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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.

Analytical criteria of static output feedback problem feasibility for second-order systems

Pakhsin P., Pozdyaev V.

Systems Science

2009

Vol. 35, no 1

39-45

Necessary and sufficient conditions of feasibility of second-order linear matrix inequality systems reducible to two or three scalar quadratic inequalities are presented. These conditions are applied to the problem of static output feedback-based stabilization of a second-order system to obtain two feasibility criteria. The first one is based on the general theorems; the second one is tailored specifically for this problem and is easier to use.

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.

Adaptive control through on-line optimization. The MPCI paradigm and variants

Nikolaou M., Eker S. A.

International Journal of Applied Mathematics and Computer Science

1999

Vol. 9, no 1

25-52

A new variant of Model Predictive Control and Identification (MPCI) is proposed. The on-line objective is not to minimize the sum of square errors, but to maximize on-line the sum of the lower bounds on the minimum eigenvalues of the information matrices over finite horizons. In that way, inputs to the controlled process are allowed to excite the process highly enough to generate as much modelling information as possible, while the process goes off-spec as little as possible. Constraints can be loosened or tightened according to the need for identification. The effectiveness of the proposed new methodology is illustrated through a number of simulations.