Abstract. We consider the problem of seeking the maximum of a scalar signal using a swarm of autonomous vehicles equipped with sensors that can take point measurements of the signal. Vehicles are not able to measure their current position or to communicate with each other. Our approach induces the vehicles to perform a biased random walk inspired by bacterial chemotaxis and controlled by a stochastic hybrid automaton. With such a controller, it is shown that the positions of the vehicles evolve towards a probability density that is a specified function of the spatial profile of the measured signal, granting higher vehicle densities near the signal maxima.

In lossy networks the probability of successful communication can be significantly increased by transmitting multiple copies of a same message through independent channels. In this paper we show that communication protocols that exploit this by dynamically assigning the number of transmitted copies of the same data can significantly improve the control performance in a networked control system with only a modest increase in the total number of transmissions. We develop techniques to design communication protocols that exploit the transmission of multiple packets while seeking a balance between stability/estimation performance and communication rate. An average cost optimality criterion is employed to obtain a number of optimal protocols applicable to networks with different computational capabilities. We also discuss stability results under network contention when multiple nodes utilize these protocols.

We investigate the problem of controlling the probability density of the state of a process that is observed by the controller via a fixed but unknown function of the state. The goal is to control the process so that its probability density at a point in the state space becomes proportional to the value of the function observed at that point. Our solution, inspired by bacterial chemotaxis, involves a randomized controller that switches among different deterministic modes. We show that under appropriate controllability conditions, this controller guarantees convergence of the probability density to the desired function. The results can be applied to the problem of in loco optimization of a measurable signal using a team of autonomous vehicles that use point measurements of the signal but do not have access to position measurements. Alternative applications in the area of mobile robotics include deployment and environmental monitoring.

Abstract-In wireless networks the probability of successful communication can be significantly increased by transmitting multiple copies of a same packet. Communication protocols that exploit this by dynamically assigning the number of transmitted copies of the same data can significantly improve the control performance in a networked control system with only a modest increase in the total number of transmissions. In this paper we develop techniques to design communication protocols that exploit multiple packets transmissions while seeking a balance between stability/estimation performance and communication rate. An average cost optimality criterion is employed to obtain optimal protocols. Optimal protocols are also obtained for networks whose nodes are subject to limited computation.

On-off thrusters are frequently used as actuators for attitude control and are typically subject to switching constraints. In systems with switching actuators, different types of persistent motions may be found, and in the presence of model uncertainties, the occurrence of bifurcations in such systems can seriously affect performance. In this paper the nature of persistent motions in an attitude control system with actuators subject to switching-time restrictions is examined to provide useful information for control design in the presence of uncertainty. The main tools used are bifurcation diagrams, Poincaré maps and Lyapunov spectrum. Border-collision type bifurcations are characterized in this piecewise affine system, as well as unusual patterns of persistent motion. Multistability and complex-switching sequences are also observed, revealing the existence of motions with sensitive dependence on initial conditions.

No abstract

Abstract-The purpose of this contribution is twofold: 1) to present for the first time a Lyapunov function that proves exponential ergodicity of a process studied by the authors in [1], where the problem of controlling the probability density of a swarm of robotic agents was solved; 2) to introduce alongside the method used to construct this Lyapunov function, which is of interest in its own since it may be applicable to a wide class of piecewise deterministic Markov processes. Our method searches for the Lyapunov function that maximizes a measure of the rate of convergence that appears in the theory of large deviations. Analytical solutions are often possible as shown by examples.

No abstract