The project proposes a concept of piezoelectric adaptive thin shell reflector for future space telescopes; it exhibits excellent
areal density and stowability, and thus, paves the way to future large aperture space telescopes. Controlling the surface figure of
spherical or parabolic shell with in-plane stresses induced by a piezoelectric layer raises two problems: 
(1) Doubly curved
shells are significantly stiffer than flat plates and 
(2) When using segmented electrodes with different voltages, the surface figure
is subject to edge fluctuations. 
This results in a very large number of electrodes, leading to ill-conditioning in the Jacobian
matrix of the system; to solve this, a hierarchical approach is proposed to inverse the Jacobian, based on Saint-Venant’s
principle. This research also provides a petal configuration design which aims at reducing the hoop stiffness and improving the
foldability of the reflector.