Rahman Mirzaei - Science and Research Branch, Islamic Azad University (IAU)
Omid Bahar - IIEES

During past decades, many control algorithms with some advantages/weaknesses have been proposed. However, the most famous and historic algorithm which has found widespread applications in different fields of science, is the family of optimal control method (OCM). Today, this family includes many different approaches using various performance indices in continuous or discrete domain of consideration. The main stem of OCM is rooted in a simple definition, say performance index (PI), which should be minimized with respect to the main independent variables of the system. Although, different proposed algorithms are employed various performance indices besides simple or stable weighting matrices, their performances are noticeably similar. Extensive analysis shows that the main aspect, which results in reasonable similar performances in spite of their assumption for determining control force, arise from solving the Riccati matrix equation (RME) during their procedure or their stability criteria. This idea is examined by introducing a new simple but unusual assumption, named the simplified LQR (SLQR), via considering seismic behavior of an eight-story shear type building structure.

Optimal Control Method, Riccati Matrix Equation, Simplified LQR, SLQR, AMD