arXiv subjects
Publications and source records attributed to Larisa Manita.
In this paper we study an optimal control problem that is affine in two-dimensional bounded control. The problem is related to the stabilization of an inverted spherical pendulum in the vicinity of the upper unstable equilibrium. We find solutions stabilizing the pendulum in a finite time, wherein the corresponding optimal controls perform an infinite number of rotations along the circle $S^{1}$.
Energy-saving optimization is very important for various engineering problems related to modern distributed systems. We consider here a control problem for a wireless sensor network with a single time server node and a large number of client nodes. The problem is to minimize a functional which accumulates clock synchronization errors in the clients nodes and the energy consumption of the server over some time interval $[0,T]$. The control function $u=u(t)$, $0\leq u(t)\leq u_{1}$, corresponds to the power of the server node transmitting synchronization signals to the clients. For all possible parameter values we find the structure of optimal trajectories. We show that for sufficiently large $u_{1}$ the solutions contain singular arcs.