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When employing autonomous helicopters, it is desirable to use navigation approaches, which firmly ensure safety. In this paper, we propose and compare two approaches to navigation through environments containing obstacles. The first uses sliding mode boundary following to maintain a prespecified distance to obstacles, and the second uses a model predictive control approach to plan short horizon trajectories around detected objects, while ensuring that the helicopter is brought to a halt within the sensor visibility radius. The navigation approaches are subjected to analysis for robustness, and simulations are carried out with a realistic helicopter model for verification. Additional real-world experiments were performed with a wheeled robot to demonstrate potential for real-time application. [ABSTRACT FROM PUBLISHER]

This paper considers a general optimal control problem with a small time delay Δ in both the state and control. The objective is to find a correct way to neglect the delay or, in other words, to construct a well-posed instantaneous approximation of the delayed problem. The natural way to do so is by merely ignoring the delay in the model. It is shown that this way is almost always incorrect: it gives rise to an error that does not vanish as Δ → +0, and so results in an ill-posed model. A proper approximation of the delayed problem is offered. [ABSTRACT FROM AUTHOR]

Cancer chemotherapy for the case of one drug is studied. The negative andinhibiting effect of the tumour on normal cells is taken into account. Undercertain assumptions, we determine the optimal regimen that minimizes the tumourburden at the end of a fixed period of therapy while maintaining certain normalcell populations above prescribed levels. More precisely, it is demonstratedthat the optimal strategy corresponds to injection of the drug at the maximalrate. [ABSTRACT FROM PUBLISHER]

In the context of control and estimation under information constraints, restoration entropy measures the minimal required data rate above which the state of a system can be estimated so that the estimation quality does not degrade over time and, conversely, can be improved. The remote observer here is assumed to receive its data through a communication channel of finite bit-rate capacity. In this paper, we provide a new characterization of the restoration entropy which does not require to compute any temporal limit, i.e., an asymptotic quantity. Our new formula is based on the idea of finding a specific Riemannian metric on the state space which makes the metric-dependent upper estimate of the restoration entropy as tight as one wishes. [ABSTRACT FROM AUTHOR]

A nonholonomic under-actuated robot with a bounded control range travels inside an unknown and unstructured 3D tunnel bounded by a generic 2D surface. The robot has access to the nearest point of the surface and measures the distance to the surface along any ray from a narrow beam emitted from the robot around the direction to the nearest point. We present a new navigation law that ensures constant advancement of the robot through the tunnel, along with respecting a given safety margin to its surface, driving the robot to the desired distance to it, and subsequently maintaining this distance. This law is reactive: it generates the current control as a reflex-like reaction to the current observation. Rigorous justification of the proposed guidance approach is provided; its applicability and performance are confirmed by computer simulation tests. [ABSTRACT FROM AUTHOR]

In this paper, the design of a data-rate constrained observer for a dynamical system is presented. This observer is designed to function both in discrete time and continuous time. The system is connected to a remote location via a communication channel which can transmit limited amounts of data per unit of time. The objective of the observer is to provide estimates of the state at the remote location through messages that are sent via the channel. The observer is designed such that it is robust toward losses in the communication channel. Upper bounds on the required communication rate to implement the observer are provided in terms of the upper box dimension of the state space and an upper bound on the largest singular value of the system's Jacobian. Results that provide an analytical bound on the required minimum communication rate are then presented. These bounds are obtained by using the Lyapunov dimension of the dynamical system rather than the upper box dimension in the rate. The observer is tested through simulations for the Lozi map and the Lorenz system. For the Lozi map, the Lyapunov dimension is computed. For both systems, the theoretical bounds on the communication rate are compared to the simulated rates. [ABSTRACT FROM AUTHOR]

We propose a novel distributed random algorithm for self-deployment of a network of mobile wireless sensors in the problem of blanket coverage. The aim is to deploy sensors in a bounded region so that any point of the region is sensed by at least one sensor. The algorithm is based only on information about the closest neighbours of each sensor. The monitoring region is of an arbitrary shape and not known to the sensors a priori. We give mathematically rigorous proofs of asymptotic optimality and convergence with probability 1 of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

This paper provides a solution for the preservation of consensus in a network of several agents, described by discrete-time nonlinear dynamical systems. Consensus preservation is the problem of maintaining a certain distance between the states of several systems, given that the systems' initial states are close to each other. The agents are equipped with both a smart sensor, capable of measuring the state of the system and performing some computations, and a controller. The sensors and controllers are placed at locations that are remote from one another. A network of communication channels with limited transmission capacity connects the agents by allowing the sensors to send messages to the controllers of their system as well as to the controllers of other systems. The controllers use the messages that they receive to steer the agents such that the consensus is preserved. Sensors and controllers that achieve this feature are called consensus-preserving protocols. In this paper, three distinct consensus-preserving protocols are presented, each with an increasing degree of interaction between the systems. For each of these protocols, a theorem providing conditions on the minimum communication capacity sufficient to implement them is presented. The protocols are tested by simulations for a network of logistic maps and a network of Hénon maps. For both of these networks, analytical bounds on the sufficient transmission capacities in the communication channels to implement the protocols are provided. These bounds are compared to rates observed in simulations of the consensus-preserving protocols. [ABSTRACT FROM AUTHOR]