Reduced order functional observers with application to partial state estimation of linear systems with input delay

Reduced order multi-functional observer design for multi-input multi-utput (MIMO) linear time-invariant (LTI) systems with constant delayed inputs is studied. This research is useful in the input estimation of LTI systems with actuator delay, as well as system monitoring and fault detection of these systems. Two approaches for designing an asymptotically stable functional observer for the system are proposed: delay-dependent and delay-free. The delay-dependent observer is infinite-dimensional, while the delay-free structure is finite-dimensional. Moreover, since the delay-free observer does not require any information on the time delay, it is more practical in real applications. However, the delay-dependent observer contains less restrictive assumptions and covers more variety of systems. The proposed observer design schemes are novel, simple to implement, and have improved numerical features compared to some of the other available approaches to design (unknown-input) functional observers. In addition, the proposed observers usually possess lower order than ordinary Luenberger observers, and the design schemes do not need the observability or detectability requirements of the system. The necessary and sufficient conditions of the existence of an asymptoticobserver in each scenario are explored. The extensions of the proposed observers to systems with multiple delayed-inputs are also discussed. Several numerical examples and simulation results are employed to support our theories.

Is optimistic bias influenced by control or delay?

Optimistic bias is a commonly observed but poorly explained phenomenon. Our aim was to determine whether optimistic bias varied according to the nature of the event. Two event characteristics were explored: control and delay. A sample of 100 participants aged 18–30 years was randomly selected from the local residential telephone directory. Respondents were interviewed over the telephone. The highly structured interview schedule assessed respondents' perceptions of their own risk, and the risk of an average person of their age and sex for experiencing four negative life events: developing skin cancer, being involved in a serious car accident as the driver, being involved in a serious car accident as a passenger and having to wear a hearing aid. It also assessed respondents' perceptions of control and delay for each event. Data analysis using a repeated-measures MANOVA showed that optimistic bias occurred for all four events. Optimistic bias was significantly greater for the two events high in control (skin cancer and accident as the driver) than for those low in control (accident as a passenger and hearing aid). Delay was not related to the magnitude of optimistic bias. These findings have implications for health promotion campaigns and self-protective behaviors.

Gait termination in young and older adults : effect of stopping stimulus probability and stimulus delay

Sixteen young (25±2.6 years) and 16 older individuals (69±4.4 years) walked normally then terminated walking rapidly. A visual stopping stimulus was presented 10 ms following ground contact (short delay) and in another condition, at 450 ms prior to toe-off (long delay). Stimulus probability was either high (80% of trials) or low (10%). The younger group stopped faster (463 vs. 574 ms) despite also walking faster (1.29 vs. 1.17 m s⁻¹). Longer delay decreased one-step responses but older participants used significantly more (slower) two-step stopping, which increased stopping time and distance. The additional step may have been pre-planned to maintain medial–lateral stability.

An observer design procedure for a class of nonlinear time-delay systems

This paper considers a class of uncertain, nonlinear differential state delayed control systems and presents a reduced-order observer design procedure to asymptotically estimate any vector state functionals. The method proposed involves decomposition of the delayed portion of the system into two parts: a matched and mismatched part. Provided that the rank of the mismatched part is less than the number of the outputs, a reduced-order linear functional observer, with any prescribed stability margin, can be constructed by using a simple procedure. A numerical example is given to illustrate the new design procedure and its features.

Node localization using mobile robots in delay-tolerant sensor networks

We present a novel scheme for node localization in a Delay-Tolerant Sensor Network (DTN). In a DTN, sensor devices are often organized in network clusters that may be mutually disconnected. Some mobile robots may be used to collect data from the network clusters. The key idea in our scheme is to use this robot to perform location estimation for the sensor nodes it passes based on the signal strength of the radio messages received from them. Thus, we eliminate the processing constraints of static sensor nodes and the need for static reference beacons. Our mathematical contribution is the use of a Robust Extended Kalman Filter (REKF)-based state estimator to solve the localization. Compared to the standard extended Kalman filter, REKF is computationally efficient and also more robust. Finally, we have implemented our localization scheme on a hybrid sensor network test bed and show that it can achieve node localization accuracy within 1m in a large indoor setting.

The impossible infinite: Les Murray, poetry, and the sacred

In 1983, the provocative and idiosyncratic Australian poet Les Murray published a volume entitled The People's Otherworld. At the heart of that middle volume of Murray's work is a poem about grace entitled Equanimity. Here, McCredden examines how does the poetry of Murray seek to represent the sacred.

Deborah Walker : hommage to the infinite

Spirtuality is at the heart of Deborah Walker's enigmatically engaging works. Drawing on the interpretive nature of a philosophical world view, Walker presents a figurative structure imbued with a calmness, stillness, and sophistication. Elegantly dressed characters are warmly depicted witha touch of theatre and drama, their serene gaze gentle, sometimes melancholy and reflective. 

State and input simultaneous estimation for a class of time-delay systems with uncertainties

This brief addresses the problem of estimation of both the states and the unknown inputs of a class of systems that are subject to a time-varying delay in their state variables, to an unknown input, and also to an additive uncertain, nonlinear disturbance. Conditions are derived for the solvability of the design matrices of a reduced-order observer for state and input estimation, and for the stability of its dynamics. To improve computational efficiency, a delay-dependent asymptotic stability condition is then developed using the linear matrix inequality formulation. A design procedure is proposed and illustrated by a numerical example.

Does elite competition inhibit growth and delay maturation in some gymnasts? quite possibly

Today, elite young gymnasts undertake training programs of progressive volume and intensity from an early age. For example, talented young female gymnasts often commence training at age 5 or 6 and train more than 20 to 30 hours per week year-round throughout childhood and adolescence. Despite the "normal" short stature of top-level gymnasts and the obvious health benefits of physical activity during growth, there is concern that elite level or those gymnasts involved in heavy training regimens may be at risk for adverse effects on growth and maturation. This concern has been the source of much debate in the literature and is complicated by the difficulties in distinguishing between the genetic predisposition to short stature and late or delayed maturation, and the effect of environmental factors such as nutrition and exercise that may influence growth and maturation. The effect of gymnastics training on growth and maturation is often reported as averaged data: an approach that does not identify individual growth patterns. Finding no difference between groups is not proof that there is "in fact" no difference. Accepting the null hypothesis without the appropriate critical review of both the methodological and statistical power to detect differences is a flawed endeavor. We believe there is compelling "circumstantial" evidence to build a case that preparation for advanced gymnastics competition may place some children and youth at risk of reduced growth and delayed maturation.

Delay control and parallel admission algorithms for real-time anycast flow

An anycast flow is a flow that can be connected to any one of the members in a group of designated (replicated) servers (called anycast group). In this paper, we derive a set of formulas for calculating the end-to-end delay bound for the anycast flows and present novel admission control algorithms for anycast flows with real-time constraints. Given such an anycast group, our algorithms can effectively select the paths for anycast flows' admission and connection based on the least end-to-end delay bounds evaluated. We also present a parallel admission control algorithm that can effectively calculate the available paths with a short delay bound for different destinations in the anycast group so that a best path with the shortest delay bound can be chosen.

Design of linear functional observers for time-delay systems of the neutral-type

This paper presents the design of reduced-order linear functional observers for a class of linear time-delay systems of the neutral-type. The type of the observer proposed in this paper is without internal delay and its order is the same as the number of linear functions to be estimated. First, conditions for the existence of the reduced-order functional observers that are capable of asymptotically estimating any given function of the state vector are derived. Then, based on the newly derived existence conditions, a procedure is given for the determination of the observer parameters. The results derived in this paper include a range of linear systems and extend some existing results of linear functional observers to linear neutral delay systems. A numerical example is given to illustrate the design procedure.

Scope for further analytical solutions for constant flux infiltration into a semi-infinite soil profile or redistribution in a finite soil profile.

We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.