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.

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.

Reachable sets bounding for switched systems with time-varying delay and bounded disturbances

In this paper, we address the problem of finding outer bound of forward reachable sets and inter-bound of backward reachable sets of switched systems with an interval time-varying delay and bounded disturbances. By constructing a flexible Lyapunov–Krasovskii functional combining with some recent refined integral-based inequalities, some sufficient conditions are derived for the existence of (1) the smallest possible outer bound of forwards reachable sets; and (2) the largest possible inter-bound of backward reachable sets. These conditions are delay dependent and in the form of linear matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. A constructive geometric design of switching laws is also presented. Two numerical examples with simulation results are provided to demonstrate the effectiveness of our results.

Reachable sets bounding for generalized neural networks with interval time-varying delay and bounded disturbances

This paper deals with the problem of finding outer bound of forwards reachable sets and interbound of backwards reachable sets of generalized neural network systems with interval nondifferentiable time-varying delay and bounded disturbances. Based on constructing a suitable Lyapunov–Krasovskii functional and utilizing some improved Jensen integral-based inequalities, two sufficient conditions are derived for the existence of: (1) the smallest possible outer bound of forwards reachable sets and (2) the largest possible interbound of backwards reachable sets. These conditions are delay dependent and in the form of matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. Three numerical examples with simulation results are provided to demonstrate the effectiveness of our results.

Functional range of movement of the hand : declination angles to reachable space

 The measurement of the range of hand joint movement is an essential part of clinical practice and rehabilitation. Current methods use three finger joint declination angles of the metacarpophalangeal, proximal interphalangeal and distal interphalangeal joints. In this paper we propose an alternate form of measurement for the finger movement. Using the notion of reachable space instead of declination angles has significant advantages. Firstly, it provides a visual and quantifiable method that therapists, insurance companies and patients can easily use to understand the functional capabilities of the hand. Secondly, it eliminates the redundant declination angle constraints. Finally, reachable space, defined by a set of reachable fingertip positions, can be measured and constructed by using a modern camera such as Creative Senz3D or built-in hand gesture sensors such as the Leap Motion Controller. Use of cameras or optical-type sensors for this purpose have considerable benefits such as eliminating and minimal involvement of therapist errors, non-contact measurement in addition to valuable time saving for the clinician. A comparison between using declination angles and reachable space were made based on Hume's experiment on functional range of movement to prove the efficiency of this new approach.

Deducing the reachable space from fingertip positions

The reachable space of the hand has received significant interests in the past from relevant medical researchers and health professionals. The reachable space was often computed from the joint angles acquired from a motion capture system such as gloves or markers attached to each bone of the finger. However, the contact between the hand and device can cause difficulties particularly for hand with injuries, burns or experiencing certain dermatological conditions. This paper introduces an approach to find the reachable space of the hand in a non-contact measurement form utilizing the Leap Motion Controller. The approach is based on the analysis of each position in the motion path of the fingertip acquired by the Leap Motion Controller. For each position of the fingertip, the inverse kinematic problem was solved under the physiological multiple constraints of the human hand to find a set of all possible configurations of three finger joints. Subsequently, all the sets are unified to form a set of all possible configurations specific for that motion. Finally, a reachable space is computed from the configuration corresponding to the complete extension and the complete flexion of the finger joint angles in this set.

Describing human finger flexibility via reachable subspaces

In recent years, the reachable space concept has attracted the attention of many researchers as a mean of describing finger flexibility. Existing approaches such as exhaustive scanning or Monte Carlo methods to obtain the reachable space are resource-hungry techniques. In this paper, we introduce a novel approach to determine and quantify the reachable space of the finger. The approach was developed around a set of formulae determining the boundary of the reachable space. The Monte Carlo simulation is proposed to estimate the capacity of the reachable space. Using the new technique, reachable spaces can be visualised and quantified in order to effectively compare the functionality of different subjects and their therapeutic status. The performance of the proposed method was evaluated against the kinematic feed-forward approach. The computational cost to obtain the reachable space is significantly less than the standard kinematic feed-forward approach due to exclusive description of the reachable space boundary, unique to the proposed approach.

The association between the investment opportunity set and corporate financing and dividend decisions: some Australian evidence

Summarizes previous research on the investment opportunity set (IOS) using price-based and investment-based proxies and variance measures; and develops hypotheses on the relationship between IOS, debt/equity ratios and dividend policies. Tests them on 1990-1998 data from listed Australian companies and explains the methodology, which builds on Gover and Gover (1993) by including more recent proxy variables. Finds no significant results from low growth firms, although some high growth firms show lower debt/equity ratios and dividends. Questions the robustness of existing IOS proxies in the Australian context and calls for further research.

Selected Ranked Set Sampling

This paper proposes a sampling procedure called selected ranked set sampling (SRSS), in which only selected observations from a ranked set sample (RSS) are measured. This paper describes the optimal linear estimation of location and scale parameters based on SRSS, and for some distributions it presents the required tables for optimal selections. For these distributions, the optimal SRSS estimators are compared with the other popular simple random sample (SRS) and RSS estimators. In every situation the estimators based on SRSS are found advantageous at least in some respect, compared to those obtained from SRS or RSS. The SRSS method with errors in ranking is also described. The relative precision of the estimator of the population mean is investigated for different degrees of correlations between the actual and erroneous ranking. The paper reports the minimum value of the correlation coefficient between the actual and the erroneous ranking required for achieving better precision with respect to the usual SRS estimator and with respect to the RSS estimator.

Sensory adaptability of foods with added Lupin (Lupinus angustifolius) kernel fibre using pre-set criteria

Fiber-enriched white bread, muffin. pasta, orange juice, and breakfast bar were prepared with lupin (Lupin us angusti/olius) kernel fiber. Consumer panelists (n = 44) determined that all these fiber-enriched foods, except orange juice, fulfilled pre-set acceptability criteria. Fiber enrichment did not change overall acceptability (p> 0.05) of the bread and pasta, but reduced overall acceptability (p < 0.05) of the muffin, orange juice, and breakfast bar. In all fiber-enriched products, flavor was the attribute most highly correlated with overall acceptability (p < 0.05). The lupin kernel fiber used in this study therefore appears to have potential as a 'nonintrusive' ingredient in some processed cereal-based foods_ For other applications, fiber modification appears worthy of investigation to accomplish 'nonintrusive' fiber enrichment.