In this article, the authors propose and investigate a new concept of HAPS aerostat design in a modular form, which allows for sequential increasing or decreasing of the total volume, up to the desired size. In its initial form, the aerostat has relatively small dimensions but its central cylindrical part is multi-segmented and can be easily extended. The application of controllable construction couplings enables precise control of the aerostat expansion process and significantly improves its vertical mobility. The paper describes details of telescopic aerostat construction, presents a mathematical model of its vertical motion and investigates numerically two volume control strategies aimed at maximization of operation efficiency and minimization of operation cost. The results obtained reveal the main problems that have to be addressed and the factors that play a key role in design of such telescopic aerostats and control of their vertical mobility.