series with unknown parameters. The method gives the information of the quadratic programming problem explicitly (The Hessian, the gradient of the cost function and the Jacobian of the constraints). To show the effectiveness of the proposed method, the simulation results of two constrained nonlinear optimal control problems are presented.  相似文献   

13.
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   

14.
The operational properties of the integration and product of Chebyshev polynomials are used in the analysis of bilinear systems by the approximation of time functions by truncated Chebyshev series. The operational properties are also applied to determine the unknown parameters of a general bilinear system from the input-output data. Examples with excellent results are given.  相似文献   

15.
The correlation function of two Walsh functions appears in image processing, signal multiplexing, detection and spectral analysis using Walsh functions. Though Walsh functions are two-valued, their correlation functions are real-valued and rather difficult to evaluate. A recursive formula is developed in this paper to evaluate the correlation functions. Some other properties of the correlation function are also discussed.  相似文献   

16.
This paper discusses the identification problem for a class of nonlinear systems. A member of this class may be represented by a single-valued power-law type nonlinearity preceded and succeeded by linear dyadic invariant systems. Such an arrangement allows for a Voltera functional series representation. The identification problem is then concerned with the specification of the associated Voltera kernels.Two approaches are presented for dealing with this problem. Both approaches are, however, based on Walsh function techniques. The first approach relies on direct output measurements when the input is a Walsh function. This approach is suitable for a deterministic case. The second approach assumes ergodic processes for the input. Based on measurements drawn from an input-output dyadic correlation function, determination of the Voltera kernels is made.  相似文献   

17.
This paper considers the problem of identifying the parameters of dynamic systems from input-output records. Both lumped-parameter and distributed-parameter systems, deterministic and stochastic, are studied. The approach adopted is that of expanding the system variables in Walsh series. The key point is an operational matrix P which relates the coefficient matrix Г of the Walsh series of a given function with the coefficient matrix of its first derivative. Using this operational matrix P one overcomes the necessity to use differentiated data, a fact that usually is avoided either by integration of the data or by using discrete-time models. Actually, the original differential input-output model is converted to a linear algebraic (or regression) model convenient for a direct (or a least squares) solution. A feature of the method is that it permits the identification of unknown initial conditions simultaneously with the parameter identification. The results are first derived for single-input single-output systems and then are extended to multi-input multi-output systems. The case of non-constant parameters is treated by assuming polynomial forms. Some results are also included concerning the identification of state-space and integral equation models. The theory is supported by two examples, which give an idea of how effective the method is expected to be in the real practice.  相似文献   

18.
Chebyshev滤波器是一种常用的高性能滤波器。本文通过对Chebyshev滤波器的系统函数的推导分解,提出了一种可以快速实现高阶Chebyshev低通滤波器电路的方法,并给出了设计高阶Chebyshev低通滤波器电路的各元器件参数的计算公式。最后运用该算法快速设计了一个7阶Chebyshev低通滤波器,并采用Saber软件对设计的7阶Chebyshev低通滤波器进行了理论分析验证。  相似文献   

19.
A new direct method of the block-pulse functions technique of the inverse Laplace transform for irrational and transcendental transfer functions is presented. It is shown that the existing indirect method can be used equivalently with the new one. Two illustrative examples are given.  相似文献   

20.
This paper is devoted to the issue of a robust predictive control for linear discrete-time systems by using Meixner-like model. The Meixner-like functions are an extension of Laguerre functions and convenient when the system has a slow start or delay. To ensure the reduction of the parameter number in the Meixner-like model, the optimization of parameters characterizing the Meixner-like functions is proposed. This proposed robust predictive control copes with physical constraints and geometrical constraints due to parameter uncertainties, which are estimated by using the Unknown But Bounded Error (UBBE) approach, and leads to the min-max optimization problem.  相似文献   

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