Non-linear effects of landscape properties on mistletoe parasitism in fragmented agricultural landscapes

Ecological processes such as plant–animal interactions have a critical role in shaping the structure and function of ecosystems, but little is known of how such processes are modified by changes in landscape structure. We investigated the effect of landscape change on mistletoe parasitism in fragmented agricultural environments by surveying mistletoes on eucalypt host trees in 24 landscapes, each 100 km² in size, in south-eastern Australia. Landscapes were selected to represent a gradient in extent (from 60% to 2% cover) and spatial pattern of remnant wooded vegetation. Mistletoes were surveyed at 15 sites in each landscape, stratified to sample five types of wooded elements in proportion to their relative cover. The incidence per landscape of box mistletoe (Amyema miquelii), the most common species, was best explained by the extent of wooded cover (non-linear relationship) and mean annual rainfall. Higher incidence occurred in landscapes with intermediate levels of cover (15–30%) and higher rainfall (>500 mm). Importantly, a marked non-linear decline in the incidence of A. miquelii in low-cover landscapes implies a disproportionate loss of this species in remaining wooded vegetation, greater than that attributable to decreasing forest cover. The most likely mechanism is the effect of landscape change on the mistletoebird (Dicaeum hirundinaceum), the primary seed-dispersal vector for A. miquelii. Our results are consistent with observations that habitat fragmentation initially enhances mistletoe occurrence in agricultural environments; but in this region, when wooded vegetation fell below a threshold of ~15% landscape cover, the incidence of A. miquelii declined precipitously. Conservation management will benefit from greater understanding of the components of landscape structure that most influence ecological processes, such as mistletoe parasitism and other plant–animal mutualisms, and the critical stages in such relationships. This will facilitate action before critical thresholds are crossed and cascading effects extend to other aspects of ecosystem function.

A state space based approach in non-linear hemodynamic response modeling with fMRI data

In this paper we use the modified and integrated version of the balloon model in the analysis of fMRI data. We propose a new state space model realization for this balloon model and represent it with the standard A,B,C and D matrices widely used in system theory. A second order Padé approximation with equal numerator and denominator degree is used for the time delay approximation in the modeling of the cerebral blood flow. The results obtained through numerical solutions showed that the new state space model realization is in close agreement to the actual modified and integrated version of the balloon model. This new system theoretic formulation is likely to open doors to a novel way of analyzing fMRI data with real time robust estimators. With further development and validation, the new model has the potential to devise a generalized measure to make a significant contribution to improve the diagnosis and treatment of clinical scenarios where the brain functioning get altered. Concepts from system theory can readily be used in the analysis of fMRI data and the subsequent synthesis of filters and estimators.

Optimal actuator fault tolerance for static nonlinear systems based on minimum output velocity jump

Fault tolerance for a class of non linear systems is addressed based on the velocity of their output variables. This paper presents a mapping to minimize the possible jump of the velocity of the output, due to the actuator failure. The failure of the actuator is assumed as actuator lock. The mapping is derived and it provides the proper input commands for the healthy actuators of the system to tolerate the effect of the faulty actuator on the output of the system. The introduced mapping works as an optimal input reconfiguration for fault recovery, which provides a minimum velocity jump suitable for static nonlinear systems. The proposed mapping is validated through different case studies and a complementary simulation. In the case studies and the simulation, the mapping provides the commands to compensate the effect of different faults within the joints of a robotic manipulator. The new commands and the compare between the velocity of the output variables for the health and faulty system are presented.

Rock slope risk analysis based on non-linear failure criterion

The probability of failure of a rock slope is generally estimated by using the Limit Equilibrium Method (LEM) in conjunction with a reliability analysis. Although the LEM is relatively simple and time efficient, recent studies have indicated that using the LEM may overestimate the factor of safety by 21%, when based on a non-linear failure criterion. Fortunately, the solutions presented by Li et al. (2008, 2009) can provide more accurate evaluations for rock slope stability as the numerical upper and lower bound limit analysis methods (2002a, 2002b, 2005) were employed. The advantages of these methods are used in this study to assess the rock slope probability of failure. The motivation is that with more accurate methods to evaluate the factor of safety, more economic designs can be performed.

Partial state estimation for linear systems with output and input time delays.

This paper deals with the problem of partial state observer design for linear systems that are subject to time delays in the measured output as well as the control input. By choosing a set of appropriate augmented Lyapunov-Krasovskii functionals with a triple-integral term and using the information of both the delayed output and input, a novel approach to design a minimal-order observer is proposed to guarantee that the observer error is ε-convergent with an exponential rate. Existence conditions of such an observer are derived in terms of matrix inequalities for the cases with time delays in both the output and input and with output delay only. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality and effectiveness of the proposed observer.

A new algorithm to design minimal multi-functional observers for linear systems

Designing minimum possible order (minimal) observers for Multi-Input Multi-Output (MIMO) linear systems have always been an interesting subject. In this paper, a new methodology to design minimal multi-functional observers for Linear Time-Invariant (LTI) systems is proposed. The approach is applicable, and it also helps in regulating the convergence rate of the observed functions. It is assumed that the system is functional observable or functional detectable, which is less conservative than assuming the observability or detectability of the system. To satisfy the minimality of the observer, a recursive algorithm is provided that increases the order of the observer by appending the minimum required auxiliary functions to the desired functions that are going to be estimated. The algorithm increases the number of functions such that the necessary and sufficient conditions for the existence of a functional observer are satisfied. Moreover, a new methodology to solve the observer design interconnected equations is elaborated. Our new algorithm has advantages with regard to the other available methods in designing minimal order functional observers. Specifically, it is compared with the most common schemes, which are transformation based. Using numerical examples it is shown that under special circumstances, the conventional methods have some drawbacks. The problem partly lies in the lack of sufficient numerical degrees of freedom proposed by the conventional methods. It is shown that our proposed algorithm can resolve this issue. A recursive algorithm is also proposed to summarize the observer design procedure. Several numerical examples and simulation results illustrate the efficacy, superiority and different aspects of the theoretical findings.

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.

New results in common functional state estimation for two linear systems with unknown inputs

This paper presents new developments in common functional observers for two systems. We improve an existing common functional observer scheme by reducing its order, and then investigate its existence conditions in terms of the original system matrices. These conditions have never been explored and they enable the users to know at the outset the class of systems for which the scheme is applicable. They also show that both observers can be designed independently of each other which significantly simplifies the design process. A numerical simulation verifies the findings.

On unknown-input functional observability of linear systems

Finding the least possible order of a stable Unknown-Input Functional Observer (UIFO) has always been a challenge in observer design theory. A practical recursive algorithm is proposed in this technical note to design a minimal multi-functional observer for multi-input multi-output (MIMO) linear time-invariant (LTI) systems with unknown-inputs. The concept of unknown-input functional observability is introduced,and it is used as a certificate of the convergence of our algorithm. The proposed procedure looks for a number of additional auxiliary functions to be augmented to the original functions desired for reconstruction. The resulting UIFO is proper, and minimal (of minimum possible order). Moreover, the algorithm does not need the system to be unknown-input observable. A numerical example shows the procedure as well as the effectiveness of the proposed algorithm.

Minimal multi-functional observers for linear systems using a direct approach

The direct approach in designing functional observers was first presented in [1] for estimating a single function of the states of a Linear Time-Invariant (LTI) system. One of the benefits of the direct scheme is that it does not require solving the interconnected Sylvester equations that appear in the other observer design approaches. In the present paper, the direct approach is extended to reconstruct multiple functions of the states in such a way that the minimum possible order of the observer is achieved. The observer is designed so that an asymptotic functional observer can be obtained with arbitrary convergence rate. In the proposed methodology, it is not necessary that a reduced order observer exists for the desired functions to be estimated. To release this limitation, an algorithm is employed to find some auxiliary functions in the minimum required number to be appended to the desired functions. This method assumes that the system is functional observable. This assumption however is less restrictive than the observability and detectability conditions of the system. A numerical example and simulation results explain the efficacy and the benefits of the proposed algorithm.