A Maximum Time Optimal Control Approach to Routing in Sensor Networks

An optimal control approach is used to solve the problem of routing in sensor networks where the goal is to maximize the network´s lifetime. We show that in a fixed topology case there exists an optimal policy consisting of fixed routing probabilities which may be obtained by solving a set of relatively simple Non-Linear Programming (NLP) problems. An alternative problem is also considered where, in addition to routing, we also allocate a total initial energy over the network nodes with the same network lifetime maximization objective. We prove that the solution to this problem is given by a policy that depletes all node energies at the same time and that the corresponding energy allocation and routing probabilities are obtained by solving a single NLP problem. Numerical examples are included to contrast the maximum lifetime we obtain to that resulting from alternative routing policies.