An optimal robot tracking controller with application in the finite horizon case

A control law for a rigid robotic manipulator optimizing quadratic cost functional composed of sliding surface and its derivative for fixed final time and free final state was proposed by Z. Ahmad (1995; 2000). Closed form solutions for such a control law corresponding to constant in time and specific diagonal time-varying weighting matrices are presented. These closed form solutions for the two point boundary value problem greatly reduce computational load and allow for real time implementation. Simulation results for a two degree of freedom manipulator are also provided.