Nonlinear closed loop optimal control: A modified state-dependent Riccati equation

► A modified SDRE based on supplementing constraints into Q matrix is introduced. ► The PSA for solving the modified SDRE is presented. ► An example with control nonlinearities and time varying Q is solved by three methods. ► Obstacle avoidance via SDRE, as a result, in robotics is expressed. ► A planar and a 3D robot as examples are simulated.