Control systems engineering: modelling and simulation, control theory and microprocessor implementation
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Adaptive control: stability, convergence, and robustness
Adaptive control: stability, convergence, and robustness
Numerical analysis: mathematics of scientific computing
Numerical analysis: mathematics of scientific computing
Fuzzy engineering
Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence
Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence
On the solution of differential equations with fuzzy spline wavelets
Fuzzy Sets and Systems
Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach
Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach
Novel determination of differential-equation solutions: universal approximation method
Journal of Computational and Applied Mathematics
Fuzzy transforms: Theory and applications
Fuzzy Sets and Systems
An approach to fuzzy control of nonlinear systems: stability and design issues
IEEE Transactions on Fuzzy Systems
H∞ tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach
IEEE Transactions on Fuzzy Systems
Robustness design of nonlinear dynamic systems via fuzzy linear control
IEEE Transactions on Fuzzy Systems
Composite Fuzzy Control of Nonlinear Singularly Perturbed Systems
IEEE Transactions on Fuzzy Systems
Robust Fuzzy Filter Design for a Class of Nonlinear Stochastic Systems
IEEE Transactions on Fuzzy Systems
Spreadsheet solution of hyperbolic partial differential equations[for EM field calculations]
IEEE Transactions on Education
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
On fuzzy solutions for partial differential equations
Fuzzy Sets and Systems
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A new technique using an adaptive fuzzy algorithm to obtain the solutions to a class of partial differential equations (PDEs) is presented. The design objective is to find a fuzzy solution to satisfy precisely the PDEs with boundary conditions. According to the adaptive scheme of fuzzy logic systems, a fuzzy solution with adjustable parameters for the PDE is first described. Then, a set of adaptive laws for tuning the free parameters in the consequent part is derived from minimizing an appropriate error function. In addition, an elegant approximated error bound between the exact solution and the proposed fuzzy solution with respect to the number of fuzzy rules and solution errors has also been derived. Furthermore, the convergence of error equations in mesh points is also discussed from the energy perspective. In this paper, we show that the proposed method can solve a variety of PDEs encountered in engineering. Comparisons are alsomade with solutions obtained by the finite-element method.