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A group of targets moves in 3D in an unknown way. This group should be localized, approached, and circumnavigated by a nonholonomic under-actuated mobile robot. The robot measures only the distances to the targets and also has access to a certain space direction, along with its own coordinate (called “altitude”) along it. A novel navigation law is presented that guides the robot to the locus of space points at a desired root mean square distance from the targets and then ensures repeatedly sweeping over the part of this locus between given lower and upper “altitudes”. This law is reactive, i.e., it converts the current observations into current control in a reflex-like fashion. The proposed navigation approach is rigorously justified by a global convergence result; its performance is confirmed by computer simulation tests.

We present a method for guidance of a Dubins-like vehicle towards a target in a cluttered maze-like environment. The vehicle is strongly information and memory limited. In particular, it has no knowledge about the environment and is not capable of memorizing its characteristics. The sensor system provides only the distance to the nearest obstacle if this distance is within the given sensor range, and also gives a partial access to the target relative bearing angle. We examine the simple memoryless static local controller that implements the simple pursuit guidance at a large distance from the obstacles and combines this guidance with collision avoidance activity in a vicinity of obstacles. This activity is undertaken when and only when the distance to the obstacle is decreasing and consists in a maximally sharp turn. At the start of this turn, its direction is randomly chosen; evidence in favor of the random choice option is presented. Mathematically rigorous analysis of this law is provided and it is proved that the vehicle necessarily reaches the destination. Convergence and performance of the proposed controller are confirmed by computer simulations.

Cancer chemotherapy with application of several drugs is studied. The negative and inhibiting effect of the tumors on normal cells is taken into account. Under certain hypotheses, we determine the optimal regimen that minimizes the tumor burden at the end of a fixed period of therapy while maintaining several normal cell populations above prescribed levels. More precisely, it is demonstrated that the optimal strategy corresponds to injection of the drugs at the maximal rates.

The paper deals with qualitative analysis of the so-called switched fluid networks. Such networks are used to model communication, computer, and flexible manufacturing systems. We prove that for any deterministic network from a certain specific class, there exists a finite number of limit cycles attracting all trajectories. Furthermore, we determine this number.

The paper analyzes an example of the discrete control of a continuous variable system. We prove that the switched server system with one server and an arbitrary number of buffers has a set of periodic trajectories which attracts all other trajectories of the system.