continuous representation and control of hybrid systems this article introduces a continuous representation for controlled model and state jump hybrid systems such a representation is valuable in that it manages to cope with the difficulties related to discontinuities by replacing the study of these systems by that of continuous ones which is simple the studied hybrid systems are first introduced together with their associated continuous systems some localized and global convergences of the states of continuous systems to those of hybrid systems are proved then the continuous representation is used within the optimal control framework free end time and trajectory pursuit hybrid problems are studied as well as their respective continuous versions convergences of solutions between continuous and hybrid problems are established which shows that the resolution of a problem ensuing from the representation enables one to obtain an approximation of the solution of the initial hybrid problem finally the formalism of calculus of variations is used to obta

battle outcome prediction for an extended system of lanchester type differential equations abstract battle outcome prediction conditions are given for an extended system of lanchester type differential equations for two different types of battle termination conditions a fixed force level breakpoint battles and b fixed force ratio breakpoint battles necessary and sufficient conditions for predicting battle outcome are given in the former case for a fight to the finish while sufficient conditions are given in the latter case the former results are equivalent to those for the problem of classical analysis of determining explicitly as a function of the initial conditions the occurrence of a zero point for the solution to this extended system although such results as given here have not appeared previously for nonoscillatory in the strict sense solutions

dynamic feedback stabilization of an unstable wave equation abstract in this paper we consider the stabilization of an unstable wave equation through a dynamic boundary compensator the measurement which is one internal point of the state of the wave equation is fluxed into the compensator while the output of the compensator is forced into the boundary of the wave equation the well posedness of the closed loop system is proved by using the semigroup method by choosing appropriate controller parameters and adopting nyquist criterion for distributed parameter systems the eigenvalues of the closed loop systems are shown to be inside the left half complex plane then the closed loop system is proved to be exponentially stable by using the riesz basis approach numerical simulations are presented to verify the effectiveness of the proposed compensator

robust exact differentiation via sliding mode technique abstract the main problem in differentiator design is to combine differentiation exactness with robustness in respect to possible measurement errors and input noises the proposed differentiator provides for proportionality of the maximal differentiation error to the square root of the maximal deviation of the measured input signal from the base signal such an order of the differentiation error is shown to be the best possible one when the only information known on the base signal is an upper bound for lipschitz s constant of the derivative

new results on the synthesis of pid controllers this paper considers the problem of stabilizing a first order plant with dead time using a proportional integral derivative pid controller using a version of the hermite biehler theorem that is applicable to quasi polynomials the complete set of stabilizing pid parameters is determined for both open loop stable and unstable plants the range of admissible proportional gains is first determined in closed form for each proportional gain in this range the stabilizing set in the space of the integral and derivative gains is shown to be either a trapezoid a triangle or a quadrilateral for the case of an open loop unstable plant a necessary and sufficient condition on the time delay is determined for the existence of stabilizing pid controllers

spatial attrition modeling stability conditions for a 2d t fd formulation a new general formulation for the spatial modeling of combat is presented where the main drivers are movement attitudes and struggle evolution this model in its simplest form is represented by a linear set of two coupled partial differential equations for two independent functions of the space and time variables even though the problem has a linear shape non negative values for the two functions render this problem as nonlinear in contrast with other attempts this model ensures stability and theoretical consistency with the original lanchester equations allowing for a better understanding and interpretation of the spatial modeling as a numerical illustration a simple combat situation is developed the model is calibrated to simulate different troop movement tactics that allow an invader force to provoke maximum damage at a minimum cost the analysis provided here reviews the trade off between spatial grid and time stepping for attrition cases and then extends it to a new method for guaranteeing good numerical behavior when the solution is expected to grow along the time variable there is a wide variety of spatial problems that could benefit from this analysis

an inverse problem of the lanchester square law in estimating time dependent attrition coefficients this paper considers the inverse problem of estimating time varying attrition coefficients in lanchester s square law with reinforcements using observed data on some or all of the battle s strength histories and the reinforcement schedules the method employed is a nonparametric extension of the parametric conjugate gradient method p cgm we use hypothetical strength histories and reinforcement schedules that are known to be without error at several points in time to illustrate the method however the method has application in other circumstances the problem of estimating the time dependent attrition coefficients that best fit a set of given strength histories is inherently a nonparametric inverse problem in this paper we cast it into a nonlinear optimization problem and show how to solve it numerically by using a nonparametric conjugate gradient method np cgm two numerical test cases are provided to illustrate the application of the method

a globally convergent frequency estimator online estimation of the frequency of a sinusoidal signal is a classical problem in systems theory that has many practical applications in this paper the authors provide a solution to the problem of ensuring a globally convergent estimation more specifically they propose a new adaptive notch filter whose dynamic equations exhibit the following remarkable features 1 all signals are globally bounded and the estimated frequency is asymptotically correct for all initial conditions and all frequency values 2 the authors obtain a simple tuning procedure for the estimator design parameters which trades off the adaptation tracking capabilities with noise sensitivity ensuring exponential stability of the desired orbit and 3 transient performance is considerably enhanced even for small or large frequencies as witnessed by extensive simulations to reveal some of the stability instability mechanisms of the existing algorithms and motivate our modifications the authors make appeal to a novel nonlinear state dependent time scaling the main advantage of working in the new time scale is that they remove the coupling between the parameter update law and the filter itself decomposing the system into a feedback form where the required modifications to ensure stability become apparent even though they limit their attention here to the simplest case of a single constant frequency without noise the algorithm is able to track time varying frequencies preserve local stability in the presence of multiple sinusoids and is robust with respect to noise

the topological asymptotic for pde systems the elasticity case the aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a design functional with respect to the creation of a small hole in this paper such an expansion is obtained and analyzed in the context of linear elasticity for general functionals and arbitrary shaped holes by using an adaptation of the adjoint method and a domain truncation technique the method is general and can be easily adapted to other linear pdes and other types of boundary conditions

topology optimization with optimality criteria and transmissible loads the paper describes how to take into consideration the presence of transmissible loads in a topology optimization method based on optimality criteria the optimization problem has been defined as a total potential energy maximization problem with stress displacement or stiffness constraints the final volume of the optimal structural configuration has not to be specified a priori and is a consequence of the imposed structural constraints the implementation of the proposed method is quite simple and leads to the identification of well defined optimal structures the results obtained by solving several benchmark problems are shown

weak convergence of nonlinear high gain tracking differentiator in this technical note the weak convergence of a nonlinear high gain tracking differentiator based on finite time stable system is presented under some easy checkable conditions an example is constructed by using homogeneity numerical simulation shows that this tracking differentiator takes advantages over the existing ones this result relaxes the strict conditions required in existing literature that the lyapunov function satisfies the global lipschitz condition and the setting time function is continuous at zero both of them seem very restrictive in applications

spatial lanchester models abstract lanchester equations have been widely used to model combat for many years nevertheless one of their most important limitations has been their failure to model the spatial dimension of the problems despite the fact that some efforts have been made in order to overcome this drawback mainly through the use of reaction diffusion equations there is not yet a consistently clear theoretical framework linking lanchester equations with these physical systems apart from similarity in this paper a spatial modeling of lanchester equations is conceptualized on the basis of explicit movement dynamics and balance of forces ensuring stability and theoretical consistency with the original model this formulation allows a better understanding and interpretation of the problem thus improving the current treatment modeling and comprehension of warfare applications finally as a numerical illustration a new spatial model of responsive movement is developed confirming that location influences the results of modeling attrition conflict between two opposite forces

finite time convergent differentiator based on singular perturbation technique a finite time convergent differentiator is presented that is based on singular perturbation technique the merits of this differentiator exist in three aspects rapidly finite time convergence compared with other typical differentiators no chattering phenomenon and besides the derivatives of the derivable signals the generalized derivatives of some classes of signals can be obtained for example the generalized derivative of a triangular wave is square wave etc the theoretical results are confirmed by computer simulations

a homogenization method for shape and topology optimization abstract shape and topology optimization of a linearly elastic structure is discussed using a modification of the homogenization method introduced by bendsoe and kikuchi together with various examples which may justify validity and strength of the present approach for plane structures

mappings sharing a value on finite dimensional spaces sufficient conditions are given to assert that differentiable mappings and differentiable proper mappings between r n and r m share a value the proof of the result is constructive and is based upon continuation methods

on the spatial dynamics of vaccination a spatial sirs v model abstract in this paper we analyze the effects of vaccination from a spatial perspective we propose a spatial deterministic sirs v model which considers a non linear system of partial differential equations with explicit attrition and diffusion terms for the vaccination process the model allows us to simulate numerically the spatial and temporal dynamics of an epidemic considering different spatial strategies for the vaccination policy in particular in our first example we analyze the classical sirs v evolution with the addition of movements due to diffusion while in the second one we focus on modeling one ring vaccination policy we expect this model can improve spatial predictions of sir vaccination models by taking into account the spatial dimension of the problem

on convergence of the nonlinear active disturbance rejection control for mimo systems in this paper the global and semiglobal convergence of the nonlinear active distur bance rejection control adrc for a class of multi input multi output nonlinear systems with large uncertainty that comes from both dynamical modeling and external disturbance are proved as a result a class of linear systems with external disturbance that can be dealt with by the adrc is classified the adrc is then compared both analytically and numerically to the well known in ternal model principle a number of illustrative examples are presented to show the efficiency and advantage of the adrc in dealing with unknown dynamics and in achieving fast tracking with lower overstriking

on convergence of tracking differentiator the tracking differentiator was first proposed by han in 1989 and the proof of convergence was presented the first time in han and wang han j q and wang w 1994 nonlinear tracking differentiator journal of systems science and mathematical science 14 177 183 in chinese unfortunately the proof there is incomplete this problem has been open for over two decades in this article we give a rigorous proof under some additional conditions an application for online estimation of the unknown frequencies for the finite sum of the sinusoidal signals is presented the numerical simulations illustrate the effectiveness of the estimation for both linear and nonlinear tracking differentiators

on the use of reduced models obtained through identification for feedback optimal control problems in a heat convection diffusion problem abstract this paper deals with the use of reduced models for solving some optimal control problems more precisely the reduced model is obtained through the modal identification method the test case which the algorithms is tested on is based on the flow over a backward facing step though the reduction for the velocity fields for different reynolds numbers is treated elsewhere 1 only the convection diffusion equation for the energy problem is treated here the model reduction is obtained through the solution of a gradient type optimization problem where the objective function gradient is computed through the adjoint state method the obtained reduced models are validated before being coupled to optimal control algorithms in this paper the feedback optimal control problem is considered a riccati equation is solved along with the kalman gain equation additionally a kalman filter is performed to reconstruct the reduced state through previous and actual measurements the numerical test case shows the ability of the proposed approach to control systems through the use of reduced models obtained by the modal identification method

on the convergence of an extended state observer for nonlinear systems with uncertainty abstract the extended state observer first proposed by jingqing han in j q han a class of extended state observers for uncertain systems control decis 10 1 1995 85 88 in chinese is the key link toward the active disturbance rejection control that is taking off as a technology after numerous successful applications in engineering unfortunately there is no rigorous proof of convergence to date in this paper we attempt to tackle this long unsolved extraordinary problem the main idea is to transform the error equation of objective system with its extended state observer into a asymptotical stable system with a small disturbance for which the effect of total disturbance error is eliminated by the high gain

combat modeling with partial differential equations abstract we propose an extension of the classical modeling of combat via lanchester equations to include one dimensional spatial effects the usual coupled set of ordinary differential lanchester equations is replaced by a system of partial differential equations we discuss the proposed model report preliminary numerical results and consider possible applications and extensions

analysis of an algorithm for generating locally optimal meshes for l 2 approximation by discontinuous piecewise polynomials this paper discusses the problem of constructing a locally optimal mesh for the best l 2 approximation of a given function by discontinuous piecewise polynomials in the one dimensional case it is shown that under certain assumptions on the approximated function baines algorithm m j baines math comp 62 1994 pp 645 669 for piecewise linear or piecewise constant polynomials produces a mesh sequence which converges to an optimal mesh the rate of convergence is investigated a two dimensional modification of this algorithm is proposed in which both the nodes and the connection between the nodes are self adjusting numerical results in one and two dimensions are presented

finite time intercept angle guidance in this paper new nonsingular terminal sliding mode control guidance laws ntsmcgls to unknown maneuvering target intercept are proposed and their finite time convergences are proved a novel nonsingular terminal sliding mode surface based on a predefined angle is designed to improve intercept performance and avoid singularity problem the presented guidance law requires no information on maneuvering target that is estimated and compensated by extended state observer eso and it can be used in practical systems where the target can evade freely also undesired chattering is restrained effectively by real time estimation and compensation of eso simulation results show that the ntsmcgls can achieve exact interception

error estimates in w 2 semi norms for discrete interpolating d 2 splines we derive error estimates in w 2 semi norms for multivariate discrete d 2 splines that interpolate an unknown function at the vertices of given triangulations these results are widely based on the construction of approximation operators and linear projectors onto piecewise polynomial spaces having weakly stable local bases

linear time derivative trackers the design of an ideal differentiator is a difficult and a challenging task in this paper we discuss the properties and the limitations of two different structures of linear differentiation systems the first time derivative observer is formulated as a high gain observer where the observer gain is calculated through a lyapunov like dynamical equation the second one is given in brunovski form in which the output to be differentiated appears as a control input and the differentiation gain is calculated from the dual lyapunov equation of the first differentiation observer a discrete time version of the second form is given finally illustrative examples are presented to show their strengths and weaknesses

discrete time implementation of high gain observers for numerical differentiation high gain observers have been used in non linear control to estimate derivatives of the output in this paper we study discrete time implementation of high gain observers and their use as numerical differentiators in noise free as well as noisy measurements we show that discretization using the bilinear transformation method gives better results than other discretization methods we also show that many of the available numerical differentiators are special cases of the bilinear discrete time equivalents of full order or reduced order high gain observers

global frequency estimation using adaptive identifiers online estimation of the frequencies of a signal which is the sum of n sinusoidals with unknown amplitudes frequencies and phases is made through yet another well known and simple system theoretical tool adaptive identifiers convergence of the proposed estimator is proved the new frequency estimator is of 3n order as compared to the order 5n 1 resulting from marino tomei observers results are demonstrated via simulation

improved error bounds for the liouville green or wkb approximation a variant of the gronwall bellman inequality is used to develop new bounds on solutions to the fundamental singular integral equations that arise in the error analysis of the liouville green or wkb approximation consequently new improved error bounds are obtained from the liouville green approximation to the solution of the differential equation d2wdt2 q t w 0 where the function q is real and twice continuously differentiable and does not vanish

total value adjustment for european options with two stochastic factors mathematical model analysis and numerical simulation abstract in the present paper we derive novel non linear pde models for pricing european options and the associated total value adjustment xva when incorporating the counterparty risk the main innovative aspect is the consideration of stochastic spreads instead of less realistic constant spreads previously used in the literature for the nonlinear model a rigorous mathematical analysis based on sectorial differential operators allows to state the existence and uniqueness of a solution moreover for the numerical solution we propose an appropriate set of techniques based on the method of characteristics for time discretization finite element for spatial discretization and fixed point iteration for the nonlinear terms finally numerical examples illustrate the expected behaviour of the option prices and the total value adjustment

second order sliding mode observer for mechanical systems the super twisting second order sliding mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems the finite time convergence of the observer is proved thus the observer can be designed independently of the controller a discrete version of the observer is considered and the corresponding accuracy is estimated

solution of lanchester equation models for combat abstract this paper provides a methodology for the study of quantitative behavior of solutions to the extended system of lanchester type differential equations for the prediction of the outcome of battles under different condition the method is sufficiently general for use with nonlinear and or stochastic adaptations as well

annihilation prediction for lanchester type models of modern warfare this paper introduces important new functions for analytic solution of lanchester type equations of modem warfare for combat between two homogeneous forces modeled by power attrition rate coefficients with no offset tabulations of these lanchester clifford schlafli or lcs functions allow one to study this particular variable coefficient model almost as easily and thoroughly as lanchester s classic constant coefficient one lcs functions allow one to obtain important information in particular force annihilation prediction without having to spend the time and effort of computing force level trajectories the choice of these particular functions is based on theoretical considerations that apply in general to lanchester type equations of modern warfare and provide guidance for developing other canonical functions moreover our new lcs functions also provide valuable information about related variable coefficient models also we introduce an important transformation of the battle s time scale that not only simplifies the force level equations but also shows that relative fire effectiveness and intensity of combat are the only two weapon system parameters determining the course of such variable coefficient lanchester type combat