Optimal Control of Distributed-Parameter Systems based on Differentiable Orthogonal Functions

Q. Wang and Y. Zhu (PRC)


Chebyshev sequences, distributed-parameter systems, optimal control, differentiable operation matrices


Taking the advantages of the properties of the differentiability of differentiable orthogonal functions, such as the Chebyshev function sequences, we can apply differential operation matrices, instead of the corresponding integral operation matrices, to the solution of the optimal control of distributed-parameter systems. The advantage of this method is that we can solve the optical control problems through differential operations and obtain an analytical linear presentation of the optimal solutions. As we know, the operation process based on the method of integral operations for solving such problems is quite sophisticated and tedious. The method based on differentiable orthogonal functions presented in this paper can greatly simplify the solution process and avoid such complex work and the solution results are quite satisfactory. The proposed method of the differentiable function sequences approach for the solution in this paper avoids tedious integral operations and is characterized by directness and feasibility.

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