Reachable set bounding for nonlinear perturbed time-delay systems: the smallest bound

In this letter, we propose a new approach to obtain the smallest box which bounds all reachable sets of a class of nonlinear time-delay systems with bounded disturbances. A numerical example is studied to illustrate the obtained result.

On backwards and forwards reachable sets bounding for perturbed time-delay systems

Linear systems with interval time-varying delay and unknown-but-bounded disturbances are considered in this paper. We study the problem of finding outer bound of forwards reachable sets and inter bound of backwards reachable sets of the system. Firstly, two definitions on forwards and backwards reachable sets, where initial state vectors are not necessary to be equal to zero, are introduced. Then, by using the Lyapunov-Krasovskii method, two sufficient conditions for the existence of: (i) the smallest possible outer bound of forwards reachable sets; and (ii) the largest possible inter bound of backwards reachable sets, are derived. These conditions are presented in terms of linear matrix inequalities with two parameters need to tuned, which therefore can be efficiently solved by combining existing convex optimization algorithms with a two-dimensional search method to obtain optimal bounds. Lastly, the obtained results are illustrated by four numerical examples.

Regional avian species declines estimated from volunteer-collected long-term data using List Length Analysis

Long-term systematic population monitoring data sets are rare but are essential in identifying changes in species abundance. In contrast, community groups and natural history organizations have collected many species lists. These represent a large, untapped source of information on changes in abundance but are generally considered of little value. The major problem with using species lists to detect population changes is that the amount of effort used to obtain the list is often uncontrolled and usually unknown. It has been suggested that using the number of species on the list, the "list length," can be a measure of effort. This paper significantly extends the utility of Franklin's approach using Bayesian logistic regression. We demonstrate the value of List Length Analysis to model changes in species prevalence (i.e., the proportion of lists on which the species occurs) using bird lists collected by a local bird club over 40 years around Brisbane, southeast Queensland, Australia. We estimate the magnitude and certainty of change for 269 bird species and calculate the probabilities that there have been declines and increases of given magnitudes. List Length Analysis confirmed suspected species declines and increases. This method is an important complement to systematically designed intensive monitoring schemes and provides a means of utilizing data that may otherwise be deemed useless. The results of List Length Analysis can be used for targeting species of conservation concern for listing purposes or for more intensive monitoring. While Bayesian methods are not essential for List Length Analysis, they can offer more flexibility in interrogating the data and are able to provide a range of parameters that are easy to interpret and can facilitate conservation listing and prioritization. © 2010 by the Ecological Society of America.

Generalization of deviated linear cyclic pursuit

Earlier work on cyclic pursuit systems has shown that using heterogeneous gains for agents in linear cyclic pursuit, the point of convergence (rendezvous point) can be chosen arbitrarily. But there are some restrictions on this set of reachable points. The use of deviated cyclic pursuit, as discussed in this paper, expands this set of reachable points to include points which are not reachable by any known linear cyclic pursuit scheme. The limits on the deviations are determined by stability considerations. Such limits have been analytically obtained in this paper along with results on the expansion in reachable set and the latter has also been verified through simulations.

Deviated linear cyclic pursuit

This paper analyses deviated linear cyclic pursuit in which an agent pursues its leader with an angle of deviation in both the continuous- and discrete-time domains, while admitting heterogeneous gains and deviations for the agents. Sufficient conditions for the stability of such systems, in both the domains, are presented in this paper along with the derivation of the reachable set, which is a set of points where the agents may converge asymptotically. The stability conditions are derived based on Gershgorin's theorem. Simulations validating the theoretical results presented in this paper are provided.

A method for stereo-vision-based tracking for robotic applications

Vision-based tracking of an object using perspective projection inherently results in non-linear measurement equations in the Cartesian coordinates. The underlying object kinematics can be modelled by a linear system. In this paper we introduce a measurement conversion technique that analytically transforms the non-linear measurement equations obtained from a stereo-vision system into a system of linear measurement equations.We then design a robust linear filter around the converted measurement system. The state estimation error of the proposed filter is bounded and we provide a rigorous theoretical analysis of this result. The performance of the robust filter developed in this paper is demonstrated via computer simulation and via practical experimentation using a robotic manipulator as a target. The proposed filter is shown to outperform the extended Kalman filter (EKF).

Linear functional state bounding for perturbed time-delay systems and its application

This paper considers time-delay systems with bounded disturbances. We study a new problem of finding an upper bound of an absolute value function of any given linear functional of the state vector starting from the origin of the system. Based on the Lyapunov-Krasovskii method combining with the recent Wirtinger-based integral inequality that has just been proposed by Seuret & Gouaisbaut (2013. Wirtinger-based integral inequality: application to time-delay systems. Automatica, 49, 2860-2866), sufficient conditions for the existence of an upper bound of the function are derived. The obtained results are shown to be more effective than those adapted from the existing works on reachable set bounding. Furthermore, the obtained results are applied to refine existing ellipsoidal bounds of the reachable sets. The effectiveness of the obtained results is illustrated by two numerical examples.

Controlabilidade para sistemas de equações diferenciais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with Gaussian process models

Several methods based on Kriging have recently been proposed for calculating a probability of failure involving costly-to-evaluate functions. A closely related problem is to estimate the set of inputs leading to a response exceeding a given threshold. Now, estimating such a level set—and not solely its volume—and quantifying uncertainties on it are not straightforward. Here we use notions from random set theory to obtain an estimate of the level set, together with a quantification of estimation uncertainty. We give explicit formulae in the Gaussian process set-up and provide a consistency result. We then illustrate how space-filling versus adaptive design strategies may sequentially reduce level set estimation uncertainty.

Solution of optimal continuous low-thrust transfer using Lie transforms

This paper addresses the problem of optimal constant continuous low-thrust transfer in the context of the restricted two-body problem (R2BP). Using the Pontryagin’s principle, the problem is formulated as a two point boundary value problem (TPBVP) for a Hamiltonian system. Lie transforms obtained through the Deprit method allow us to obtain the canonical mapping of the phase flow as a series in terms of the order of magnitude of the thrust applied. The reachable set of states starting from a given initial condition using optimal control policy is obtained analytically. In addition, a particular optimal transfer can be computed as the solution of a non-linear algebraic equation. Se investiga el uso de series y transformadas de Lie en problemas de optimización de trayectorias de satélites impulsados por motores de bajo empuje

High-Order Control Variations and Small-Time Local Controllability

The importance of “control variations” for obtaining local approximations of the reachable set of nonlinear control systems is well known. Heuristically, if one can construct control variations in all possible directions, then the considered control system is small-time locally controllable (STLC). Two concepts of control variations of higher order are introduced for the case of smooth control systems. The relation between these variations and the small-time local controllability is studied and a new sufficient STLC condition is proved.

Garbage collection optimization for non uniform memory access architectures

Cache-coherent non uniform memory access (ccNUMA) architecture is a standard design pattern for contemporary multicore processors, and future generations of architectures are likely to be NUMA. NUMA architectures create new challenges for managed runtime systems. Memory-intensive applications use the system’s distributed memory banks to allocate data, and the automatic memory manager collects garbage left in these memory banks. The garbage collector may need to access remote memory banks, which entails access latency overhead and potential bandwidth saturation for the interconnection between memory banks. This dissertation makes five significant contributions to garbage collection on NUMA systems, with a case study implementation using the Hotspot Java Virtual Machine. It empirically studies data locality for a Stop-The-World garbage collector when tracing connected objects in NUMA heaps. First, it identifies a locality richness which exists naturally in connected objects that contain a root object and its reachable set— ‘rooted sub-graphs’. Second, this dissertation leverages the locality characteristic of rooted sub-graphs to develop a new NUMA-aware garbage collection mechanism. A garbage collector thread processes a local root and its reachable set, which is likely to have a large number of objects in the same NUMA node. Third, a garbage collector thread steals references from sibling threads that run on the same NUMA node to improve data locality. This research evaluates the new NUMA-aware garbage collector using seven benchmarks of an established real-world DaCapo benchmark suite. In addition, evaluation involves a widely used SPECjbb benchmark and Neo4J graph database Java benchmark, as well as an artificial benchmark. The results of the NUMA-aware garbage collector on a multi-hop NUMA architecture show an average of 15% performance improvement. Furthermore, this performance gain is shown to be as a result of an improved NUMA memory access in a ccNUMA system. Fourth, the existing Hotspot JVM adaptive policy for configuring the number of garbage collection threads is shown to be suboptimal for current NUMA machines. The policy uses outdated assumptions and it generates a constant thread count. In fact, the Hotspot JVM still uses this policy in the production version. This research shows that the optimal number of garbage collection threads is application-specific and configuring the optimal number of garbage collection threads yields better collection throughput than the default policy. Fifth, this dissertation designs and implements a runtime technique, which involves heuristics from dynamic collection behavior to calculate an optimal number of garbage collector threads for each collection cycle. The results show an average of 21% improvements to the garbage collection performance for DaCapo benchmarks.