Output-feedback stabilisation control for a class of under-actuated mechanical systems

Output-feedback control of general underactuated mechanical systems is currently considered a major open problem. This study is focused on the output-feedback stabilisation control problems for a special class of underactuated mechanical systems, which appear in robotics and aerospace applications. For the synthesis of controller, first, the considered underactuated mechanical system is explicitly transformed into two cascade connected subsystems, and then an auxiliary filter-based virtual stabilisation controller is developed to locally asymptotically stabilise the first subsystem. Further, the designed virtual controller is again involved into the second subsystem using backstepping procedure to construct the actual control law, in which a series of auxiliary time-varying first-order low-pass filters are also implemented to avoid using the derivative of the system non-linear functions. Moreover, in the second step, finite-time observer technique is utilised to precisely reconstruct the immeasurable states to achieve the finite-time stabilisation control in the sense of output feedback. Lyapunov analysis shows the local asymptotic stability of the closed-loop system through the cascade system stability criteria. Simulation results are presented by using two benchmark non-linear underactuated mechanical systems to demonstrate the feasibility and the effectiveness of the proposed controller.