On solving semidefinite programming by quantifier elimination

H. Anai
1998 Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)  
In this paper we report one successful application of Quantifier Elimination $(\mathrm{Q}\mathrm{E})$ method to control problems; We focus on the Semidefinite Programming $(SDP)$ problems, which are the central among the generic Linear Matrix Inequality $(LMI)$ problems. Since many control problems and design specifications are reduced to LMI formulations, the LMI problems are that of great practical and theoretical interest in control theory. Though the SDP problems are usually solved as
more » ... optimization problem numerically, when we take the real parametric uncertainties into account, the SDP problems often become non-convex and most of existing numerical methods fails. Hence we present a new symbolic method based on QE and show some experiments by using existing QE package to demonstrate the capability of the method. The method gives us exact solutions and enables us to deal with non-convex and also parametric case. Moreover, by this method, model or parameter uncertainties are $\mathrm{e}\mathrm{a}s\mathrm{y}$ to incorporate in the SDP problems. 1038 1998 154-162
doi:10.1109/acc.1998.688368 fatcat:e2gll7p4e5hpznawxj6wlhn5ii