12,667 research outputs found
Deterministic continutation of stochastic metastable equilibria via Lyapunov equations and ellipsoids
Numerical continuation methods for deterministic dynamical systems have been
one of the most successful tools in applied dynamical systems theory.
Continuation techniques have been employed in all branches of the natural
sciences as well as in engineering to analyze ordinary, partial and delay
differential equations. Here we show that the deterministic continuation
algorithm for equilibrium points can be extended to track information about
metastable equilibrium points of stochastic differential equations (SDEs). We
stress that we do not develop a new technical tool but that we combine results
and methods from probability theory, dynamical systems, numerical analysis,
optimization and control theory into an algorithm that augments classical
equilibrium continuation methods. In particular, we use ellipsoids defining
regions of high concentration of sample paths. It is shown that these
ellipsoids and the distances between them can be efficiently calculated using
iterative methods that take advantage of the numerical continuation framework.
We apply our method to a bistable neural competition model and a classical
predator-prey system. Furthermore, we show how global assumptions on the flow
can be incorporated - if they are available - by relating numerical
continuation, Kramers' formula and Rayleigh iteration.Comment: 29 pages, 7 figures [Fig.7 reduced in quality due to arXiv size
restrictions]; v2 - added Section 9 on Kramers' formula, additional
computations, corrected typos, improved explanation
Geometry-aware Manipulability Learning, Tracking and Transfer
Body posture influences human and robots performance in manipulation tasks,
as appropriate poses facilitate motion or force exertion along different axes.
In robotics, manipulability ellipsoids arise as a powerful descriptor to
analyze, control and design the robot dexterity as a function of the
articulatory joint configuration. This descriptor can be designed according to
different task requirements, such as tracking a desired position or apply a
specific force. In this context, this paper presents a novel
\emph{manipulability transfer} framework, a method that allows robots to learn
and reproduce manipulability ellipsoids from expert demonstrations. The
proposed learning scheme is built on a tensor-based formulation of a Gaussian
mixture model that takes into account that manipulability ellipsoids lie on the
manifold of symmetric positive definite matrices. Learning is coupled with a
geometry-aware tracking controller allowing robots to follow a desired profile
of manipulability ellipsoids. Extensive evaluations in simulation with
redundant manipulators, a robotic hand and humanoids agents, as well as an
experiment with two real dual-arm systems validate the feasibility of the
approach.Comment: Accepted for publication in the Intl. Journal of Robotics Research
(IJRR). Website: https://sites.google.com/view/manipulability. Code:
https://github.com/NoemieJaquier/Manipulability. 24 pages, 20 figures, 3
tables, 4 appendice
Time-delay systems : stability, sliding mode control and state estimation
University of Technology, Sydney. Faculty of Engineering and Information Technology.Time delays and external disturbances are unavoidable in many practical control systems such as robotic manipulators, aircraft, manufacturing and process control systems and it is often a source of instability or oscillation. This thesis is concerned with the stability, sliding mode control and state estimation problems of time-delay systems. Throughout the thesis, the Lyapunov-Krasovskii (L-K) method, in conjunction with the Linear Matrix Inequality (LMI) techniques is mainly used for analysis and design.
Firstly, a brief survey on recent developments of the L-K method for stability analysis, discrete-time sliding mode control design and linear functional observer design of time-delay systems, is presented. Then, the problem of exponential stability is addressed for a class of linear discrete-time systems with interval time-varying delay. Some improved delay-dependent stability conditions of linear discrete-time systems with interval time-varying delay are derived in terms of linear matrix inequalities.
Secondly, the problem of reachable set bounding, essential information for the control design, is tackled for linear systems with time-varying delay and bounded disturbances. Indeed, minimisation of the reachable set bound can generally result in a controller with a larger gain to achieve better performance for the uncertain dynamical system under control. Based on the L-K method, combined with the delay decomposition approach, sufficient conditions for the existence of ellipsoid-based bounds of reachable sets of a class of linear systems with interval time-varying delay and bounded disturbances, are derived in terms of matrix inequalities. To obtain a smaller bound, a new idea is proposed to minimise the projection distances of the ellipsoids on axes, with respect to various convergence rates, instead of minimising its radius with a single exponential rate. Therefore, the smallest possible bound can be obtained from the intersection of these ellipsoids.
This study also addresses the problem of robust sliding mode control for a class of linear discrete-time systems with time-varying delay and unmatched external disturbances. By using the L-K method, in combination with the delay decomposition technique and the reciprocally convex approach, new LMI-based conditions for the existence of a stable sliding surface are derived. These conditions can deal with the effects of time-varying delay and unmatched external disturbances while guaranteeing that all the state trajectories of the reduced-order system are exponentially convergent to a ball with a minimised radius. Robust discrete-time quasi-sliding mode control scheme is then proposed to drive the state trajectories of the closed-loop system towards the prescribed sliding surface in a finite time and maintain it there after subsequent time.
Finally, the state estimation problem is studied for the challenging case when both the system’s output and input are subject to time delays. By using the information of the multiple delayed output and delayed input, a new minimal order observer is first proposed to estimate a linear state functional of the system. The existence conditions for such an observer are given to guarantee that the estimated state converges exponentially within an Є-bound of the original state. Based on the L-K method, sufficient conditions for Є-convergence of the observer error, are derived in terms of matrix inequalities. Design algorithms are introduced to illustrate the merit of the proposed approach.
From theoretical as well as practical perspectives, the obtained results in this thesis are beneficial to a broad range of applications in robotic manipulators, airport navigation, manufacturing, process control and in networked systems
Density functional theory for dense nematics with steric interactions
The celebrated work of Onsager on hard particle systems, based on the
truncated second order virial expansion, is valid at relatively low volume
fractions for large aspect ratio particles. While it predicts the
isotropic-nematic phase transition, it fails to provide a realistic equation of
state in that the pressure remains finite for arbitrarily high densities. In
this work, we derive a mean field density functional form of the Helmholtz free
energy for nematics with hard core repulsion. In addition to predicting the
isotropic-nematic transition, the model provides a more realistic equation of
state. The energy landscape is much richer, and the orientational probability
distribution function in the nematic phase possesses a unique feature: it
vanishes on a nonzero measure set in orientational space
The critical merger distance between two co-rotating quasi-geostrophic vortices
This paper examines the critical merger or strong interaction distance between two equal-potential-vorticity quasi-geostrophic vortices. The interaction between the two vortices depends on five parameters: their volume ratio, their height-to-width aspect ratios and their vertical and horizontal offsets. Due to the size of the parameter space, a direct investigation solving the full quasi-geostrophic equations is impossible. We instead determine the critical merger distance approximately using an asymptotic approach. We associate the merger distance with the margin of stability for a family of equilibrium states having prescribed aspect and volume ratios, and vertical offset. The equilibrium states are obtained using an asymptotic solution method which models vortices by ellipsoids. The margin itself is determined by a linear stability analysis. We focus on the interaction between oblate to moderately prolate vortices, the shapes most commonly found in turbulence. Here, a new unexpected instability is found and discussed for prolate vortices which is manifested by the tilting of vortices toward each other. It implies than tall vortices may merge starting from greater separation distances than previously thought.Publisher PDFPeer reviewe
A Comparison of Stealthy Sensor Attacks on Control Systems
As more attention is paid to security in the context of control systems and
as attacks occur to real control systems throughout the world, it has become
clear that some of the most nefarious attacks are those that evade detection.
The term stealthy has come to encompass a variety of techniques that attackers
can employ to avoid detection. Here we show how the states of the system (in
particular, the reachable set corresponding to the attack) can be manipulated
under two important types of stealthy attacks. We employ the chi-squared fault
detection method and demonstrate how this imposes a constraint on the attack
sequence either to generate no alarms (zero-alarm attack) or to generate alarms
at a rate indistinguishable from normal operation (hidden attack)
- …