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This paper deals with the stabilization of a class of linear infinite-dimensional systems with unbounded control operators and subject to a boundary disturbance. We assume that there exists a linear feedback law that makes the origin of the closed-loop system globally asymptotically stable in the absence of disturbance. To achieve our objective, we follow a sliding mode strategy and we add another term to this controller in order to reject the disturbance. We prove the existence of solutions to the closed-loop system and its global asymptotic stability, while making sure the disturbance is rejected.

Passivity property gives a sense of energy balance. The classical definitions and theorems of passivity in dynamical systems require time invariance and locally Lipschitz functions. However, these conditions are not met in many systems. A characteristic example is nonautonomous and discontinuous systems due to presence of Coulomb friction. This paper presents an extended result for the negative feedback connection of two passive nonautonomous systems with set-valued right-hand side based on an invariance-like principle. Such extension is the base of a structural passivity-based control synthesis for underactuated mechanical systems with Coulomb friction. The first step consists in designing the control able to restore the passivity in the considered friction law, achieving stabilization of the system trajectories to a domain with zero velocities. Then, an integral action is included to improve the latter result and perform a tracking over a constant reference (regulation). At last, the control is designed considering dynamics in the actuation. These control objectives are obtained using fewer control inputs than degrees of freedom, as a result of the underactuated nature of the plant. The presented control strategy is implemented in an earthquake prevention scenario, where a mature seismogenic fault represents the considered frictional underactuated mechanical system. Simulations are performed to show how the seismic energy can be slowly dissipated by tracking a slow reference, thanks to fluid injection far from the fault, accounting also for the slow dynamics of the fluid's diffusion.

Robust output tracking is addressed in this paper for a heat equation with Neumann boundary conditions and anti-collocated boundary input and output. The desired reference tracking is solved using the well-known flatness and Lyapunov approaches. The reference profile is obtained by solving the motion planning problem for the nominal plant. To robustify the closed-loop system in the presence of the disturbances and uncertainties, it is then augmented with PI feedback plus a discontinuous component responsible for rejecting matched disturbances with \textit{a priori} known magnitude bounds. Such control law only requires the information of the system at the same boundary as the control input is located. The resulting dynamic controller globally exponentially stabilizes the error dynamics while also attenuating the influence of Lipschitz-in-time external disturbances and parameter uncertainties. For the case when the motion planning is performed over the uncertain plant, an exponential Input-to-State Stability is obtained, preserving the boundedness of the tracking error norm. The proposed controller relies on a discontinuous term that however passes through an integrator, thereby minimizing the chattering effect in the plant dynamics. The performance of the closed-loop system, thus designed, is illustrated in simulations under different kinds of reference trajectories in the presence of external disturbances and parameter uncertainties.

This paper addresses the possibility of using robust control theory for preventing earthquakes through fluid injections in the earth's crust. The designed robust controllers drive aseismically a fault system to a new equilibrium point of lower energy by tracking a slow reference signal. The control design is based on a reduced-order nonlinear model able to reproduce earthquake-like instabilities. Uncertainties related to the frictional and mechanical properties of the underlying physical process and external perturbations are considered. Two types of controllers are derived. The first one is based on sliding-mode theory and leads to local finite-time convergence of the tracking error and rejection of Lipschitz w.r.t. time perturbations. The second controller is based on LQR control and presents global exponential stability of the tracking error and rejection of Lipschitz w.r.t. states perturbations. Both controllers generate a continuous control signal, attenuating the chattering effect in the case of the sliding-mode algorithms. The developed controllers are tested extensively and compared on the basis of numerical simulations and experiments in the laboratory. The present work opens new perspectives for the application of robust nonlinear control theory to complex geosystems, earthquakes and sustainable energy production.

This paper addresses the problem of control of a twin wind turbine which is subject to an electrical fault affecting only one stator phase of one turbine. An active fault tolerant control is proposed. The performance and robustness of the proposed control, comparing to a passive fault tolerant one developed in the literature, are shown through numerical simulations.

This article presents a new hand architecture with three under-actuated fingers. Each finger performs spatial movements to achieve more complex and varied grasping than the existing planar-movement fingers. The purpose of this hand is to grasp complex-shaped workpieces as they leave the machining centres. Among the taxonomy of grips, cylindrical and spherical grips are often used to grasp heavy objects. A combination of these two modes makes it possible to capture most of the workpieces machined with 5-axis machines. However, the change in grasping mode requires the fingers to reconfigure themselves to perform spatial movements. This solution requires the addition of two or three actuators to change the position of the fingers and requires sensors to recognize the shape of the workpiece and determine the type of grasp to be used. This article proposes to extend the notion of under-actuated fingers to spatial movements. After a presentation of the kinematics of the fingers, the problem of stability is discussed as well as the transmission of forces in this mechanism. The complete approach for calculating the stability conditions is presented from the study of Jacobian force transmission matrices. CAD representations of the hand and its behavior in spherical and cylindrical grips are presented.