Numerical solution to uncertainties in the finite time optimal control systems design

Application of Optimal Control Laws in autonomous systems with finite energy sources, such as freestanding and aerial robots, is a real need for today. This paper presents a finite horizon optimal controlled design with fixed initial and final states, for such complex and autonomous self-propelled systems. While its design methodology is well known, inconsistencies and singularities may occur in the control law computation, mainly for higher order systems. It is a critical issue in real-time design, which is not mentioned and treated in classical optimal control theory. In this paper, we propose and show, how the problem of the numerical spread error in the path computation a singularity can be reached. This type of problem is critical and unwanted for real-time design, in which is necessary to recalculate the path to get the desired final state online. A solution for this problem is presented, and computational simulation is also shown.