The general problem of multi-agent persistent monitoring finds applications in a variety of domains ranging from macro systems, such as surveillance or environmental monitoring, down to nano-scale systems such as tracking biological macromolecules for studying basic biology and disease. The problem can be cast as moving the agents between targets, acquiring information from or in some fashion controlling the states of the targets. Under this formulation, at least two questions need to be addressed. The first is the design of motion trajectories for the agents as they move among the spatially distributed targets and jointly optimize a given cost function that describes some desired application. The second is the design of the controller that an agent will use at a target to steer the target’s state as desired.
The first question can be viewed in at least two ways: first, as an optimal control problem and second as a discrete scheduling task. Under the first approach, the domain of the targets is described as a continuous space. We parameterize the agent trajectories to allow the use of gradient descent approaches, such as Infinitesimal Perturbation Analysis, to yield scalable solutions (in the number of targets and agents). The second formulates the target dynamics as a hybrid automaton, and the geometry of the targets as a graph. We show how to find solutions by translating scheduling problem into a search for the optimal route. With a route specifying the visiting sequence in place, we derive the optimal dwell time analytically.
The second question, namely that of steering the target’s state, can be formulated from the perspective of the target, rather than the agent. The mobile nature of the agents leads to intermittent control, such that the controller is assumed to be disconnected when no agent is at the target. The design of the visiting schedule of agents to one target can affect the reachability (controllability) of this target’s control system and the design of any specific controller. Existing test techniques for reachability are combined with the idea of lifting to provide conditions on systems such that reachability is maintained in the presence of periodic disconnections from the controller. While considering an intermittently connected control with constraints on the control authority and in the presence of a disturbance, the concept of degree of controllability is introduced. The degree is measured by a region of states that can be brought back to the origin in a given finite time. The size of this region is estimated to evaluate the performance of a given sequence.