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Mini-Workshop: Recent Developments on Approximation Methods for Controlled Evolution Equations
This mini-workshop brought together mathematicians engaged in partial differential equations, functional analysis, numerical analysis and systems theory in order to address a number of current problems in the approximation of controlled evolution equations
Finite-time disturbance reconstruction and robust fractional-order controller design for hybrid port-Hamiltonian dynamics of biped robots
In this paper, disturbance reconstruction and robust trajectory tracking
control of biped robots with hybrid dynamics in the port-Hamiltonian form is
investigated. A new type of Hamiltonian function is introduced, which ensures
the finite-time stability of the closed-loop system. The proposed control
system consists of two loops: an inner and an outer loop. A fractional
proportional-integral-derivative filter is used to achieve finite-time
convergence for position tracking errors at the outer loop. A fractional-order
sliding mode controller acts as a centralized controller at the inner-loop,
ensuring the finite-time stability of the velocity tracking error. In this
loop, the undesired effects of unknown external disturbance and parameter
uncertainties are compensated using estimators. Two disturbance estimators are
envisioned. The former is designed using fractional calculus. The latter is an
adaptive estimator, and it is constructed using the general dynamic of biped
robots. Stability analysis shows that the closed-loop system is finite-time
stable in both contact-less and impact phases. Simulation studies on two types
of biped robots (i.e., two-link walker and RABBIT biped robot) demonstrate the
proposed controller's tracking performance and disturbance rejection
capability
Models and Feedback Stabilization of Open Quantum Systems
At the quantum level, feedback-loops have to take into account measurement
back-action. We present here the structure of the Markovian models including
such back-action and sketch two stabilization methods: measurement-based
feedback where an open quantum system is stabilized by a classical controller;
coherent or autonomous feedback where a quantum system is stabilized by a
quantum controller with decoherence (reservoir engineering). We begin to
explain these models and methods for the photon box experiments realized in the
group of Serge Haroche (Nobel Prize 2012). We present then these models and
methods for general open quantum systems.Comment: Extended version of the paper attached to an invited conference for
the International Congress of Mathematicians in Seoul, August 13 - 21, 201
An Overview of Integral Quadratic Constraints for Delayed Nonlinear and Parameter-Varying Systems
A general framework is presented for analyzing the stability and performance
of nonlinear and linear parameter varying (LPV) time delayed systems. First,
the input/output behavior of the time delay operator is bounded in the
frequency domain by integral quadratic constraints (IQCs). A constant delay is
a linear, time-invariant system and this leads to a simple, intuitive
interpretation for these frequency domain constraints. This simple
interpretation is used to derive new IQCs for both constant and varying delays.
Second, the performance of nonlinear and LPV delayed systems is bounded using
dissipation inequalities that incorporate IQCs. This step makes use of recent
results that show, under mild technical conditions, that an IQC has an
equivalent representation as a finite-horizon time-domain constraint. Numerical
examples are provided to demonstrate the effectiveness of the method for both
class of systems
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