The dynamics of a robotic hand is highly non-linear and needs nonlinear feedback control strategies for its functionality. One of the highly promising and rapidly developing techniques for nonlinear, optimal, feedback control is based on the State Dependent Differential Riccati Equation (SD-DRE), also commonly called SDRE. In this technique, an analytical approach is used to transform the original nonlinear differential Riccati equation to a linear differential Lyapunov equation that can be solved in closed form at each time step in real time. In the present case of optimal tracking problems, it is necessary to formulate an additional State Dependent Differential Vector Equation (SD-DVE) to be simultaneously solved with the SD-DRE. This paper presents a unique application of the SD-DRE and SD-DVE strategies for optimal tracking of the robotic hand. Simulations with the finite-horizon optimal tracking controller for a two-link thumb of a robotic hand are given to support the effectiveness of the proposed technique.