Energy Efficient and Reliable Wireless Sensor Networks - An Extension to IEEE 802.15.4e

Collecting sensor data in industrial environments from up to some tenth of battery powered sensor nodes with sampling rates up to 100Hz requires energy aware protocols, which avoid collisions and long listening phases. The IEEE 802.15.4 standard focuses on energy aware wireless sensor networks (WSNs) and the Task Group 4e has published an amendment to fulfill up to 100 sensor value transmissions per second per sensor node (Low Latency Deterministic Network (LLDN) mode) to satisfy demands of factory automation. To improve the reliability of the data collection in the star topology of the LLDN mode, we propose a relay strategy, which can be performed within the LLDN schedule. Furthermore we propose an extension of the star topology to collect data from two-hop sensor nodes. The proposed Retransmission Mode enables power savings in the sensor node of more than 33%, while reducing the packet loss by up to 50%. To reach this performance, an optimum spatial distribution is necessary, which is discussed in detail

The quasi-Weierstraß form for regular matrix pencils

AbstractRegular linear matrix pencils A-E∂∈Kn×n[∂], where K=Q, R or C, and the associated differential algebraic equation (DAE) Ex˙=Ax are studied. The Wong sequences of subspaces are investigate and invoked to decompose the Kn into V∗⊕W∗, where any bases of the linear spaces V∗ and W∗ transform the matrix pencil into the quasi-Weierstraß form. The quasi-Weierstraß form of the matrix pencil decouples the original DAE into the underlying ODE and the pure DAE or, in other words, decouples the set of initial values into the set of consistent initial values V∗ and “pure” inconsistent initial values W∗⧹{0}. Furthermore, V∗ and W∗ are spanned by the generalized eigenvectors at the finite and infinite eigenvalues, resp. The quasi-Weierstraß form is used to show how chains of generalized eigenvectors at finite and infinite eigenvalues of A-E∂ lead to the well-known Weierstraß form. So the latter can be viewed as a generalized Jordan form. Finally, it is shown how eigenvector chains constitute a basis for the solution space of Ex˙=Ax

Quasi feedback forms for differential-algebraic systems

We investigate feedback forms for linear time-invariant systems described by differential-algebraic equations. Feedback forms are representatives of certain equivalence classes. For example state space transformations, invertible transformations from the left, and proportional state feedback constitute an equivalence relation. The representative of such an equivalence class, which we call proportional feedback form for the above example, allows to read off relevant system theoretic properties. Our main contribution is to derive a quasi proportional feedback form. This form is advantageous since it provides some geometric insight and is simple to compute, but still allows to read off the relevant structural properties of the control system. We also derive a quasi proportional and derivative feedback form. Similar advantages hold

Funnel control of nonlinear systems

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by $r$-th order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems)

Funnel control of nonlinear systems

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by r-th-order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems)

Using Geographically Referenced Data on Environmental Exposures for Public Health Research: A Feasibility Study Based on the German Socio-Economic Panel Study (SOEP)

Background: In panel datasets information on environmental exposures is scarce. Thus, our goal was to probe the use of area-wide geographically referenced data for air pollution from an external data source in the analysis of physical health. Methods: The study population comprised SOEP respondents in 2004 merged with exposures for NO2, PM10 and O3 based on a multi-year reanalysis of the EURopean Air pollution Dispersion-Inverse Model (EURAD-IM). Apart from bivariate analyses with subjective air pollution we estimated cross-sectional multilevel regression models for physical health as assessed by the SF-12. Results: The variation of average exposure to NO2, PM10 and O3 was small with the interquartile range being less than 10µg/m3 for all pollutants. There was no correlation between subjective air pollution and average exposure to PM10 and O3, while there was a very small positive correlation between the first and NO2. Inclusion of objective air pollution in regression models did not improve the model fit. Conclusions: It is feasible to merge environmental exposures to a nationally representative panel study like the SOEP. However, in our study the spatial resolution of the specific air pollutants has been too little, yet.SOEP, Geographically Referenced Data, Feasibility Study, Air Pollution, EURAD-IM, Physical Health

Time-varying linear DAEs transferable into standard canonical form

We introduce a solution theoryfor time-varying linear differential-algebraic equations(DAEs) E(t)˙x = A(t)x which can be transformed into standard canonical form (SCF), i.e. the DAE is decoupled into an ODE ˙z1 = J(t)z1 and a pure DAE N(t)˙z1 = z1 , where N is pointwise strictly lower triangular. This class is a time-varying generalization of time-invariant DAEs where the corresponding matrix pencil is regular. It will be shown in which sense the SCF is a canonical form, that it allows for a transition matrix similar to the one for ODEs, and how this can be exploited to derive a variation of constants formula. Furthermore, we show in which sense the class of systems transferable into SCF is equivalent to DAEs which are analytically solvable, and relate SCF to the derivative array approach, differentiation index and strangeness index. Finally, an algorithm is presented which determines the transformation matrices which put a DAE into SCF

On stability of time-varying linear differential-algebraic equations

We develop a stability theory for time-varying linear differential algebraic equations (DAEs). Standard stability concepts for ODEs are formulated for DAEs and characterized. Lyapunov’s direct method is derived as well as the converse of the stability theorems. Stronger results are achieved for DAEs which are transferable into standard canonical form; in this case the existence of the generalized transition matrix is exploited

Dedicated to the memory of Christopher I. Byrnes

The Byrnes-Isidori form with respect to the relative degree is studied for time-varying linear multi-input, multi-output systems. It is clarified in which sense this form is a normal form. (A,B)-invarianttime-varying subspaces are defined and the maximal(A,B)-invariant time-varying subspace included in the kernel of C is characterized. This is exploited to characterize the zero dynamics of the system. Finally, a high-gain derivative output feedback controller is introduced for the class of systems with higher relative degree and stable zero dynamics. All results are also new for time-invariant linear systems.MSC 93C05, 93D1

Normal forms, high-gain and funnel control for linear differential-algebraic systems

We consider linear differential-algebraic m-input m-output systems with positive strict relative degree or proper inverse transfer function; in the single-input single-output case these two disjoint classes make the whole of all linear DAEs without feedthrough term. Structural properties - such as normal forms (i.e. the counterpart to the Byrnes-Isidori form for ODE systems), zero dynamics, and high-gain stabilizability - are analyzed for two purposes: first, to gain insight into the system classes and secondly, to solve the output regulation problem by funnel control. The funnel controller achieves tracking of a class of reference signals within a pre-specified funnel; this means in particular, the transient behaviour of the output error can be specified and the funnel controller does neither incorporate any internal model for the reference signals nor any identification mechanism, it is simple in its design. The results are illuminated by position and velocity control of a mechanical system encompassing springs, masses, and dampers