Optimal control and stabilization of building maintenance units based on minimum principle

Abstract

In this paper we present a mathematical model describing the physical dynamics of a building maintenance unit (BMU) equipped with reaction jets. The momentum provided by reaction jets is considered as the control variable. We introduce an objective functional based on the deviation of the BMU from its equilibrium state due to external high-wind forces. Pontryagin minimum principle is then used to determine the optimal control policy so as to minimize possible deviation from the rest state thereby increasing the stability of the BMU and reducing the risk to the workers as well as the public. We present a series of numerical results corresponding to three different scenarios for the formulated optimal control problem. These results show that, under high-wind conditions the BMU can be stabilized and brought to its equilibrium state with appropriate controls in a short period of time. Therefore, it is believed that the dynamic model presented here would be potentially useful for stabilizing building maintenance units thereby reducing the risk to the workers and the general public.2010 Mathematics Subject Classification. Primary: 49J15; Secondary: 93C95.