The Relaxed State-Dependent Riccati Equation Technique: Concept and applications

A new concept in nonlinear control methods, called the Relaxed State-Dependent Riccati Equation (RSDRE) technique, is introduced in the current paper. This concept is derived from the State-Dependent Riccati Equation (SDRE) technique, which is known as one of the well defined nonlinear controllers. By gridding the states and obtaining representative states, the control gains can be obtained in advance of applying them to systems. Hence, the RSDRE technique is similar to the LQR technique in local state block and can be treated as a discretized SDRE technique in all of the state regions. The RSDRE technique has the same characteristics as the SDRE technique: it has nonlinear, sub-optimal, and robust control. Moreover, this technique can overcome some of the main drawbacks of the SDRE technique, specifically the computational burden in calculating the values of the optimal control gain matrix and the possibility of being unable to solve the algebraic Riccati equation in real-time for some internal or external problems. Examples of attitude controls for inverted pendulum and satellite attitude control systems are presented to show the effectiveness of the RSDRE technique.