Stabilization of a linear Korteweg-de Vries equation with a saturated internal control

This article deals with the design of saturated controls in the context of partial differential equations. It is focused on a linear Korteweg-de Vries equation, which is a mathematical model of waves on shallow water surfaces. In this article, we close the loop with a saturating input that renders the equation nonlinear. The well-posedness is proven thanks to the nonlinear semigroup theory. The proof of the asymptotic stability of the closed-loop system uses a Lyapunov function.Comment: European Control Conference, Jul 2015, Linz, Austri

Global tracking for an underactuated ships with bounded feedback controllers

In this paper, we present a global state feedback tracking controller for underactuated surface marine vessels. This controller is based on saturated control inputs and, under an assumption on the reference trajectory, the closed-loop system is globally asymptotically stable (GAS). It has been designed using a 3 Degree of Freedom benchmark vessel model used in marine engineering. The main feature of our controller is the boundedness of the control inputs, which is an essential consideration in real life. In absence of velocity measurements, the controller works and remains stable with observers and can be used as an output feedback controller. Simulation results demonstrate the effectiveness of this method

Solving the Jitter Problem in Microwave Compressed Ultrafast Electron Diffraction Instruments: Robust Sub-50 fs Cavity-Laser Phase Stabilization

We demonstrate the compression of electron pulses in a high-brightness ultrafast electron diffraction (UED) instrument using phase-locked microwave signals directly generated from a mode-locked femtosecond oscillator. Additionally, a continuous-wave phase stabilization system that accurately corrects for phase fluctuations arising in the compression cavity from both power amplification and thermal drift induced detuning was designed and implemented. An improvement in the microwave timing stability from 100 fs to 5 fs RMS is measured electronically and the long-term arrival time stability ($>$10 hours) of the electron pulses improves to below our measurement resolution of 50 fs. These results demonstrate sub-relativistic ultrafast electron diffraction with compressed pulses that is no longer limited by laser-microwave synchronization.Comment: Accepted for publication in Structural Dynamic

Global stabilization of linear systems with bounds on the feedback and its successive derivatives

We address the global stabilization of linear time-invariant (LTI) systems when the magnitude of the control input and its successive time derivatives, up to an order $p\in\mathbb N$, are bounded by prescribed values. We propose a static state feedback that solves this problem for any admissible LTI systems, namely for stabilizable systems whose internal dynamics has no eigenvalue with positive real part. This generalizes previous work done for single-input chains of integrators and rotating dynamics

Robust observer design under measurement noise with gain adaptation and saturated estimates

We use incremental homogeneity, gain adaptation and incremental observability for proving new results on robust observer design for systems with noisy measurement and bounded trajectories. A state observer is designed by dominating the incrementally homogeneous nonlinearities of the observation error system with its linear approximation, while gain adaptation and incremental observability guarantee an asymptotic upper bound for the estimation error depending on the limsup of the norm of the measurement noise. A characteristic and innovative feature of this observer is the mixed low/high-gain structure in combination with saturated state estimates and dynamically tuned gains and saturation levels. The gain adaptation is implemented as the output of a stable filter using the squared norm of the measured output estimation error and the mismatch between each estimate and its saturated value