General orthogonal polynomials approximation of the linear-quadratic-gaussian control design

The solution of the linear-quadratic-gaussian control design is obtained by orthogonal polynomial approximation. The operational matrices of forward and backward integration are derived. It is shown that the product of two arbitrary matrix time functions can be expressed in terms of a matrix of general orthogonal polynomials. It is also shown that both the filter gain and the regulator gain can be approximated by an orthogonal polynomial. An illustrative example is included to show the validity and applicability of the orthogonal polynomial approximations.