Suboptimal tracking control of nonlinear systems via state-dependent differential Riccati equation for robotic manipulators

Abstract

This work investigates state-dependent differential Riccati equation (SDDRE) controller for tracking problem. The system in question is a class of time-varying nonlinear systems with control nonlinearities. Regulation case needs only the solution to the SDDRE to provide suboptimal gain of control law, though derivation of tracking problem generates a feedforward differential equation in addition to the SDDRE. In that case, the SDDRE stabilizes the system towards equilibrium point and feedforward equation keeps the output following desired trajectory. The new structure imposes complexity on analysis of stability and solution method, which are addressed in this work. Backward integration (BI) technique is selected to solve the governing equations to obtain suboptimal and feedforward control gains. The application of the proposed controller is applied to robotic field. Trajectory tracking is one of the critical issues in manipulator control area; hence this work is dedicated to it. The BI method released an outstanding precise tracking performance based on its two-round solution in comparison with conventional state dependent Riccati equation (SDRE) controller.