A direct method for computing optimal feedback control for linear systems†

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Abstract
This paper presents a direct method for computing the optimal feedback control law for linear systems. The method is based on representing each control function by a finite number of polynomials, either algebraic or orthogonal. The usual restriction on the weighting matrix of the control vector in the performance index, namely the non-singularity of this matrix, could be removed if the direct method is used. This means that it is possible to have some unconstrained control functions. The direct method handles also the fixed-end problem, which cannot be solved using the Riccati-equation formalism, in a straightforward manner. An example for a system with six state variables and two control functions is given.

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