Optimal scheduling of multiple sensors in continuous time

This paper considers an optimal sensor scheduling problem in continuous time. In order to make the model more close to the practical problems, suppose that the following conditions are satisfied: only one sensor may be active at any one time; an admissible sensor schedule is a piecewise constant function with a finite number of switches; and each sensor either doesn't operate or operates for a minimum non-negligible amount of time. However, the switching times are unknown, and the feasible region isn't connected. Thus, it's difficult to solve the problem by conventional optimization techniques. To overcome this difficulty, by combining a binary relaxation, a time-scaling transformation and an exact penalty function, an algorithm is developed for solving this problem. Numerical results show that the algorithm is effective.