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• W29897944 abstract "This report describes research aimed to develop a general analytical and numerical tool for designing the near optimal trajectories of lumped-parameter dynamical systems. The approach is based on a method which approximates each generalized coordinate of a dynamical system by the sum of a fifth-order polynomial and a finite term Fourier-type series. Optimality is achieved by adjusting the free boundary conditions and the coefficients of the Fourier-type series such that a performance index is minimized. The adjusted variables can be used to determine the near optimal trajectories of the generalized coordinates and the control variables. Reported herein is a specialization of this approach for linear structural systems, represented by simultaneous second-order differential equations. In contrast to standard linear optimal control approaches which typically require the solution of differential Riccati equations, the method presented is a near optimal approach in which the necessary and sufficient condition of optimality is represented by simultaneous linear algebraic equations, which can be solved directly. Simulation results show that the approach is computationally efficient, numerically robust, and capable of solving for the optimal control of linear systems of high order andlor of linear systems with fixed (or highly penalized) terminal configuration variables. Future work is planned to continue investigating this innovative idea of Fourier-based optimal control. In particular, it is proposed to (i) utilize quadratic programming techniques to extend the approach to problems with linear constraints on configuration andlor control variables, (ii) develop sensitivity functions to determine the influence of system parameters on the near optimal control, (Hi) generalize the approach to apply to general linear systems, represented by simultaneous first order differential equations (state equations), and (iv) solve for the near optimal trajectories of nonlinear dynamical systems via sequential linearization. The results of this project will lead to a powerful methodology for solving optimal control problems, applicable to high order and nonlinear problems, which have previously been difficult, if not impossible, to solve." @default.
• W29897944 created "2016-06-24" @default.
• W29897944 creator A5048125338 @default.
• W29897944 creator A5067052751 @default.
• W29897944 date "1988-01-01" @default.
• W29897944 modified "2023-09-27" @default.
• W29897944 title "Designing near optimal trajectories of structural systems by Fourier-based methods" @default.
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• W29897944 hasPublicationYear "1988" @default.
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