Vincent Yen

Fourier-Based Optimal Control of Nonlinear Dynamic Systems

A method for generating near optimal trajectories of linear and nonlinear dynamic systems, represented by deterministic, lumped-parameter models, is proposed. The method is based on a Fourier series approximation of each generalized coordinate that converts the optimal control problem into an algebraic nonlinear programming problem. The results of computer simulation studies compare favorably to optimal solutions obtained by closed-form analyses and/or by other numerical schemes

Fourier-based optimal control approach for structural systems

This paper considers the optimal control of structural systems with quadratic performance indices. The proposed approach approximates each configuration variable of a structural model by the sum of a fifth order polynomial and a finite term Fourier-type series. In contrast to standard linear optimal control approaches which typically require the solution of Riccati equations, the method adopted here is a near optimal approach in which the necessary and sufficient condition of optimality is derived as a system of linear algebraic equations. These equations can be solved directly by a method such as Gaussian elimination. The proposed approach is computationally efficient and can be applied to structural systems of high dimension and/or to structural systems with fixed (or highly penalized) terminal states without numerical difficulties.

Optimal trajectory planning of robotic manipulators via quasi-linearization and state parametrization

A numerical algorithm has been developed to solve the problem of optimal control of robotic manipulators. A quasi-linearization method is used to convert a nonlinear optimal control problem into a sequence of LQ (linear quadratic) problems, which are solved by an efficient Fourier-based state parameterization approach. The update laws for the nominal trajectory ensure satisfaction of the terminal conditions. In contrast to dynamic-programming-based methods, the proposed approach does not demand extensive computer storage requirements and thus is capable of achieving optimality without limiting the degrees of freedom of the trajectory. Compared to nonlinear-programming-based methods, the approach offers significant advantages in computational efficiency. Compared to calculus-of-variations-based methods, the approach eliminates the requirement of solving a two-point boundary-value problem and therefore is more robust and efficient.<<ETX>>

Development of linear quadratic control laws via control parametrization

A control parametrization approach for determining the near optimal solution of linear quadratic (LQ) problems is developed. By assuming each control variable to be piecewise continuous, the proposed approach converts an LQ problem into an unconstrained quadratic programming problem. The near optimal control response can then be determined by solving a system of linear algebraic equations. The control parametrization approach can eliminate the major repetitive computations in designing an LQ control law, a process that often involves multiple adjustments of different weighting matrices. This feature makes the proposed approach a computationally attractive tool for LQ controller design. Simulation studies show that the control parametrization approach is particularly well suited for large scale systems that possess a small control/state dimension ratio.