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Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems

Muhafzan

International Journal of Applied Mathematics and Computer Science

2010

Vol. 20, no 4

655-664

This paper deals with the Linear Quadratic Regulator (LQR) problem subject to descriptor systems for which the semidefinite programming approach is used as a solution. We propose a new sufficient condition in terms of primal dual semidefinite programming for the existence of the optimal state-control pair of the problem considered. The results show that semidefinite programming is an elegant method to solve the problem under consideration. Numerical examples are given to illustrate the results.

A new nonlinear Lagrangian method for nonconvex semidefinite programming

Li Y., Zhang L.

Journal of Applied Analysis

2009

Vol. 15, nr 2

149-172

We study convergence properties of a new nonlinear Lagrangian method for nonconvex semidefinite programming. The convergence analysis shows that this method converges locally when the penalty parameter is less than a threshold and the error bound of solution is proportional to the penalty parameter under the constraint nondegeneracy condition, the strict complementarity condition and the strong" second order sufficient conditions. The major tools used in the analysis include the second implicit function theorem and differentials of Lowner operators.