Optimal Control
Hamid Tabatabaee; Mahdi Memari
Abstract
The problem of solving optimal control of Singular problems in the classic method has a complexity that is solved by approximation of the equations in the problem with orthogonal bases instead of solving the dynamic equation system of a set of static problems. In return for a more relaxed solution, it ...
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The problem of solving optimal control of Singular problems in the classic method has a complexity that is solved by approximation of the equations in the problem with orthogonal bases instead of solving the dynamic equation system of a set of static problems. In return for a more relaxed solution, it will face some errors in the computation .however, it has an appropriate precision. Legendre and Fourier series are presented using the specifications of the Fourier transform of Legendre and Fourier series . In this algorithm, the state variables, and the state - derivative variables and the control vector are extended by the orthogonal basis of Legendre and Fourier series with unknown coefficients. in order to compute optimal control vector and optimal path of linear Singular systems with quadratic cost function , we are introduced by using the properties of orthogonal functions introduced by the coefficients and .using the proposed method , the system dynamics are converted into algebraic equations and the problem of dynamic optimization of dynamic space has been mapped to static space optimization problem with quadratic cost function and linear constraints . First, it is used to solve the problem using an orthogonal basis of raw material and then the problem solving with orthogonal basis of Fourier series is repeated. Finally, the application and effectiveness of the proposed method are presented.
stochastic/Probabilistic/fuzzy/dynamic modeling
Hamid Tabatabaee; Shirin Rikhtegar Mashhad
Abstract
Nonlinear dynamical systems modeling is one of the real challenges of the real world due to the nonlinear and variable nature of time. In this paper, an Online Self-organizing Takagi-SugenoNeuro-Fuzzy System(OSO-NFS) for dynamic Nonlinear System Identification is proposed. OSO-NFS is built based on radial ...
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Nonlinear dynamical systems modeling is one of the real challenges of the real world due to the nonlinear and variable nature of time. In this paper, an Online Self-organizing Takagi-SugenoNeuro-Fuzzy System(OSO-NFS) for dynamic Nonlinear System Identification is proposed. OSO-NFS is built based on radial basis function(RBF). The algorithm has the ability to adaptive adjustment of the system’s parameter and continuous evolution of the system’s structure. Structure identification and parameters estimation are performed simultaneously. The OSO-NFS starts with no hidden neuron. In structural learning, the proposed OSO-NFS uses a two-step algorithm to create a suitable number of rules. A pruning algorithm is used for detecting inactive hidden units and removing them as learning progresses. The weighted recursive least square (WRLS) algorithm is used to adjust all the consequent parameters. Finally, two benchmark examples of nonlinear system identification are demonstrated to show the effectiveness of the proposed method, compared with the other methods. The accuracy of this modeling has been compared with the other methods according to two criteria of the number of neurons (rules) and the root mean square error. According to the results, the average percentage of improvement of the answers in the number of rules obtained in comparison to the chosen method in the modeling of these two systems in both the noise and non-noise modes in the first example is 42.35% and in the second example is 29 %.