Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non-Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using continuous Lyapunov functions. In this paper, we develop a framework for addressing the problem of optimal nonlinear analysis and feedback control for finitetime stability and finite-time stabilization. Finite-time stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that satisfies a differential inequality involving fractional powers. This Lyapunov function can clearly be seen to be the solution to a partial differential equation that corresponds to a steady-state form of the Hamilton-Jacobi-Bellman equation, and hence, guaranteeing both finite-time stability and optimality.

Following an European Space Agency announcement of opportunity in 1996 for "Externally mounted payloads for 1st utilization phase" on the International Space Station (ISS), scientists working in the fields of astrobiology proposed experiments aiming at longterm exposure of a variety of chemical compounds and extremely resistant microorganisms to the hostile space environment. The ESA exposure facility EXPOSE was built and an operations' concept was prepared. The EXPOSE experiments were developed through an intensive pre-flight experiment verification test program. 12 years later, two sets of astrobiological experiments in two EXPOSE facilities have been successfully launched to the ISS for external exposure for up to 1.5 years. EXPOSE-E, now installed at the balcony of the European Columbus module, was launched in February 2008, while EXPOSE-R took off to the ISS in November 2008 and was installed on the external URM-D platform of the Russian Zvezda module in March 2009.

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