existence results for operator equations in partially ordered sets and applications in this paper we prove existence results for operator equations in partially ordered sets and apply the obtained results to operator equations in ordered banach spaces and to semilinear functional parabolic and elliptic problems involving discontinuous nonlinearities

discrete time hybrid control in borel spaces average cost optimality criterion abstract this paper addresses an optimal hybrid control problem in discrete time with borel state and action spaces by hybrid we mean that the evolution of the state of the system may undergo deep changes according to structural modifications of the dynamic such modifications occur either by the position of the state or by means of the controller s actions the optimality criterion is of a long run ratio average or ratio ergodic type we provide the existence of optimal average policies for this hybrid control problem by analyzing an associated dynamic programming equation we also show that this problem can be translated into a standard or non hybrid optimal control problem with cost constraints besides we show that our model includes some special and important families of control problems such as those with an impulsive or switching mode finally to illustrate our results we provide an example on a pollution accumulation problem

stochastic hybrid control the objective of this paper is to study the stochastic version of a previous paper of the authors in which hybrid control for deterministic systems was considered the modelling is quite similar to the deterministic case we have a system whose state is composed of a continuous part and a discrete part they are affected by a continuous type control and an impulse control the dynamics is moreover perturbed by noise also a continuous and a discrete noise process the markovian character of the sate process is preserved we develop the model and show how the dynamic programming approach leads to some involved quasi variational inequality

elliptic problems with lack of compactness via a new fixed point theorem abstract this paper provides a new fixed point theorem for increasing self mappings g b b of a closed ball b x where x is a banach semilattice which is reflexive or has a weakly fully regular order cone x by means of this fixed point theorem we are able to establish existence results of elliptic problems with lack of compactness

optimal stochastic scheduling of power generation systems with scheduling delays and large cost differentials the optimal scheduling or unit commitment of power generation systems to meet a random demand involves the solution of a class of dynamic programming inequalities for the optimal cost and control law we study the behavior of this optimality system in terms of two parameters i a scheduling delay e g the startup time of a generation unit and ii the relative magnitudes of the costs operating or starting of different units in the first case we show that under reasonable assumptions the optimality system has a solution for all values of the delay and as the delay approaches zero that the solutions converge uniformly to those of the corresponding system with no delays in the second case we show that as the cost of operating or starting a given machine increases relative to the costs of the other machines there is a point beyond which the expensive machine is not used except in extreme situations we give a formula for the relative costs that characterize this point moreover we show that as

differential automata and their discrete simulators on presente la notion d automate differentiel pour la formulation d une classe de problemes aux valeurs initiales sur des champs vectoriels hysteretiques

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

a stochastic games framework for verification and control of discrete time stochastic hybrid systems we describe a framework for analyzing probabilistic reachability and safety problems for discrete time stochastic hybrid systems within a dynamic games setting in particular we consider finite horizon zero sum stochastic games in which a control has the objective of reaching a target set while avoiding an unsafe set in the hybrid state space and a rational adversary has the opposing objective we derive an algorithm for computing the maximal probability of achieving the control objective subject to the worst case adversary behavior from this algorithm sufficient conditions of optimality are also derived for the synthesis of optimal control policies and worst case disturbance strategies these results are then specialized to the safety problem in which the control objective is to remain within a safe set we illustrate our modeling framework and computational approach using both a tutorial example with jump markov dynamics and a practical application in the domain of air traffic management

differential and integral equations with henstock kurzweil integrable functions abstract in this paper we apply fixed point theorems for increasing mappings in ordered normed spaces to prove existence and comparison results for solutions of discontinuous functional differential and integral equations containing henstock kurzweil integrable functions

a monotone iterative technique for stationary and time dependent problems in banach spaces an abstract monotone iterative method is developed for operators between partially ordered banach spaces for the nonlinear problem lu nu and the nonlinear time dependent problem u l n u under appropriate assumptions on l and n we obtain maximal and minimal solutions as limits of monotone sequences of solutions of linear problems the results are illustrated by means of concrete examples

controlled diffusion processes with markovian switchings for modeling dynamical engineering systems abstract in this paper the intrinsic complex nature of engineering systems under control is treated by introducing an approach based on controlled stochastic differential equations with markovian switchings in short csdems technical conditions for the existence and uniqueness of the solutions of the csdems are provided in this context it is not unusual to deal with non linear csdems that cannot be solved analytically therefore we develop a new two step predictor corrector method for finding numerical approximations to solutions of csdems this method utilizes the euler maruyama method an illustrative application to the biochemical engineering area is presented to highlight the usefulness of our approach as a simulation tool

statistical analysis of pisarenko s method for sinusoidal frequency estimation statistical analysis is performed for pisarenko s method of sinusoidal frequency estimation by using the periodogram technique under the assumption that the data consist of several sinusoids plus white noise we give an asymptotic expression of the error variance of the sinusoidal frequency estimator also a modified method is proposed this is computationally efficient but the statistical property is not improved we also present simulation results and compare them to the theoretical ones lastly we point out that the pisarenko s method can be implemented as an on line bias compensated least squares algorithm thus avoiding the eigenvalue and eigenvector calculations

an exact direct method of sinusoidal parameter estimation derived from finite fourier integral of differential equation in this paper we propose a novel method for estimating the parameters frequency amplitude and phase of real sinusoids to derive the estimator we start from the characteristic differential equation of a sinusoid to remove differentials and obtain an algebraic relation for frequency we introduce finite period weighted integrals of the differential equation which become equivalent to the differential equation when a sufficient number of weight functions are applied as weight functions we show that fourier kernels have excellent properties terms related to integral boundaries are readily eliminated observations are provided by fourier coefficients and the relation becomes independently accurate for multiple sinusoids if they are sufficiently spaced we solve the obtained equations in two ways one is for approaching to the cramer rao lower bound crlb and the other is for enhancing the interference rejection capability also methods are proposed to calculate the weighted integrals from sampled signals with an improved accuracy proposed algorithms are examined under noise and sinusoidal interference error variances are compared with the crlb and other fast fourier transform fft based methods

a unified framework for hybrid control model and optimal control theory we propose a very general framework that systematizes the notion of a hybrid system combining differential equations and automata governed by a hybrid controller that issues continuous variable commands and makes logical decisions we first identify the phenomena that arise in real world hybrid systems then we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems evolving on continuous variable state spaces and subject to continuous controls and discrete transitions the model captures the identified phenomena subsumes previous models yet retains enough structure to pose and solve meaningful control problems we develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework in particular we demonstrate the existence of optimal relaxed and near optimal precise controls and derive generalized quasi variational inequalities that the associated value function satisfies we summarize algorithms for solving these inequalities based on a generalized bellman equation impulse control and linear programming

technical communique near optimal control for a class of stochastic hybrid systems to address a computationally intractable optimal control problem for a class of stochastic hybrid systems this paper proposes a near optimal state feedback control scheme which is constructed by using a statistical prediction method based on approximate numerical solution that samples over the entire state space a numerical example illustrates the potential of the approach

existence and comparison results for operator and differential equations in abstract spaces in this paper we apply the chain methods developed in heikkila and lakshmikantham 1994 to obtain new fixed point theorems and new existence and comparison results for operator equations in partially ordered sets these results are then applied to discontinuous implicit functional differential equations in ordered banach spaces

existence results for operator and differential equations and inclusions abstract this paper contains a brief summary of existence results for operator and differential equations and inclusions derived recently via a recursion method and generalized iteration methods introduced in 11 12 23

asymptotic properties of the high order yule walker estimates of sinusoidal frequencies the asymptotic properties of the high order yule walker hoyw estimator of sinusoidal frequencies are analyzed an explicit formula for the covariance matrix of the hoyw frequency estimation error is derived the effects on estimation accuracy of the number of yw equations the model order and a certain weighting matrix are investigated analytically the optimally weighted hoyw estimator is described the analysis presented together with the already existing empirical evidence provides enough motivation for the use of an overdetermined and high order yule walker estimator

a parameter estimation approach to estimation of frequencies of sinusoids it is shown that with uniform sampling a sample of the sum of m sinusoids at time nt can be uniquely expressed as a linear combination of the 2m samples at times n 1 t n 2m t the 2m coefficients of linear combination are also the coefficients of a 2m order polynomial whose roots are e pmj omega i omega i being the frequencies of the sinusoids given the samples of sinusoids plus noise a consistent estimate of the 2m coefficients are obtained by the instrumental variable method of parameter estimation it is also possible to track time varying frequencies by a recursive algorithm that exponentially weighs out the past data simulation examples of one and two sinusoids are given

a computable approach to measure and integration theory we introduce a computable framework for lebesgue s measure and integration theory in the spirit of domain theory for an effectively given second countable locally compact hausdorff space and an effectively given finite borel measure on the space we define a recursive measurable set which extends the corresponding notion due to s anin for the lebesgue measure on the real line we also introduce the stronger notion of a computable measurable set where a measurable set is approximated from inside and outside by sequences of closed and open subsets respectively the more refined property of computable measurable sets give rise to the idea of partial measurable subsets which naturally form a domain for measurable subsets we then introduce interval valued measurable functions and develop the notion of recursive and computable measurable functions using interval valued simple functions this leads us to the interval versions of the main results in classical measure theory the lebesgue integral is shown to be a continuous operator on the domain of interval valued measurable functions and the interval valued lebesgue integral provides a computable framework for integration

controllability and observability of hybrid systems abstract a special class of hybrid systems is considered whose state space is a cross product space of a euclidean space and a finite state space such models may be used to represent systems subject to known abrupt parameter variations such as commu tated networks they may also be used to approximate some types of time varying systems controllability observability and stability of hybrid systems are inves tigated in particular a necessary and sufficient algebraic condition a simple algebraic criterion and a computationally simple algebraic sufficient test for controllability and observability are derived moreover a simple sufficient stability condition is provided

existence results for operator equations in abstract spaces and an application in this paper we apply the recursion method presented in heikkila and lakshmikantham 1994 to derive fixed point theorems and existence results for operator equations in partially ordered sets the obtained results combined with related results of heikkila 2002 are then applied to operator equations in ordered hilbert spaces and to a functional elliptic boundary value problem