particle swarm optimization in electromagnetics the particle swarm optimization pso new to the electromagnetics community is a robust stochastic evolutionary computation technique based on the movement and intelligence of swarms this paper introduces a conceptual overview and detailed explanation of the pso algorithm as well as how it can be used for electromagnetic optimizations this paper also presents several results illustrating the swarm behavior in a pso algorithm developed by the authors at ucla specifically for engineering optimizations ucla pso also discussed is recent progress in the development of the pso and the special considerations needed for engineering implementation including suggestions for the selection of parameter values additionally a study of boundary conditions is presented indicating the invisible wall technique outperforms absorbing and reflecting wall techniques these concepts are then integrated into a representative example of optimization of a profiled corrugated horn antenna

robust control in the gap a state space solution in the presence of a single input delay a solution is provided to the problem of sub optimal robust design in the gap for a system with a single input lag the problem is shown to reduce to two matrix algebraic riccati equations that solve an allied linear quadratic gaussian h sub 2 problem and a parameterized differential matrix riccati equation the analysis intertwines finite dimensional delay equations and distributed abstract evolution models the parameterized family of suboptimal compensators is presented in terms of a neutral equation model

dynamics of a predator prey model we describe the bifurcation diagram of limit cycles that appear in the first realistic quadrant of the predator prey model proposed by r m may stability and complexity in model ecosystems princeton university press princeton nj 1974 in particular we give a qualitative description of the bifurcation curve when two limit cycles collapse on a semistable limit cycle and disappear moreover we show that locally asymptotic stability of a positive equilibrium point does not imply global stability for this class of predator prey models

versatile beam forming with concentric excitations based on multiple weighted sinc or bessel function distribution in this paper we propose a beam forming approach capable of synthesizing versatile pre specified beam shapes using concentric excitations satisfying multiple weighted sinc or bessel function distribution we show by both theoretical calculation and full wave simulation that by tuning different weights of a sinc or bessel function distribution not only radiation beams with pencil flat topped and bimodal shapes can be synthesized but also the beam width and the side lobe level can be independently adjusted an example is provided to demonstrate how an isoflux beam aiming at a better coverage of the earth surface is synthesized and how an optimized continuous distribution is properly discretized for a physical realization of a satellite aperture array antenna the approach proposed in this paper can be applied to a wide range of applications that require performance optimization of concentric ring array antennas

multiple focus and hopf bifurcations in a predator prey system with nonmonotonic functional response in this paper we develop a criterion to calculate the multiplicity of a multiple focus for general predator prey systems as applications of this criterion we calculate the largest multiplicity of a multiple focus in a predator prey system with nonmonotonic functional response p x frac x ax 2 bx 1 studied by zhu campbell and wolkowicz siam j appl math 63 2002 pp 636 682 and prove that the degenerate hopf bifurcation is of codimension two furthermore we show that there exist parameter values for which this system has a unique positive hyperbolic stable equilibrium and exactly two limit cycles the inner one unstable and outer one stable numerical simulations for the existence of the two limit cycles bifurcated from the multiple focus are also given in support of the criterion

the number of limit cycles of certain polynomial differential equations two dimensional differential systems are considered where p and q are polynomials the question of interest is the maximum possible numberof limit cycles of such systems in terms of the degree of p and q an algorithm is described for determining a so called focal basis this can be implemented on a computer estimates can then be obtained for the number of small amplitude limit cycles the technique is applied to certain cubic systems a class of examples with exactly five small amplitude limit cycles is constructed quadratic systems are also considered

the standard h problem and the maximum principle the general linear case the classical relatively simple ideas of linear quadratic lq optimization are used in a time domain treatment of the standard h infty problem given the power of time domain analysis the problem can be solved in the general framework of linear time varying possibly infinite dimensional finite as well as infinite horizon systems under no structural restrictions such as block dimensions zero blocks in the d operator etc in the spirit of recent finite dimensional linear time invariant lti results the solution is given in terms of two coupled riccati equations it includes a criterion for suboptimality and a parametrization of all suboptimal compensators results pertinent to lti periodic and asymptotic systems are obtained as corollaries

receding horizon estimation for discrete time linear systems the problem of estimating the state of a discrete time linear system can be addressed by minimizing an estimation cost function dependent on a batch of recent measure and input vectors this problem has been solved by introducing a receding horizon objective function that includes also a weighted penalty term related to the prediction of the state for such an estimator convergence results and unbiasedness properties have been proved the issues concerning the design of this filter are discussed in terms of the choice of the free parameters in the cost function the performance of the proposed receding horizon filter is evaluated and compared with other techniques by means of a numerical example

bifurcation analysis of a predator prey system involving group defence a class of odes of generalized gause type modeling predator prey interaction is considered the prey are assumed to exhibit a phenomenon called group defence that is predation is decreased or even eliminated due to the ability of the prey to defend or disguise themselves as their numbers increase using the carrying capacity of the environment as the bifurcation parameter it is shown that the model undergoes a sequence of bifurcations that includes a homoclinic bifurcation as well as a hopf bifurcation conditions that hold even in the case of no group defence that ensure a subcritical hopf bifurcation and also the spontaneous appearance of a semistable periodic orbit that splits into a pair one stable and one unstable of periodic orbits are given ecological ramifications are considered unlike the classical model sufficient enrichment of the environment combined with group defence leads to extinction of the predator deterministically for almost all initial conditions providing strong support fo

robust controller design for delay systems in the gap metric a robust stabilization problem in the gap metric is discussed for a system with delays in control the authors derive a design procedure of robust controllers based on finite dimensional ricatti equations and it is shown that the resulting controller has a structure of observer based predictive action by employing completing the square argument a game theoretic interpretation is also provided on the trade off between the initial uncertainties and attenuating the disturbance caused by plant uncertainties

brief h performance of preview control systems performance of the preview control is investigated in terms of h criterion in the infinite horizon time setting the limitation of h performance in preview control action is characterized with the hamiltonian matrix by employing the property of hamiltonian matrix the solvability and analytic solution for the preview full information control problem are clarified based on an auxiliary introduced matrix riccati equation the property of resulting control law is illustrated with a numerical example

moving horizon estimation for hybrid systems we propose a state smoothing algorithm for hybrid systems based on moving horizon estimation mhe by exploiting the equivalence between hybrid systems modeled in the mixed logic dynamical form and piecewise affine systems we provide sufficient conditions on the time horizon and the penalties on the state at the beginning of the estimation horizon to guarantee asymptotic convergence of the mhe scheme moreover we propose two practical algorithms for the computation of penalties that allow us to implement mhe by solving a mixed integer quadratic program

on geometric and analytic constraints in the h infty fixed lag smoothing limiting factors on achievable performance in the continuous and discrete time fixed lag smoothing problems are shown to include geometric constraints inherited from the fixed interval linfin problem and analytic constraints affected by the preview interval thus the fixed lag problem is viewed as a constrained version of its fixed interval counterpart the analysis sheds light on the dependence of achievable performance on the preview length and in particular on the generic presence of performance saturation at a finite preview interval

h spl infin deconvolution filtering prediction and smoothing a krein space polynomial approach this correspondence is concerned with the infinite horizon h spl infin deconvolution for discrete time invariant systems described by polynomial equations a simple frequency domain approach in krein space is developed for the deconvolution problem with the help of an arma innovation model solutions to the problems of deconvolution filtering prediction and fixed lag smoothing are obtained the estimators are calculated by performing one j spectral factorization

advances in the deterministic synthesis of uniform amplitude pencil beam concentric ring arrays we present some modifications to the deterministic approach da recently proposed for fast design of aperiodic concentric ring arrays such modifications are aimed at improving the array performances in terms of directivity side lobe level sll and number of control points in particular an easy implementation of the size tapering concept is provided within the processing scheme of the da procedure moreover an improved collocation criterion is presented finally a local optimization procedure tailored to the concentric ring array case is addressed

h sup spl infin control and estimation with preview part i matrix are solutions in continuous time preview control and fixed lag smoothing allow a noncausal component in the controller estimator time domain variational analysis is used in a reduction to an open loop differential game leading to a complete necessary and sufficient characterization of suboptimal values and an explicit state space design in terms of a parameterized nonstandard algebraic matrix riccati equation in a general continuous time linear system setting the solution offers insight into the appropriate structure of the associated hamiltonian where the state and co state are not the usual state of the original dynamic system and that of its adjoint rather the state and co state are selected to capture the respective lumped effects of initial data and future input selection in the allied game

global analysis in a predator prey system with nonmonotonic functional response a predator prey system with nonmonotonic functional response is considered global qualitative and bifurcation analyses are combined to determine the global dynamics of the model the bifurcation a

game theory approach to h sub spl infin optimal discrete time fixed point and fixed lag smoothing optimal h sub spl infin fixed point and fixed lag discrete time smoothing estimators are developed by applying a game theory approach a deterministic discrete time game is defined where the estimator plays against nature nature determines the system initial condition the driving input and the measurement noise whereas the estimator tries to find an estimate that brings a prescribed cost function that is based on the error of the estimation at a fixed time instant to a saddle point equilibrium the latter estimate yields the h sub spl infin optimal fixed point smoothing differently from the usual case in h sub spl infin optimal estimation and control the critical value of the scalar design parameter of the smoothing game is obtained in closed form explicitly in the terms of the corresponding h sub 2 solution unlike the h sub 2 case the recursive application of the h sub spl infin fixed point smoothing algorithm does not lead to fixed lag smoothing in the h sub spl infin norm sense the h sub spl infin fixed lag smoothing filter is derived by augmenting the state vector of the system with additional delayed states

squaring down lti systems a geometric approach in this paper the problem of reducing a given lti system into a left or right invertible one is addressed and solved with the standard tools of the geometric control theory first it will be shown how an lti system can be turned into a left invertible system thus preserving key system properties like stabilizability phase minimality right invertibility relative degree and infinite zero structure moreover the additional invariant zeros introduced in the left invertible system thus obtained can be arbitrarily assigned in the complex plane by duality the scheme of a right inverter will be derived straightforwardly moreover the squaring down problem will be addressed in fact when the left and right reduction procedures are applied together a system with an unequal number of inputs and outputs is turned into a square and invertible system furthermore as an example it will be shown how these techniques may be employed to weaken the standard assumption of left invertibility of the plant in many optimization problems

cosine pattern synthesis for single and multiple main beam uniformly spaced linear arrays the method of cosine pattern synthesis for single and multiple main beam equispaced linear arrays is introduced the cosine pattern function is characterized by the position of the main beam in the theta domain and its half power beamwidth the fourier series and woodward lawson methods are applied to the special cases of single or multiple main beam cosine pattern synthesis the patterns produced by application of these classical shaped beam synthesis methods can then be used as initial patterns for iterative and perturbational techniques examples are presented and discussed including the use of multiple main beam cosine pattern synthesis to design a high power high frequency ground based transmitter for the creation of an array of wireless ionospheric dipoles

an innovation approach to h sub spl infin fixed lag smoothing for continuous time varying systems this note studies the finite horizon h sub spl infin fixed lag smoothing problem for linear continuous time varying systems a technique named as reorganized innovation analysis in krein space is developed to give a necessary and sufficient condition for the existence of an h sub spl infin fixed lag smoother the condition is given in terms of the boundedness of two matrix functions which are derived from the solutions of two riccati differential equations rdes one standard h sub spl infin filtering rde and one h sub 2 type of rde examples demonstrate the proposed h sub spl infin fixed lag smoother design and the fact that the existence of an h sub spl infin smoother does not depend on the solvability of h sub spl infin filtering

an autopolyploidy based genetic algorithm for enhanced evolution of linear polyfractal arrays there has been considerable recent interest in techniques for the optimization of large n antenna arrays unfortunately the successful development of such techniques has been hindered by the large number of independent parameters that must be optimized and the complexity of the calculations needed for the electromagnetic evaluation of large n arrays one promising new design methodology for large n arrays which has recently been introduced is based on properties of a subset of fractal random arrays called polyfractal arrays polyfractal arrays have many embedded self similar structures thereby allowing very large and seemingly complex array layouts to be described with only a small set of independent parameters in addition by effectively utilizing the self similarity of polyfractal arrays a considerable reduction can be achieved in the amount of time required to evaluate the radiation patterns of large n arrays this paper introduces a type of nature based design process that applies a specially formulated genetic algorithm ga technique to evolve optimal polyfractal array layouts the most unique aspect of this optimization technique is a new autopolyploidy based chromosome expansion that maximizes the efficiency of the gas simple polyfractal geometries are used in the initial stage or first epoch of the optimization because the number of independent parameters is small and the computation times are relatively fast after the optimization converges for the first epoch more complicated descriptions of these polyfractal arrays are introduced to provide additional independent parameters for the optimizer as it progresses through later epochs of evolution this process has been shown to be very effective in creating optimized large n arrays the largest example considered here being a 1616 element linear array with a 24 30 db sidelobe level and a 0 056deg half power beamwidth

h fixed lag smoothing for discrete linear time varying systems this paper is concerned with the finite horizon h fixed lag smoothing problem for discrete linear time varying systems the existence of an h smoother is first related to certain inertia condition of an innovation matrix the innovation matrix is traditionally computed via a riccati difference equation rde associated with the h filtering of an augmented system which is computationally expensive to avoid solving the rde of high dimension we introduce a re organized innovation and apply innovation analysis and projection theory in krein space to give a simple method of computing the innovation matrix the h smoother is computed as a projection in krein space by performing two rdes of the same dimension as that of the original system

receding horizon unbiased fir filters for continuous time state space models without a priori initial state information a receding horizon unbiased finite impulse response filter rhuff is proposed for continuous time state space models linearity unbiasedness finite impulse response fir structure and independence of the initial state information will be required in advance in addition to a performance index of minimum variance the proposed rhuff is obtained by directly minimizing the performance index with the unbiasedness constraint the proposed rhuff is represented first in a standard fir form and then in an iterative form it is shown that the rhuff is equivalent to the existing receding horizon rh kalman fir filter the former is more systematic and logical while the latter is heuristic due to the handling of infinite covariance of the initial state information

brief paper minimax fir smoothers for deterministic continuous time state space models in order to design a smoother for a deterministic continuous time state space model a new performance criterion is proposed which is given by a ratio of the current estimation error to the weighted energy of the deterministic disturbance applied during the recent finite horizon among smoothers with the deadbeat property and finite impulse response fir structure a minimax fir smoother mfs is obtained to optimize the proposed performance criterion to begin with the functional optimization problem is formulated with respect to kernel functions of the mfs and then its solution is explicitly presented the mfs depends only on inputs and outputs on the finite recent horizon and is independent of any a priori state information the mfs is first represented in an integral form for simple representation and then a differential form is introduced for efficient numerical computation as in h iir smoothing and h 2 iir filtering it is shown that the proposed mfs for a deterministic system can be interpreted as the minimum variance unbiased fir smoother for a stochastic system

l_ 2 e fir smoothers for deterministic discrete time state space signal models in this note a new type of l2 e performance criterion for a fixed lag smoother is introduced which is given by a gain between the energy of the external disturbances during the recent time horizon and the estimation error at the fixed delayed time from the current one by minimizing the maximum value of the l2 e performance criterion the l2 e finite impulse response fir smoother lefs is obtained for a deterministic discrete time state space signal model the lets is designed to meet requirements such as linearity and fir structure with respect to measured inputs and outputs unbiased property in the deterministic sense and independence of any state information simultaneously the proposed lets is represented in a batch form for simplicity the lets is compared with a conventional h infin infinite impulse response iir smoother via simulation

optimal and robust noncausal filter formulations the paper describes an optimal minimum variance noncausal filter or fixed interval smoother the optimal solution involves a cascade of a kalman predictor and an adjoint kalman predictor a robust smoother involving h sub spl infin predictors is also described filter asymptotes are developed for output estimation and input estimation problems which yield bounds on the spectrum of the estimation error these bounds lead to a priori estimates for the scalar spl gamma in the h sub spl infin filter and smoother design the results of simulation studies are presented which demonstrate that optimal robust and extended kalman smoothers can provide performance benefits

brief on the h fixed lag smoothing how to exploit the information preview the problem of the continuous time h fixed lag smoothing over the infinite horizon is studied the first solution to the problem is derived in terms of one algebraic riccati equation of the same dimension as in the filtering case and the mechanism by which the performance improvements with respect to the h filtering occur is clarified it is shown that the h smoother exploits the information preview in an h 2 manner

spatiotemporal dynamics in a delayed diffusive predator model in this paper we investigate the spatiotemporal dynamics of a delayed reaction diffusion leslie gower model based on the stability analysis we demonstrate that delayed feedback may generate hopf and turing instability under some conditions resulting in spatial patterns one of the most interesting findings is that the model exhibits complex pattern replication pure turing instability gives birth to spots spots stripes mixture stripes stripes holes mixture and holes patterns pure hopf instability to spiral wave pattern and hopf turing instability to chaotic wave pattern our results well extend the findings of spatiotemporal dynamics in the delayed reaction diffusion predator prey model and indicate that time delay play an important roles in pattern formation

fourier synthesis of linear arrays based on the generalized scattering matrix and spherical modes this paper presents a novel simple pattern synthesis procedure for linear equispaced arrays which can be characterized by a generalized scattering matrix gsm and whose radiated field can be expressed as a weighted sum of shifted spherical waves it can be viewed as an extension of the classic design techniques of the fourier series fs method or the woodward lawson frequency sampling method to the case in which the individual antenna elements patterns and all interelement couplings are taken into account the design procedure which yields the excitations needed to achieve the desired pattern is based on either the fs or the discrete fourier transform dft of the spherical mode expansion of the array radiated field as well as on various properties associated to the fs or dft coefficients in this work to compute the gsm of the array and the spherical mode expansion of the field a validated hybrid full wave methodology based on the finite element method and rotation and translation properties of spherical waves is used numerical results of different synthesized array patterns are presented for different arrays made up of dielectric resonator antennas and cavity backed microstrip circular patches

generalized scattering matrix analysis of a class of finite arrays of coupled antennas by using 3 d fem and spherical mode expansion a rigorous method for characterizing in terms of a multimode scattering matrix a finite array of antennas where each antenna can be described by means of spherical waves is presented in this paper the procedure provides the impedance coupling and radiating characteristics of the arrays and comprises two steps first the generalized scattering matrix gsm of each single antenna is numerically calculated over a wide band of frequencies for this purpose we use a previously developed methodology that combines the domain segmentation technique the three dimensional finite element method 3d fem spherical mode expansion and a reduced order model obtained using a symmetric matrix pade spl acute via lanczos sympvl algorithm second the overall gsm of the finite array is calculated starting from the gsm of each antenna and using rotation and translation of spherical waves a closed form expression for the overall gsm is given and different examples are shown in order to validate the proposed method

a spectral factorization approach for h spl infin estimation problems in discrete time this note deals with the h filtering prediction and smoothing problems for discrete time linear systems the j spectral factorization approach is pursued and for each of the three problems a computationally efficient procedure to derive a j spectral factor is presented the construction of filter smoother and predictor hinges on the stabilizing solution of the same algebraic riccati equation this fact allows for the avoidance of any fictitious augmentation of the state space dimensions

brief paper an efficient algorithm for discrete time h preview control an efficient numerical solution to the output feedback discrete time h preview control problem is presented the first step of the solution comes from embedding the preview control problem in a two degree of freedom generalised regulator framework in which the augmented system state includes a segment of the frequency weighted previewed signal an efficient method for solving the resulting inflated discrete algebraic riccati equations dares is then found it is demonstrated that one need only solve an estimation riccati equation with dimension that of the plant and a control riccati equation with dimension that of the plant and reference weighting taken together the reduced control riccati equation is the product of a recursive reduction enabled by the zero eigenvalues in the associated closed loop matrix an added feature of the presented algorithm is that no large matrix computations are required and no large matrices need be stored only the edges of the full information riccati equation solution are required when synthesising the controller

cal h _ infty control and estimation problems with delayed measurements state space solutions most physical processes exhibit transport delay in the measured output and it is well known that this can have disastrous effects on system stability and performance if it is not accounted for in this paper we give necessary and sufficient conditions for existence of estimators and controllers that achieve the desired cal h infty performance criterion when such a measurement delay is present we also give the complete characterization of all controllers and estimators that achieve the desired performance criterion the necessary and sufficient conditions are easy to check and are given in terms of the familiar pair of algebraic riccati equations that appear in the nondelay versions of the corresponding cal h infty problems along with an additional riccati differential equation explicit state space formulas for the controllers and estimators are also obtained they have a linear periodic structure and are easily implementable to obtain these results we first obtain state space results for a modified nehari problem which may be of independent interest see problem 5 in section 2

a note on two filter smoothing formulas in this note the two filter smoothing formulas are obtained from general optimal smoothers in consideration of the control inputs and the correlation between system and measurement noises the inverse of the system matrix and any backwards time model for a backwards filter are not required besides we do not take heuristic approaches such as infinite covariances we first propose a new batch form of the general optimal smoother and then represent it with two filters without any assumptions and heuristic approaches even in the case that the lag size is small the proposed formulas in this note still work without any singularity problem and thus are guaranteed to be optimal even for a singular system matrix a recursive form is introduced for efficient calculation and is shown to be reduced to the existing two filter formulas if some condition is satisfied

linear quadratic regulation and stabilization of discrete time systems with delay and multiplicative noise this paper is concerned with the long standing problems of linear quadratic regulation lqr control and stabilization for a class of discrete time stochastic systems involving multiplicative noises and input delay these fundamental problems have attracted resurgent interests due to development of networked control systems an explicit analytical expression is given for the optimal lqr controller more specifically the optimal lqr controller is shown to be a linear function of the conditional expectation of the state with the feedback gain based on a riccati zxl difference equation it is also shown that the system is stabilizable in the mean square sense if and only if an algebraic riccati zxl equation has a particular solution these results are based on a new technical tool which establishes a non homogeneous relationship between the state and the costate of this class of systems and the introduction of a new lyapunov function for the finite horizon optimal control design

stability and further analytical bifurcation behaviors of moran ricker model with delayed density dependent birth rate regulation abstract in this paper we consider moran ricker model with delayed density dependent birth rate presented by neverova et al 2016 it is well known that normal form of a dynamical system is easier to work with while it has the same qualitative properties as those of the original one firstly existence and local stability analysis of the model fixed points are addressed then normal form theory and perturbation method are applied to investigate different types of bifurcations included in the model it is demonstrated the presence of transcritical flip and neimark sacker bifurcations in the model in addition it is proved that the model has a chaotic behavior in the sense of marotto finally numerical simulations are provided to verify our analytic results compared with those obtained in neverova et al 2016 and explore further rich dynamics of the model as well

autocorrelation driven synthesis of antenna arrays the case of ds based planar isophoric thinned arrays a new methodology for the design of isophoric thinned arrays with a priori controlled pattern features is introduced a fully analytical and general i e valid for any lattice and set of weights relationship between the autocorrelation of the array excitations and the power pattern samples is first derived binary 2 d sequences with known autocorrelation properties namely the difference sets ds s are then chosen as a representative benchmark to prove that it is possible to deduce closed form synthesis formulas that a priori guarantee to fit requirements on the sidelobe level sll the directivity the half power beamwidth and the power pattern in user defined directions the selected results from a wide numerical assessment which also includes full wave simulations with realistic radiators are illustrated to validate the reliability and the accuracy of the proposed design equations and the associated performance bounds

h sub infinity fixed lag smoothing filter for scalar systems the solution of the h sub infinity optimal linear fixed lag smoothing problem is considered using a polynomial matrix description for the discrete system the smoother is obtained from the solution of a linear equation and a spectral factorization calculation the pole zero properties of the optimal smoother are obvious in the polynomial representation and insights into the measurement noise rejection properties of the smoother are obtained allowance is made for both dynamic cost weighting and colored measurement noise the polynomial form of the smoothing filter may be incorporated into a self tuning algorithm and a simple adaptive smoother is discussed

optimal estimation for continuous time systems with delayed measurements this note focuses on the traditional problem of the kalman filtering for linear continuous time systems although the problem has been studied widely in the past decades little work has been done for the time delayed systems and some fundamental problems remain to be solved this note proposes a new tool namely reorganization innovation analysis approach to investigate the filtering problem for systems with delayed measurements the kalman filter is given in terms of the solution of standard riccati equations the performance is clearly demonstrated through analytical results and simulation the solved problem in this note is related with some more complicated problems such as h sub spl infin fixed lag smoothing h sub spl infin control with preview and control with input delays

dynamical analysis of fractional order modified logistic model in this paper we study a fractional differential equation model of the single species multiplicative allee effect first we study the stability of equilibrium points further we give some sufficient conditions ensuring the existence and uniqueness of integral solution in the last section we perform several numerical simulations to validate our analytical findings

exponential extinction of a stochastic predator prey model with allee effect abstract in this paper we study a stochastic predator prey model with beddington deangelis functional response and allee effect whose coefficients are dependent on expectations we prove that there is a unique global positive solution to the system with the positive initial value moreover sufficient conditions for exponential extinction are established

when does the h sup spl infin fixed lag smoothing performance saturate for a finite smoothing lag a notable difference between the h sup 2 and h sup spl infin smoothing is that the achievable performance in the latter problem might saturate as the function of the smoothing lag in the sense that there might exist a finite smoothing lag for which the achievable performance level is the same as for the infinite smoothing lag in this note necessary and sufficient conditions under which such a saturation occurs are derived in particular it is shown that the h sup spl infin performance saturates only if the h sup spl infin norm of the optimal error system is achieved at the infinite frequency i e if the worst case disturbance for the infinite smoothing lag case can be arbitrarily fast and thus in a sense unpredictable

necessary and sufficient condition for two player stackelberg strategy this technical note revisits the open loop stackelberg strategy for a two player game by introducing a new costate which captures the future information of the control input we present a necessary and sufficient condition for the existence and uniqueness of the two player game the optimal strategy is designed in terms of three decoupled and symmetric riccati equations which improves the existing results greatly on computation

consequences of double allee effect on the number of limit cycles in a predator prey model the main goal of this work is to show a comparative analysis of simple continuous time predator prey models considering the allee effect affecting the prey population also known as depensation in fisheries sciences this phenomenon may be expressed by different mathematical forms yielding a distinct number of limit cycles surrounding a positive equilibrium point when two of these different formalizations are considered in the same system it is known that the volterra predation model using the most usual form to express the allee effect has a unique limit cycle in this work considering a more complex mathematical expression the existence of two limit cycles is proved by means of the lyapunov quantities we argue that the second equation explains the existence of two allee effects affecting the same population which could justify the difference observed between the models these results imply that the election of mathematical formulation can have consequences on the fit of the observed data thus leading to mistakes for ecologists we conclude that the oscillatory behaviors and overall dynamics depend strongly on the algebraic expression of the allee effect making difficult the proposition of general results nevertheless the techniques reviewed in this paper emerge as key tools to analyze the existence of limit cycles in the presence of multiple allee effects

three limit cycles in a leslie gower predator prey model with additive allee effect in this work a bidimensional continuous time differential equations system is analyzed which is derived of leslie type predator prey schemes by considering a nonmonotonic functional response and allee effect on population prey for the system obtained we describe the bifurcation diagram of limit cycles that appears in the first quadrant the only quadrant of interest for the sake of realism we show that under certain conditions over the parameters the system allows the existence of three limit cycles the first two cycles are infinitesimal ones generated by hopf bifurcation the third one arises from a homoclinic bifurcation furthermore we give conditions over the parameters such that the model allows long term extinction or survival of both populations in particular the presence of a weak allee effect does not imply extinction of populations necessarily for our model

optimality for a diffusive predator prey system in a spatially heterogeneous environment incorporating a prey refuge abstract in this paper we consider the optimal harvesting controls for a diffusive predator prey system which is formulated by prey refuge and modified leslie gower functional response the locally and globally asymptotic stability of unique positive constant steady state is discussed under homogeneous neumann boundary condition the nonexistence and existence of nonconstant steady states are obtained by leray schauder degree theory also the optimal harvesting strategies to get maximum sustainable yield msy and maximum economic yield mey are correspondingly given

pareto optimization of thinned planar arrays with elliptical mainbeams and low sidelobe levels a multi objective pareto genetic algorithm design methodology is applied to thinned planar arrays to simultaneously minimize peak side lobe levels and target an elliptical mainbeam with specific minimum and maximum half power beamwidths this new radiation pattern synthesis technique for thinned planar arrays provides antenna engineers with a set of tradeoffs between low side lobe levels and close adherence to mainbeam design objectives i e the specified half power beamwidths corresponding to the major and minor axes of an elliptical mainbeam one pareto optimization example is presented for a thinned low side lobe planar array with a desired minimum and maximum beamwidth of 8 4 and 12 respectively two designs from the pareto front are discussed one with a 20 92 db side lobe level and beamwidths between 11 5 and 7 5 and a second with a 18 97 db side lobe level with beamwidths between 12 and 7 93

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

a michaelis menten type food chain model with strong allee effect on the prey dynamical behaviours of a tritrophic food chain model with strong allee effect in the prey are studied in this paper positivity and boundedness of the system are discussed some global results on extinction of the species are derived stability analysis of the equilibrium points is presented the effect of discrete time delay is studied where the delay may be regarded as the gestation period of the superpredator numerical simulations are carried out to validate our analytical findings implications of our analytical and numerical findings are discussed critically

constrained state estimation for nonlinear discrete time systems stability and moving horizon approximations state estimator design for a nonlinear discrete time system is a challenging problem further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances one strategy for constrained state estimation is to employ online optimization using a moving horizon approximation we propose a general theory for constrained moving horizon estimation sufficient conditions for asymptotic and bounded stability are established we apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation examples are used to illustrate the benefits of constrained state estimation our framework is deterministic

bifurcation analysis of a predator prey system with nonmonotonic functional response we consider a predator prey system with nonmonotonic functional response p x frac mx ax 2 bx 1 by allowing b to be negative b 2 sqrt a p x is concave up for small values of x 0 a

l_2 e fir filters for deterministic continuous time state space signal models in this paper a new l2 e performance criterion is introduced which is represented as a gain between the disturbance during the recent time interval and the current estimation error based on the l2 e performance criterion the l2 e finite impulse response fir filter leff is proposed for deterministic continuous time state space signal models without requiring the stochastic information such as variances and means the leff is designed to minimize the maximum value of the l2 e performance criterion together with prior constraints such as linearity unbiased property in the deterministic sense and fir structure simultaneously via simulation the leff is compared with other deterministic infinite impulse response iir filters such as the hinfin and l2 linfin filters

h sup spl infin control and estimation with preview part ii fixed size are solutions in discrete time h sup spl infin preview control and fixed lag smoothing problems are solved in general discrete time linear systems via a reduction to equivalent open loop differential games to prevent high order riccati equations found in some solutions the state of the hamilton jacobi system resides in a quotient space of an auxiliary extended state space system the dimension of that auxiliary space is equal to the state space dimension of the original system ignoring the delay

pattern formation of a diffusive predator prey model with strong allee effect and nonconstant death rate abstract this paper is concerned with the pattern formation of a diffusive predator prey model with strong allee effect in the prey population and nonconstant death rate for the predator the necessary and sufficient conditions of turing instability are explicitly obtained by regarding the diffusion coefficient d 2 of the predator as bifurcation parameter we demonstrate that at the critical value of the bifurcation parameter d 2 a turing bifurcation occurs i e a pattern arises the conditions for the stability of the pattern are also derived in detail our results show that strong allee effect in our model plays a crucial role in the formation of stationary pattern which is a strong contrast to the case without strong allee effect

the evolution of optimal linear polyfractal arrays using genetic algorithms recently in order to successfully combine the positive attributes of both periodic and random arrays into one design a novel class of arrays known as fractal random arrays has been introduced in addition several researchers have successfully used genetic algorithms robust global optimization techniques based on natural selection to find solutions to complex array layout problems this paper introduces a type of nature based design process that applies a specially formulated genetic algorithm to evolve optimal layouts of an important subset of fractal random arrays which we call polyfractal arrays also this paper discusses how the underlying self similar properties of polyfractal arrays can be exploited to increase the speed of the associated array factor calculations this speed increase dramatically reduces the time required for the genetic algorithm to converge thereby making it possible to effectively evolve optimal array configurations which are much larger than has been previously possible moreover the fractal random properties of these polyfractal arrays are shown to provide substantially wider bandwidth performance than their conventional counterparts finally several design examples of genetically optimized linear polyfractal arrays with narrow beamwidths improved sidelobe suppression and wide bandwidths are presented