State-Dependent Riccati Equation (SDRE) Control: A Survey

Since the mid-90’s, State-Dependent Riccati Equation (SDRE) strategies have emerged as general design methods that provide a systematic and effective means of designing nonlinear controllers, observers, and filters. These methods overcome many of the difficulties and shortcomings of existing methodologies, and deliver computationally simple algorithms that have been highly effective in a variety of practical and meaningful applications. In a special session at the 17th IFAC Symposium on Automatic Control in Aerospace 2007, theoreticians and practitioners in this area of research were brought together to discuss and present SDRE-based design methodologies as well as review the supporting theory. It became evident that the number of successful simulation, experimental and practical real-world applications of SDRE control have outpaced the available theoretical results. This paper reviews the theory developed to date on SDRE nonlinear regulation for solving nonlinear optimal control problems, and discusses issues that are still open for investigation. Existence of solutions as well as stability and optimality properties associated with SDRE controllers are the main contribution in the paper. The capabilities, design flexibility and art of systematically carrying out an effective SDRE design are also emphasized.