Adaptive RBFNN finite-time control of normal forms for underactuated mechanical systems

Abstract : This paper presents a constructive design of a continuous finite-time controller for a class of mechanical systems known as underactuated systems that satisfy the symmetry properties. An adaptive radial basis function neural network (RBFNN) finite-time control scheme is proposed to stabilize the underactuated system at a given equilibrium, regardless of the various uncertainties and disturbances that the system contains. First, a coordinate transformation is introduced to decouple the control input so that an n-th order underactuated system can be represented into a special cascade form. Next, an adaptive robust finite-time controller is derived from adding a power integrator technique and the RBFNN to approximate the nonlinear unknown dynamics in the new space, whose bounds are supposedly unknown. The stability and finite-time convergence of the closed-loop system are established by using Lyapunov theory. To show the effectiveness of the proposed method, simulations are carried out on the rotary inverted pendulum, a typical example of an underactuated mechanical system.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01692560
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Submitted on : Thursday, January 25, 2018 - 11:44:37 AM
Last modification on : Monday, July 16, 2018 - 4:01:25 PM

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Jawhar Ghommam, Ahmed Chemori. Adaptive RBFNN finite-time control of normal forms for underactuated mechanical systems. Nonlinear Dynamics, Springer Verlag, 2017, 90 (1), pp.301-315. ⟨10.1007/s11071-017-3662-3⟩. ⟨lirmm-01692560⟩

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