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In this paper, the robust control problem is tackled by employing the state-dependent Riccati equation (SDRE) for uncertain systems with unmeasurable states subject to mismatched time-varying disturbances. The proposed observer-based robust (OBR) controller is applied to two highly nonlinear, coupled and large robotic systems: namely a manipulator presenting joint flexibility due to deformation of the power transmission elements between the actuator and the robot known as flexible-joint robot (FJR) and also an FJR incorporating geared permanent magnet DC motor dynamics in its dynamic model called electrical flexible-joint robot (EFJR). A novel state-dependent coefficient (SDC) form is introduced for uncertain EFJRs. Rather than coping with the OBR control problem for such complex uncertain robotic systems, the main idea is to solve an equivalent nonlinear optimal control problem where the uncertainty and disturbance bounds are incorporated in the performance index. The stability proof is presented. Solving the complicated robust control problem for FJRs and EFJRs subject to uncertainty and disturbances via a simple and flexible nonlinear optimal approach and no need of state measurement are the main advantages of the proposed control method. Finally, simulation results are included to verify the efficiency and superiority of the control scheme.

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