semiconcave solutions of partial differential inclusions abstract we obtain new results on the propagation of singularities for semiconcave solutions of partial differential inclusions these results will be used to study the behavior of singularities of the value function for a reflected control problem

the application of dynamic programming to optimal inventory control this paper concerns a class of deterministic impulse control problems arising in inventory control a notable feature of the problem formulation is the presence of an end point constraint in consequence the value function may be discontinuous viability theory provides a characterization of the value function as the unique lower semicontinuous solution to a bensoussan lions type quasi variational inequality qvi suitably interpreted for nondifferentiable extended valued functions yet there are few examples in the literature of the use of this analytical machinery this paper provides such an example the example which concerns a problem for which the value function is neither everywhere finite valued nor continuously differentiable on the interior of its effective domain illustrates what is involved in calculating subdifferentials and checking satisfaction of qvi in a generalized sense this paper also provides a summary of the underlying theory and gathers in the appendix proofs of key results

use of equivalent boundary conditions for the solution of a class of strip grating structures equivalent boundary conditions for an electromagnetic strip grating are used to derive reflection and transmission coefficients for a boundary value problem consisting of three nonconducting media where the strip grating exists at one of the planar boundaries the results are used to generate data for a number of cases where data and or theories exist the theory presented compares favorably with the literature cited for the limiting condition that the period of the grating be small when compared with the free space wavelength of the radiation

pseudo anosov maps and invariant train tracks in the disc a finite algorithm let f be an isotopy class of orientation preserving homeomorphisms of the punctured disc we construct a finite algorithm which enables one to decide whether the class f contains a pseudo anosov element in this case the algorithm defines an invariant train track and the dilatation factor which gives the minimal topological entropy of the isotropy class

viability solutions to structured hamilton jacobi equations under constraints structured hamilton jacobi partial differential equations are hamilton jacobi equations where the time variable is replaced by a vector valued variable structuring the system it could be the time age pair hamilton jacobi mckendrick equations or candidates for initial or terminal conditions hamilton jacobi cournot equations among a manifold of examples here we define the concept of viability solution which always exists and can be computed by viability algorithms this is a constructive approach allowing us to derive from the tools of viability theory dealing with sets instead of functions some known as well as new properties of its solutions regarding functions as their epigraphs we bypass the regularity issues to arrive directly at the concept of barron jensen frankowska viscosity solutions above all we take into account viability constraints and extend classical boundary conditions to other internal conditions beyond that we use the fenchel legendre transform to associate a lagrangian with the hamiltonian and uncover an underlying variational problem it is proved that the viability solution to the structured hamilton jacobi equation is the valuation function of this variational principle the optimal evolutions of which are regulated by a regulation map which is constructed from the viability solution and can be computed by viability algorithms in other words the viability solution solves all at once a class of first order partial differential equations of intertemporal optimization problems and the regulation of their optimal evolutions

convexity in hamilton jacobi theory ii envelope representations upper and lower envelope representations are developed for value functions associated with problems of optimal control and the calculus of variations that are fully convex in the sense of exhibiting convexity in both the state and the velocity such convexity is used in dualizing the upper envelope representations to get the lower ones which have advantages not previously perceived in such generality and in some situations can be regarded as furnishing at least for value functions extended hopf lax formulas that operate beyond the case of state independent hamiltonians the derivation of the lower envelope representations centers on a new function called the dualizing kernel which propagates the legendre fenchel envelope formula of convex analysis through the underlying dynamics this kernel is shown to be characterized by a kind of double hamilton jacobi equation and despite overall nonsmoothness to be smooth with respect to time and concave convex in the primal and dual states it furnishes a means whereby in principle value functions and their subgradients can be determined through optimization without having to deal with a separate and typically much less favorable hamilton jacobi equation for each choice of the initial or terminal cost data

target problems under state constraints for nonlinear controlled impulsive systems we study the problem of reaching a target without leaving a prescribed constraint set for a dynamical system described by a controlled differential equation and a controlled instantaneous reset function we characterize all initial conditions from which the objective can be reached then we characterize the value function associated with the optimal reaching time problem

scattering from dielectric structures above impedance surfaces and resistive sheets interest in understanding of electromagnetic interaction with rough surfaces has prompted the study of scattering from typical dielectric humps over impedance surfaces it is shown that the green s function of the problem for a resistive sheet resembles that of the impedance surface hence both problems are considered here a numerical solution for the scattered field of a two dimensional dielectric object possibly inhomogeneous with arbitrary cross section above the impedance surface or resistive sheet is sought first the green s function of the problem is derived based on the exact image theory this form of the green s function is amenable to numerical computation then the induced polarization currents are calculated by casting the integral equations into a matrix equation via the method of moments numerical problems in calculation of the green s function when both source and observation points are close to the surface are discussed comparison of numerical results with a perturbation solution shows excellent agreement between the two methods

an lp approach to dynamic programming principles for stochastic control problems with state constraints abstract we study a class of nonlinear stochastic control problems with semicontinuous cost and state constraints using a linear programming lp approach first we provide a primal linearized problem stated on an appropriate space of probability measures with support contained in the set of constraints this space is completely characterized by the coefficients of the control system second we prove a semigroup property for this set of probability measures appearing in the definition of the primal value function this leads to dynamic programming principles for control problems under state constraints with general bounded costs a further linearized dpp is obtained for lower semicontinuous costs

discontinuous solutions of the hamilton jacobi equation for exit time problems in general the value function associated with an exit time problem is a discontinuous function we prove that the lower upper semicontinuous envelope of the value function is a supersolution subsolution of the hamilton jacobi equation involving the proximal subdifferentials superdifferentials with subdifferential type superdifferential type mixed boundary condition we also show that if the value function is upper semicontinuous then it is the maximum subsolution of the hamilton jacobi equation involving the proximal superdifferentials with the natural boundary condition and if the value function is lower semicontinuous then it is the minimum solution of the hamilton jacobi equation involving the proximal subdifferentials with a natural boundary condition futhermore if a compatibility condition is satisfied then the value function is the unique lower semicontinuous solution of the hamilton jacobi equation with a natural boundary condition and a subdifferential type boundary condition some conditions ensuring lower semicontinuity of the value functions are also given

the reciprocity and power conservation principles for boundary conditions on a semitransparent surface generalized boundary conditions of coupling on a semitransparent surface are valid only if the lorentz reciprocity theorem and the electromagnetic power conservation principle are satisfied on the surface with these boundary conditions these criteria are reformulated as relations between the tensors in the boundary conditions some known boundary conditions of coupling are considered

uniqueness of lower semicontinuous viscosity solutions for the minimum time problem we obtain the uniqueness of lower semicontinuous lsc viscosity solutions of the transformed minimum time problem assuming that they converge to zero on a reachable part of the target in appropriate directions we present a counter example which shows that the uniqueness does not hold without this convergence assumption it was shown by soravia that the uniqueness of lsc viscosity solutions having a subsolution property on the target holds in order to verify this subsolution property we show that the dynamic programming principle dpp holds inside for any lsc viscosity solutions in order to obtain the dpp we prepare appropriate approximate pdes derived through barles inf convolution and its variant

lax hopf based incorporation of internal boundary conditions into hamilton jacobi equation part i theory this article proposes a new approach for computing a semi explicit form of the solution to a class of hamilton jacobi hj partial differential equations pdes using control techniques based on viability theory we characterize the epigraph of the value function solving the hj pde as a capture basin of a target through an auxiliary dynamical system called characteristic system the properties of capture basins enable us to define components as building blocks of the solution to the hj pde in the barron jensen frankowska sense these components can encode initial conditions boundary conditions and internal boundary conditions which are the topic of this article a generalized lax hopf formula is derived and enables us to formulate the necessary and sufficient conditions for a mixed initial and boundary conditions problem with multiple internal boundary conditions to be well posed we illustrate the capabilities of the method with a data assimilation problem for reconstruction of highway traffic flow using lagrangian measurements generated from next generation simulation ngsim traffic data

languages d0l systems sets of curves and surface automorphisms we introduce extend and apply some relationships between formal language theory and surface theory first we show how boundaries of languages topologized with the cantor metric can be mapped to sets of curves on surfaces namely laminations second we present how and when endomorphisms of free monoids i e substitutions can be mapped to automorphisms of surfaces so that d0l systems correspond to iterations of these automorphisms third we apply these ideas to construct sets of non periodic irreducible automorphisms of surfaces following 14 35 43 so that the involved proofs do not use any differential or algebraic tools but accordingly substitution and d0l system theory of 11 12 31 32 37 mainly the decidability for a d0l language 12 to be strongly repetitive or not this construction also yields effective symbolic descriptions of the stable sets of curves associated with these automorphisms

discontinuous differential games and control systems with supremum cost abstract this paper concerns with the existence of a value for a zero sum two player differential game with supremum cost of the form c t 0 x 0 u v sup t 0 t h x t 0 x 0 u v under isaacs condition we characterize the value function as the unique solution in a suitable sense to a pde namely the hamilton jacobi isaacs equation as a byproduct we obtain a pde characterization of the value function for control system

reflection from an array of conducting plates using classic edge mode current densities a new reflection coefficient is derived for a frequency selective surface composed of conducting rectangular plates the current density induced on the plates is assumed to follow the classic edge mode behavior observed by meixner using very simple functions to describe the spatial dependence of the current a simple frequency dependent solution is derived this solution is a function of the 0th and 1st order bessel functions of the first kind the new approach provides very accurate results compared to the moment method and to measured data it also provides an analytic solution that demonstrates a cause and effect correspondence between the array geometry and performance

mayer and optimal stopping stochastic control problems with discontinuous cost we study two classes of stochastic control problems with semicontinuous cost the mayer problem and optimal stopping for controlled diffusions the value functions are introduced via linear optimization problems on appropriate sets of probability measures these sets of constraints are described deterministically with respect to the coefficient functions both the lower and upper semicontinuous cases are considered the value function is shown to be a generalized viscosity solution of the associated hjb system respectively of some variational inequality dual formulations are given as well as the relations between the primal and dual value functions under classical convexity assumptions we prove the equivalence between the linearized mayer problem and the standard weak control formulation counter examples are given for the general framework

chaperoning state evolutions by variable durations mckendrick partial differential equations in demography provide the state of a population depending on chronological time t and age d and involve two time evolutions the chronological one t in 0 t mapsto t geq 0 and the calendar age t in t d t mapsto t t d geq 0 both with constant velocity equal to 1 the calendar age evolution chaperons so to speak the evolution t in t d t mapsto x t of the state of a system some physical biological and economic problems motivate the introduction of variable durations with variable velocities representing the fluidity of time offering mathematical metaphors of a subjective fleeting specious time passing more or less slowly variable durations are no longer prescribed but chosen among those available and regulated the joint evolution of the variable evolution and the state is assumed to be governed by a differential inclusion or control system and provides as a byproduct the unknown temporal windows on which they evolve toge

extended hamilton jacobi characterization of value functions in optimal control this paper examines generalized solutions to the hamilton jacobi equation the hamiltonian h t x p is assumed convex in p but is not constrained to have linear growth in this variable this corresponds to a certain class of generalized bolza problems related to optimal control lower semicontinuous solutions are considered and it is shown that there is a unique solution the so called value function of the underlying bolza problem in proving the main result we use recent improved necessary optimality conditions viability is also used in a new way in connection to differential inclusions with unbounded images

impulse capture basins of sets under impulse control systems given a target contained in a constrained set and an impulse control system governing the evolutions of runs or executions that are hybrids of continuous and discrete evolutions this paper studies and provides several characterizations of the capture basin of the target viable in the constrained set it is the subset of initial runs from which start at least one run viable in the constrained set until it reaches the target in finite time it also provides algorithms and regulation rules governing the runs that reach the targets while obeying state constraints

viability kernels for nonlinear control systems using bang controls this note develops a method to construct viability kernels for multi input single output nonlinear control systems affine in the control the safe set is the superlevel set of a smooth function and the control is constrained to take values in a compact polyhedron the results make use of the frankowska method and the notion of viable capture basins

optimal control problems on manifolds a dynamic programming approach abstract dynamic programming identifies the value function of continuous time optimal control with a solution to the hamilton jacobi equation appropriately defined this relationship in turn leads to sufficient conditions of global optimality which have been widely used to confirm the optimality of putative minimisers in continuous time optimal control the dynamic programming methodology has been used for problems with state space a vector space however there are many problems of interest in which it is necessary to regard the state space as a manifold this paper extends dynamic programming to cover problems in which the state space is a general finite dimensional c manifold it shows that also in a manifold setting we can characterise the value function of a free time optimal control problem as a unique lower semicontinuous lower bounded generalised solution of the hamilton jacobi equation the application of these results is illustrated by the investigation of minimum time controllers for a rigid pendulum

discontinuous control problems for non convex dynamics and near viability for singularly perturbed control systems abstract the aim of this paper is to study two classes of discontinuous control problems without any convexity assumption on the dynamics in the first part we characterize the value function for the mayer problem and the supremum cost problem using viscosity tools and the notion of e viability near viability these value functions are given with respect to discontinuous cost functionals in the second part we obtain results describing the e viability near viability of singularly perturbed control systems

chain differentials with an application to the mathematical fear operator abstract we introduce a concept of derivative in a topological vector space that yields the chain rule of differentiation for composition of functions akin to but simpler than the epiderivative of aubin frankowska we show that if a function has a g teaux differential with suitable continuity properties it is a chain differential as an example we show that the mathematical fear operator is chain differentiable with respect to the cost density distribution in the space of continuous functions endowed with the topology of pointwise convergence uniform on every compact subsets

characterization of the value function of final state constrained control problems with bv trajectories this paper aims to investigate a control problem governed by differential equations with radon measure as data and with final state constraints by using a known reparametrization method by dal maso and rampazzo 18 we obtain that the value function can be characterized by means of an auxiliary control problem of absolutely continuous trajectories involving time measurable hamiltonian we study the characterization of the value function of this auxiliary problem and discuss its numerical approximations

singular perturbation of optimal control problems on multidomains the goal of this paper is to study a singular perturbation problem in the framework of optimal control on multi domains we consider an optimal control problem in which the controlled system contains a fast and a slow variables this problem is reformulated as an hamilton jacobi bellman hjb equation the main difficulty comes from the fact that the fast variable lives in a multi domain the geometric singularity of the multi domains leads to the discontinuity of the hamiltonian under a controllability assumption on the fast variables the limit equation as the velocity of the fast variable goes to infinity is obtained via a pde approache and by means of the tools of the control theory

convexity in hamilton jacobi theory i dynamics and duality value functions propagated from initial or terminal costs and constraints by way of a differential inclusion or more broadly through a lagrangian that may take on infty are studied in the case where convexity persists in the state argument such value functions themselves taking on infty are shown to satisfy a subgradient form of the hamilton jacobi equation which strongly supports properties of local lipschitz continuity semidifferentiability and clarke regularity an extended method of characteristics is developed which determines them from the hamiltonian dynamics underlying the given lagrangian close relations with a dual value function are revealed

hamilton jacobi bellman equation under states constraints abstract this paper is devoted to the uniqueness of discontinuous solutions to the hamilton jacobi bellman hjb equation arising in mayer s problem under state constraints we use two types of discontinuous solutions bilateral solution and contingent solution and show that they coincide with the value function for state constraints that are backward invariant and forward viable

a garside theoretic approach to the reducibility problem in braid groups abstract let d n denote the n punctured disk in the complex plane where the punctures are on the real axis an n braid is said to be reducible if there exists an essential curve system c in d n called a reduction system of such that c c where c denotes the action of the braid on the curve system c a curve system c in d n is said to be standard if each of its components is isotopic to a round circle centered at the real axis in this paper we study the characteristics of the braids sending a curve system to a standard curve system and then the characteristics of the conjugacy classes of reducible braids for an essential curve system c in d n we define the standardizer of c as st c p b n p c is standard and show that st c is a sublattice of b n in particular there exists a unique minimal element in st c exploiting the minimal elements of standardizers together with canonical reduction systems of reducible braids we define the outermost component of reducible braids and then show that for the reducible braids whose outermost component is simpler than the whole braid including split braids each element of its ultra summit set has a standard reduction system this implies that for such braids finding a reduction system is as easy as finding a single element of the ultra summit set

lax hopf based incorporation of internal boundary conditions into hamilton jacobi equation part ii computational methods this article presents a new method for explicitly computing solutions to a hamilton jacobi partial differential equation for which initial boundary and internal conditions are prescribed as piecewise affine functions based on viability theory a lax hopf formula is used to construct analytical solutions for the individual contribution of each affine condition to the solution of the problem the results are assembled into a lax hopf algorithm which can be used to compute the solution to the partial differential equation at any arbitrary time at no other cost than evaluating a semi analytical expression numerically the method being semi analytical it performs at machine accuracy compared to the discretization error inherent to finite difference schemes the performance of the method is assessed with benchmark analytical examples the running time of the algorithm is compared with the running time of a godunov scheme

constructing and exploring wells of energy landscapes landscape paradigm is ubiquitous in physics and other natural sciences but it has to be supplemented with both quantitative and qualitatively meaningful tools for analyzing the topography of a given landscape we here consider dynamic explorations of the relief and introduce as basic topographic features wells of duration t and altitude y we determine an intrinsic exploration mechanism governing the evolutions from an initial state in the well up to its rim in a prescribed time whose finite difference approximations on finite grids yield a constructive algorithm for determining the wells our main results are thus i a quantitative characterization of landscape topography rooted in a dynamic exploration of the landscape ii an alternative to stochastic gradient dynamics for performing such an exploration iii a constructive access to the wells and iv the determination of some bare dynamic features inherent to the landscape the mathematical tools used here are not familiar in physics they co

fdtd modeling of arrays and grids of lossy conductors based on impedance sheet conditions fast finite difference time domain fdtd modeling techniques for arrays of parallel wires and wire meshes are developed the analytical basis of the models lies in the use of impedance sheet conditions kontorovich conditions for dense wire arrays and grids connecting the tangential electric fields and the averaged currents in the plane of a wire array or grid the proposed methods allow us to avoid the direct discretization of the fields inside the wires greatly simplifying the modeling task the conductor losses in the wires are accounted for assuming a strong or weak skin effect the impedance sheet conditions are formulated in the time domain using the convolution integral which is evaluated recursively in fdtd numerical examples and comparisons with analytical results are provided to verify the proposed techniques

minimum time control problems for non autonomous differential equations in this paper we investigate a minimum time problem for controlled non autonomous differential systems with dynamics depending on the final time the minimal time function associated to this problem does not satisfy the dynamic programming principle however we will prove that it is related to a standard front propagation problem via the reachability function two simple numerical examples are given to illustrate our approach

two analytic frequency dependent current density approximations for te scattering from a conducting strip grating two analytic frequency dependent current density approximations are presented for te mode incidence on a conducting strip grating the current densities are assumed to have both a spatial and a frequency dependence the first is based upon using the classic edge mode approximation the second is derived from applying conformal mapping methods and invoking babinet s theorem the solutions are compared to the moment method solution the resultant reflection coefficients are found to be good approximations at all frequencies for narrow strips and at moderately low frequencies for arbitrary strip widths although the solutions are not as accurate as a moment method solution at all frequencies they are computationally faster and provide analytic expressions that demonstrate the relationship between grating dimensions and performance

stable representation of convex hamiltonians abstract existence and uniqueness of solutions to a hamilton jacobi equation v t h t x v x 0 v 0 with h convex with respect to the last variable can be proved by associating to h either a calculus of variations or an optimal control problem the data of the new problem should be so that its hamiltonian coincides with h and should also inherit appropriate continuity local lipschitz continuity properties of h in other words h can be represented by functions describing an optimization problem in this paper we provide further developments of representation theorems from rampazzo 2005 in particular our results imply continuous dependence of representations on the mapping h we apply them to study existence of solutions to the hamilton jacobi equation with h possibly discontinuous in t

on reflecting boundary problem for optimal control this paper deals with mayer s problem for controlled systems with reflection on the boundary of a closed subset k the main result is the characterization of the possibly discontinuous value function in terms of a unique solution in a suitable sense to a partial differential equation of hamilton jacobi bellman type

invariant solutions of differential games and hamilton jacobi isaacs equations for time measurable hamiltonians we characterize invariance of time varying domains with respect to differential games with time measurable dynamics we deduce from this result a new definition of viscosity solutions to some first order hamilton jacobi equations with time measurable hamiltonians

lower semicontinuous solutions of hamilton jacobi bellman equations the value function of mayer s problem arising in optimal control is investigated and lower semicontinuous solutions of the associated hamilton jacobi bellman equation are defined in three equivalent ways under quite weak assumptions about the control system the value function is the unique solution moreover it is stable with respect to perturbations of the control system and the cost it coincides with the viscosity solution whenever it is continuous

proximal analysis and the minimal time function under general hypotheses on the target set s and the dynamics of the system we show that the minimal time function ts cdot is a proximal solution to the hamilton jacobi equation uniqueness results are obtained with two different kinds of boundary conditions a new propagation result is proven and as an application we give necessary and sufficient conditions for ts cdot to be lipschitz continuous near s a petrov type modulus condition is also shown to be sufficient for continuity of ts cdot near s

an initial condition reconstruction in hamilton jacobi equations abstract we describe the family of initial conditions for hamilton jacobi equations hje corresponding to optimal control problems that can be retrieved by solving hje backward in time

conjugate points and shocks in nonlinear optimal control in this paper the authors use the method of characteristics to extend the jacobi conjugate points theory to the bolza problem arising in nonlinear optimal control this yields necessary and sufficient optimality conditions for weak and strong local minima stated in terms of the existence of a solution to a corresponding matrix riccati differential equation the same approach allows to investigate as well smoothness of the value function

faithful representations for convex hamilton jacobi equations when a hamiltonian h h t x p is convex in the adjoint variable p the corresponding hamilton jacobi equation 0 1 ut h t x ux 0 is known to be the bellman equation of a suitable optimal control problem of course the latter is not unique so it is interesting to select a good optimal control problem among those representing 0 1 we call such a representation faithful if i it involves a dynamics which is locally lipschitz continuous in the state variable so that a unique trajectory corresponds to any given control and initial point and ii the lagrangian displays the same regularity as h in the x variable the main result of the present paper establishes the existence of faithful representations for a large class of hamiltonians including those for which the standard comparison theorems of viscosity solution theory are valid moreover our investigation includes t measurable hamiltonians as well if a faithful control theoretical representation does exist and 0 1 enjoys uniqueness properties one can infer sharp regularity results for the solution of 0 1 just by studying the regularity of the value function of the associated optimal control problem a further application consists of a simple interpretation of the front propagation phenomenon in terms of optimal trajectories of the underlying minimum problem

new frequency dependent edge mode current density approximations for tm scattering from a conducting strip grating two new frequency dependent strip grating current densities are derived for tm mode incidence on a conducting strip grating the current densities are assumed to be the product of a spatial function and a frequency function one spatial function is the traditional frequency independent edge mode current density the other is found by the use of conformal mapping the frequency function is derived by use of the radiation integral and the periodic green s function the new resultant current densities are both exact for small strip widths the conformally mapped solution is also valid for wide strips and is exact in the limit as the strip width equals the grating period although the solutions are not as accurate as the moment method at all frequencies they produce computationally faster solutions and offer further insight into strip grating behavior

power conservation in method of moments and finite element method for radiation problems conservation of energy and power can be under certain conditions exactly satisfied in an approximate numerical method in this paper necessary and sufficient conditions for this property are rigorously derived for the finite element method fem and the method of moments mom two boundary formulations of fem strong and weak and three formulations of mom mom vie mom sie for metallic and mom sie for dielectric bodies were considered for radiation problems in the frequency domain the concept of error generators fictitious generators that produce the difference between the approximate and the exact solution was introduced to state the power conservation property from another aspect it was proved that for the appropriate governing equation and the conjugated inner product power conservation is satisfied if and only if the galerkin or equivalent method is used however power conservation is corrupted if an equivalence principle surface or volume is utilized in mom to solve problems in inhomogeneous media examples are given to illustrate the power conservation and its possible advantages

viscosity solutions for partial differential equations with neumann type boundary conditions and some aspects of aubry mather theory we study partial differential inequalities pdi of the type c h x v x nk x 0 where nk is the normal cone to the set k we prove existence of a constant c c such that the pdi of hamilton jacobi type has a unique global lipschitz viscosity solution we provide a formula to calculate this constant moreover we define a subset k of k such that any two solutions of the previous pdi which coincide on k will coincide on k our paper generalizes results of the case without boundary conditions for convex hamiltonians obtained by l c evans and a fathi

value functions for differential games and control systems with discontinuous terminal cost this paper deals with mayer s problem for control systems and differential games with discontinuous terminal cost there are two main results in the paper the first one says that the value function for control systems can be characterized as the unique solution in suitable sense to the hamilton jacobi bellman equation without any regularity assumptions on the terminal cost for differential games satisfying isaacs s minmax condition the second main result says that the value function is the unique solution to the hamilton jacobi isaacs equation when the terminal cost is semicontinuous this allows to prove the existence of the value under isaacs s condition this paper extends some results already well known in the continuous case

semicontinuous solutions of hamilton jacobi bellman equations with degenerate state constraints abstract in this paper the value function of a bolza optimal control problem with state constraints is characterized as the unique lower semicontinuous solution of a hamilton jacobi equation the state constraints are given by an arbitrary closed set with possibly empty interior in particular soner s inward pointing condition is extended here to the case of degenerate state constraints

higher order impedance boundary conditions for sparse wire grids higher order impedance boundary conditions designed for modeling wire grids of thin conducting wires are established the derivation is based on the exact analytical summation of the individual wire fields this allows one to write an approximate boundary condition on the grid surface which connects the averaged electric field and the averaged current or the electric field and the averaged magnetic fields on the two sides of the grid surface the condition depends on the tangential derivatives of the averaged current up to the sixth order this approach provides an extension of the averaged boundary conditions method well established for dense grids to sparse grids numerical examples demonstrate very good accuracy of the solutions for the field reflected from grids with the wire separation as large as half of the wavelength

averaging method for discontinuous mayer s problem of singularly perturbed control systems abstract in the present paper we prove that the optimal cost of a mayer s problem for a control system with singular perturbation does converge to the optimal cost of a mayer s problem associated with control system obtained by averaging the main novelty of our result lies on the fact that we did not require any continuity assumption on the final cost

reflected differential games this paper concerns the existence of a possible discontinuous value for a zero sum two player reflected differential game under isaacs condition we characterize the value function as the unique solution in a suitable sense to a variational inequality namely the hamilton jacobi isaacs differential inclusion

stochastic verification theorems within the framework of viscosity solutions this paper studies controlled systems governed by ito s stochastic differential equations in which control variables are allowed to enter both drift and diffusion terms a new verification theorem is derived within the framework of viscosity solutions without involving any derivatives of the value functions this theorem is shown to have wider applicability than the restrictive classical verification theorems which require the associated dynamic programming equations to have smooth solutions based on the new verification result optimal stochastic feedback controls are obtained by maximizing the generalized hamiltonians over both the control regions and the superdifferentials of the value functions

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control

boundary value problems for systems of hamilton jacobi bellman inclusions with constraints we study in this paper boundary value problems for systems of hamilton jacobi bellman first order partial differential equations and variational inequalities the solutions of which are constrained to obey viability constraints they are motivated by some control problems such as impulse control and financial mathematics we shall prove the existence and uniqueness of such solutions in the class of closed set valued maps by giving a precise meaning to what a solution means in this case we shall also provide explicit formulas for this problem when we deal with hamilton jacobi bellman equations we obtain the existence and uniqueness of frankowska contingent episolutions we shall deduce these results from the fact that the graph of the solution is the viable capture basin of the graph of the boundary conditions under an auxiliary system and then from their properties and their characterizations proved in j p aubin siam j control optim 40 2001 pp 853 881