Optimal Mobile Sensing with Fractional Sensor Dynamics

Abstract

A new formulation toward solving a wide class of fractional optimal control problems is introduced in this chapter. This formulation makes use of an analytical impulse response-based approximation to model the fractional dynamics of the system in terms of a state space realization. This approximation creates a bridge with a classic optimal control problem, and a readily available optimal control solver is used to solve the fractional optimal control problem. The methodology allow us to reproduce results from the literature and to solve a more complex problem of a fractional free final time problem. Numerical results show that the methodology, though simple, achieves good results. For all examples, the solution for the integer-order case of the problem is also obtained for comparison purposes. For the first time, fractional dynamics of the mobile sensors are considered. It is important to note the fact that the introduced formulation has proven to be transcribable into an optimal control problem that can then be solved by readily available optimal control software, in our case, the MATLAB toolbox RIOTS 95. We successfully solve the example of a diffusion system for several teams of sensors and different dynamics. We are also able to use the approximation to obtain the optimal trajectories of a team of sensors with fractional dynamics.