2016/01/13 by Shuo Wang, Wang, Shuo, Jr-Shin Li +1
Biochemistry, Genetics and Molecular Biology · Chemistry · Mathematics · Medicine · #49 #Advanced MRI Techniques and Applications #Advanced NMR Techniques and Applications #Electron Spin Resonance Studies #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:49
paper · pdf · doi:10.48550/arxiv.1601.03329
23 pages, 3 figures
arxiv created 2016/01/13 · openalex publication_date 2016/01/13 · arxiv updated 2016/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are underdeveloped. In this work, we develop an iterative method to effectively and systematically solve these challenging optimal ensemble control problems, in which the bilinear ensemble system is represented as a time-varying linear ensemble system at each iteration and the optimal ensemble control law is then obtained by the singular value expansion of the input-to-state operator that describes the dynamics of the linear ensemble system. We examine the convergence of the developed iterative procedure and pose optimality conditions for the convergent solution. We also provide examples of practical control designs in magnetic resonance to demonstrate the applicability and robustness of the developed iterative method.