  We consider a single kinematically controlled robot with a bounded control
range. The robot travels in a two-dimensional region supporting an unknown
unsteady scalar field. A single sensor provides the field value at the current
location of the robot. The paper is concerned with a reactive navigation
strategy to drive the robot to the time-varying location where the field
attains its spatial maximum, with subsequent keeping the robot close to this
location. This strategy is based on a novel paradigm of kinematic control
different from conventionally trying to align the velocity vector with the
field gradient, does not employ estimation of the entire field gradient or
derivative-dependent quantities, like the rate at which the available field
reading evolves over time, and is non-demanding with respect to both
computation and motion. The paper presents the proofs of the technical facts
required to justify convergence of the proposed algorithm.
