D-Optimal Trajectories of Mobile Sensors with Fractional Dynamics for Parameter Estimation of Distributed Parameter Systems

In this paper, we propose a methodology to optimize the trajectory of mobile sensors whose dynamics contains fractional derivatives to find parameter estimates of a distributed parameter system. The problem is to maximize the determinant of the Fischer information matrix representing the amount of information gathered on parameters by the sensors. The introduced method transforms the problem to a fractional optimal control one in which both the steering of the sensors and their initial positions are optimized. The resulting fractional optimal control problem is reformulated into an integer order optimal control one which is then solved using the Matlab PDE toolbox and the RIOTS optimal control toolbox which handles various constraints imposed on the sensor motions. The effectiveness of the method is illustrated with a two-dimensional diffusion equation for different numbers of sensors and different orders.