Uncertain Underactuated Systems Research Articles

Adaptive fuzzy backstepping controller design for uncertain underactuated robotic systems

In this paper, the control problem of underactuated systems with mismatched and matched uncertainties is addressed. Adaptive fuzzy backstepping controller is proposed to solve the problem, ensuring the robustness against uncertainties and disturbances. Taking a general class of underactuated robotic systems into account, the nonlinear dynamical equations are first transformed to the so-called cascade form and then, an adaptive-based controller is constructed using the capability of fuzzy logic to tackle the perturbations. From the analytic point of view, the closed loop stability is ensured using the Lyapunov stability theorem. To demonstrate the effectiveness of the method, the proposed controller has been applied to a two-wheeled self-balancing robot with three degrees of freedom, and also to a pendubot with two degrees of freedom. In order to highlight the superiority of the proposed algorithm, the performance is compared with that of an existing robust strategy.

Robust Finite Time Controller Design for Second Order Underactuated Mechanical Systems

Stabilization and tracking control of nonlinear uncertain underactuated systems are always challenging problems because underacturated systems have fewer independent control actuators than degrees of freedom to be controlled. For a class of second order underactuated mechanical systems, a robust finite time control strategy is developed in this paper. The robust finite time controller is to drive the tracking error to be zero at the fixed final time. In fact, finite time convergence implies nonsmooth or non-Lipschitz continuous autonomous systems with nonuniqueness of solution. In order to prove the stability, we present a generalized Lyapunov stability proof for the second order underactuated mechanical system. By utilizing a Lyapunov stability theorem, we can achieve finite time tracking of desired reference signals for underactuated systems, which is subject to both external disturbances and system uncertainties. The proposed control scheme is demonstrated by actual experiments on a Furuta pendulum system. Based on the experiment results, the finite time convergence of system errors can be assured.

Adaptive Backstepping Control for Uncertain Underactuated Systems with Input Constraints

Considering a class of underactuated systems with functional uncertainties, an adaptive backstepping controller is presented. By applying backstepping control strategy and online approximation of uncertainties with wavelet networks, the desired tracking performance in presence of actuator constraints is assured. Singularity due to adaptation is tackled by incorporating a switching scheme. Proposed controller guarantees the ultimate upper boundedness of all closed loop signals. Effectiveness of proposed scheme is illustrated through simulation.