The GA approach to the eigenvalue placement of an LQ optimal system

In this paper, a new genetic approach is presented which places the closed loop eigenvalues of a linear quadratic (LQ) optimal system in a desired stable location by choice of suitable weighting matrices. The location of the closed-loop eigenvalues of the LQ optimal system is determined by the choice of positive definite symmetric weighting matrices Q and R. The problem is then to find the best weighting matrices to locate the closed-loop eigenvalues close to the desired closed-loop eigenvalues as much as possible. This work employs the genetic algorithm to find the proper weighting matrices. The solution (in this case Q and R matrices) is encoded as a chromosome. A computer simulation is given to illustrate the result.