traffic congestion control for aw rascle zhang model this paper develops boundary feedback control laws to reduce stop and go oscillations in congested traffic the macroscopic traffic dynamics are governed by aw rascle zhang arz model consisting of second order nonlinear partial differential equations pdes a criterion to distinguish free and congested regimes for the arz traffic model leads to the study of hetero directional hyperbolic pde model of congested traffic regime to stabilize the oscillations of traffic density and speed in a freeway segment a boundary input through ramp metering is considered we discuss the stabilization problem for freeway segments respectively upstream and downstream of the ramp for the more challenging upstream control problem our full state feedback control law employs a backstepping transformation both collocated and anti collocated boundary observers are designed the exponential stability in l2 sense and finite time convergence to equilibrium are achieved and validated with simulation in the absence of relaxation time and boundary parameters knowledge we propose adaptive output feedback control design control is applied at outlet and the measurement is taken from inlet of the freeway segment we use the backstepping method to obtain an observer canonical form in which unknown parameters multiply with measured output a parametric model based on this form is derived and gradient based parameter estimators are designed an explicit state observer involving the delayed values of the input and the output is introduced for state estimation using the parameter and state estimates we develop an adaptive output feedback control law which achieves convergence to the steady regulation in the l2 sense

feedback boundary control of linear hyperbolic systems with relaxation we consider boundary stabilization for one dimensional systems of linear hyperbolic partial differential equations with relaxation structure such equations appear in many applications by combining weighted lyapunov functions the structure is used to derive new stabilization results the result is illustrated with an application to boundary stabilization of water flows in open canals

singular perturbations of first order hyperbolic systems with stiff source terms abstract this work develops a singular perturbation theory for initial value problems of nonlinear first order hyperbolic systems with stiff source terms in several space variables it is observed that under reasonable assumptions many equations of classical physics of that type admit a structural stability condition this condition is equivalent to the well known subcharacteristic condition for one dimensional 2 2 systems and the well known time like condition for one dimensional scalar second order hyperbolic equations with a small positive parameter multiplying the highest derivatives under this stability condition we construct formal asymptotic approximations of the initial layer solution to the nonlinear problem furthermore assuming some regularity of the solutions to the limiting inner problem and the reduced problem we prove the existence of classical solutions in the uniform time interval where the reduced problem has a smooth solution and justify the validity of the formal approximations in any fixed compact subset of the uniform time interval the stability condition seems to be a key to problems of this kind and can be easily verified moreover this presentation unifies and improves earlier works for some specific equations

infinite horizon optimization we consider the general problem of choosing a discounted cost minimizing infinite sequence of decisions from a closed subset of the product space formed by a sequence of arbitrary compact metric spaces examples include equipment replacement production planning and more generally infinite stage mathematical programs it is shown that the optimal costs for finite horizon approximating problems converge to the optimal infinite horizon cost as the horizons diverge to infinity moreover the existence of a unique algorithmically optimal i e accumulation point solution is shown to be a necessary and sufficient condition for convergence in the product topology i e policy convergence of all finite horizon optima under the weaker condition of hausdorff convergence of the sets of finite horizon optima to the set of infinite horizon optima we show how to force policy convergence through a natural tie breaking rule finally a forward algorithm is presented which in the presence of a unique infinite horizon optimum is guaranteed to converge

finite dimensional approximation in infinite dimensional mathematical programming we consider the problem of approximating an optimal solution to a separable doubly infinite mathematical program p with lower staircase structure by solutions to the programs p n obtained by truncating after the first n variables and n constraints of p viewing the surplus vector variable associated with the nth constraint as a state and assuming that all feasible states are eventually reachable from any feasible state we show that the efficient set of all solutions optimal to all possible feasible surplus states for p n converges to the set of optimal solutions to p a tie breaking algorithm which selects a nearest point efficient solution for p n is shown for convex programs to converge to an optimal solution to p a stopping rule is provided for discovering a value of n sufficiently large to guarantee any prespecified level of accuracy the theory is illustrated by an application to production planning

singular perturbation approximation of linear hyperbolic systems of balance laws this technical note deals with a class of linear hyperbolic systems of balance laws with multiple time scales the scale of time constants is modeled by a perturbation parameter this parameter is introduced in both dynamics and boundary conditions the solution of the full system is approximated by that of the reduced subsystem when the perturbation parameter is small enough lyapunov technique is used to prove it the main result is illustrated by an academic example moreover the boundary control synthesis to a gas flow transport model is shown based on singular perturbation approach

adaptive output feedback stabilization of non local hyperbolic pdes we address the problem of adaptive output feedback stabilization of general first order hyperbolic partial integro differential equations pide such systems are also referred to as pdes with non local in space terms we apply control at one boundary take measurements on the other boundary and allow the system s functional coefficients to be unknown to deal with the absence of both full state measurement and parameter knowledge we introduce a pre transformation which happens to be based on backstepping of the system into an observer canonical form in that form the problem of adaptive observer design becomes tractable both the parameter estimator and the control law employ only the input and output signals and their histories over one unit of time prior to presenting the adaptive design we present the non adaptive baseline controller which is novel in its own right and facilitates the understanding of the more complex adaptive system the parameter estimator is of the gradient type based on a parametric model in the form of an integral equation relating delayed values of the input and output for the closed loop system we establish boundedness of all signals pointwise in space and time and convergence of the pde state to zero pointwise in space we illustrate our result with a simulation

feedback boundary control of linear hyperbolic equations with stiff source term abstractwe consider feedback boundary control of hyperbolic systems with stiff source terms by combining weighted lyapunov functions the structure is used to derive stabilisation results in our analysis we give stabilising feedback laws that allow a robust uniform exponential stabilisation for a whole range of values of an uncertain parameter with a decay rate that is independent of the parameter in particular we are interested in the limit case when the relaxation parameter approaches zero the result is illustrated with the numerical analysis on the decay rate of the lyapunov function in terms of the stiff parameter and an application to boundary stabilisation of gas dynamics in pipes

brief paper boundary control with integral action for hyperbolic systems of conservation laws stability and experiments a strict lyapunov function for boundary control with integral actions of hyperbolic systems of conservation laws that can be diagonalised with riemann invariants is presented the time derivative of this lyapunov function can be made strictly negative definite by an appropriate choice of the boundary conditions and the integral control gains previous stability results are extended to guarantee the local convergence of the state towards a desired set point furthermore the control can be implemented as a feedback of the state measured only at the boundaries the control design method is illustrated with a hydraulic application namely the level and flow regulation in a reach of the sambre river and in the micro channel of valence respectively through simulations and experimentations

output regulation for general linear heterodirectional hyperbolic systems with spatially varying coefficients abstract this article presents a backstepping solution to the output regulation problem for general linear heterodirectional hyperbolic systems with spatially varying coefficients the disturbances can act at both boundaries distributed in domain or at the output to be controlled the latter is defined at a boundary distributed or pointwise in domain and has not to be available for measurement by utilizing backstepping coordinates it is shown that all design equations are explicitly solvable this allows a simple determination of a state feedback regulator that is implemented by a reference and a disturbance observer furthermore an easy evaluation of the existence conditions for the resulting output feedback regulator is possible in terms of the plant transfer behaviour in order to facilitate the parameterization of the regulator the resulting closed loop dynamics is directly related to the design parameters the proposed backstepping based design of the output feedback regulator is demonstrated for an unstable heterodirectional 4 4 hyperbolic system

pi boundary control of linear hyperbolic balance laws with stabilization of arz traffic flow models abstract this paper investigates the proportional integral pi boundary feedback control for the linear hyperbolic systems of balance laws which control and output measures are located at the boundaries we address the issue of feedback stabilization by means of pi boundary controllers by constructing a new weighted lyapunov function the sufficient conditions in terms of matrix inequalities are developed for the exponential stability of closed loop systems these results are illustrated by the linearized aw rascle zhang arz traffic flow model we design a pi boundary controller to stabilize the oscillations of the traffic parameters of a freeway segment and evaluate the performance with numerical simulations

solution and forecast horizons for infinite horizon nonhomogeneous markov decision processes we consider a nonhomogeneous infinite horizon markov decision process mdp problem with multiple optimal first period policies we seek an algorithm that given finite data delivers an optimal first period policy such an algorithm can thus recursively generate within a rolling horizon procedure an infinite horizon optimal solution to the original problem however it can happen that no such algorithm exists i e the mdp is not well posed equivalently it is impossible to solve the problem with a finite amount of data assuming increasing marginal returns in actions with respect to states and stochastically increasing state transitions with respect to actions we provide an algorithm that is guaranteed to solve the given mdp whenever it is well posed this algorithm determines in finite time a forecast horizon for which an optimal solution delivers an optimal first period policy as an application we solve all well posed instances of the time varying version of the classic asset selling problem

boundary control of coupled reaction advection diffusion systems with spatially varying coefficients recently the problem of boundary stabilization for unstable linear constant coefficient coupled reaction diffusion systems was solved by means of the backstepping method the extension of this result to systems with advection terms and spatially varying coefficients is challenging due to complex boundary conditions that appear in the equations verified by the control kernels in this technical note we address this issue by showing that these equations are essentially equivalent to those verified by the control kernels for first order hyperbolic coupled systems which were recently found to be well posed the result therefore applies in this case allowing us to prove h 1 stability for the closed loop system it also unveils a previously unknown connection between backstepping kernels for coupled parabolic and hyperbolic problems

boundary feedback control in networks of open channels this article deals with the regulation of water flow in open channels modelled by saint venant equations by means of a riemann invariants approach we deduce stabilizing control laws for a single horizontal reach without friction the stability condition is extended to a general class of hyperbolic systems which can describe canal networks with more general topologies a control law design based on this condition is illustrated with a simple case study two reaches in cascade the proof of the main stability theorem is based on a previous result from li ta tsien concerning the existence and decay of classical solutions of hyperbolic systems

output feedback control of general linear heterodirectional hyperbolic pde ode systems with spatially varying coefficients this paper presents a backstepping solution for the output feedback control of general linear heterodirectional hyperbolic pde ode systems with spatially varying coefficients thereby the

brief paper lyapunov exponential stability of 1 d linear hyperbolic systems of balance laws explicit boundary dissipative conditions are given for the exponential stability in l 2 norm of one dimensional linear hyperbolic systems of balance laws email protected email protected email protected x 0 over a finite interval when the matrix m is marginally diagonally stable the result is illustrated with an application to boundary feedback stabilisation of open channels represented by linearised saint venant exner equations

adaptive stabilisation for a class of uncertain coupled parabolic equations adaptive stabilisation is investigated for a class of uncertain coupled parabolic equations in this paper the presence of unknown coefficients can reduce the rigorousness of system modelling and e

efficient asymptotic preserving ap schemes for some multiscale kinetic equations many kinetic models of the boltzmann equation have a diffusive scaling that leads to the navier stokes type parabolic equations as the small scaling parameter approaches zero in practical applications it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter from the rarefied kinetic regimes to the hydrodynamic diffusive regimes an earlier approach in s jin l pareschi and g toscani siam j numer anal 35 1998 pp 2405 2439 reformulates such systems into the common hyperbolic relaxation system by jin and xin for hyperbolic conservation laws used to construct the relaxation schemes and then uses a multistep time splitting method to solve the relaxation system here we observe that the combination of the two time split steps may yield hyperbolic parabolic systems that are more advantageous in both stability and efficiency for numerical computations we show that such an approach yields a class of asymptotic preserving ap schemes which are suitable for the computation of multiscale kinetic problems we use the goldstein taylor and carleman models to illustrate this approach

local exponential stabilization of fisher s equation using the backstepping technique abstract this paper deals with the boundary stabilization problem for the 1d fisher s partial differential equation pde defined on a bounded interval which is a nonlinear unstable distributed parameter system the stabilizing controller derived using the backstepping technique for linear parabolic pdes associated with fisher s pde can be extended to the nonlinear case in the work we can prove that the boundary controller based on the linear backstepping synthesis approach can make the closed loop nonlinear fisher s system exponentially stable with any desired decay rate locally in both l 2 0 1 and h 1 0 1 respectively the effectiveness of the control synthesis approach is illustrated by a numerical simulation

energy based lyapunov functions for forced hamiltonian systems with dissipation in this paper we propose a constructive procedure to modify the hamiltonian function of forced hamiltonian systems with dissipation in order to generate lyapunov functions for nonzero equilibria a key step in the procedure which is motivated from energy balance considerations standard in network modeling of physical systems is to embed the system into a larger hamiltonian system for which a series of casimir functions can be easily constructed interestingly enough for linear systems the resulting lyapunov function is the incremental energy thus our derivations provide a physical explanation to it an easily verifiable necessary and sufficient condition for the applicability of the technique in the general nonlinear case is given some examples that illustrate the method are given

backstepping boundary control for first order hyperbolic pdes and application to systems with actuator and sensor delays abstract we consider a problem of boundary feedback stabilization of first order hyperbolic partial differential equations pdes these equations serve as a model for physical phenomena such as traffic flows chemical reactors and heat exchangers we design controllers using a backstepping method which has been recently developed for parabolic pdes with the integral transformation and boundary feedback the unstable pde is converted into a delay line system which converges to zero in finite time we then apply this procedure to finite dimensional systems with actuator and sensor delays to recover a well known infinite dimensional controller analog of the smith predictor for unstable plants we also show that the proposed method can be used for the boundary control of a korteweg de vries like third order pde the designs are illustrated with simulations

compensation of wave actuator dynamics for nonlinear systems the problem of stabilization of pde ode cascades has been solved in the linear case for several pde classes whereas in the nonlinear case the problem has been solved only for the transport delay pde namely for compensation of an arbitrary delay at the input of a nonlinear plant motivated by a specific engineering application in off shore drilling we solve the problem of stabilization of the cascade of a wave pde with a general nonlinear ode due to the presence of nonlinearities of arbitrary growth and the time reversibility of the wave pde and due to the possibility of using arguments based on lyapunov functionals or explicit solutions several stability analysis approaches are possible we present stability results in the h 2 times h 1 and c 1 times c 0 norms for general nonlinear odes as well as in the h 1 times l 2 norm for linear odes we specialize our general design for wave pde ode cascades to the case of a wave pde whose uncontrolled end does not drive an ode but is instead governed by a nonlinear robin boundary condition a nonlinear spring as in the friction law in drilling this is the first global stabilization result for wave equations that incorporate non collocated destabilizing nonlinearities of superlinear growth we present two numerical examples one with a nonlinear ode and one with a nonlinear spring at the uncontrolled boundary of the wave pde

a stochastic programming approach for planning horizons of infinite horizon capacity planning problems planning horizon is a key issue in production planning different from previous approaches based on markov decision processes we study the planning horizon of capacity planning problems within the framework of stochastic programming we first consider an infinite horizon stochastic capacity planning model involving a single resource linear cost structure and discrete distributions for general stochastic cost and demand data non markovian and non stationary we give sufficient conditions for the existence of an optimal solution furthermore we study the monotonicity property of the finite horizon approximation of the original problem we show that the optimal objective value and solution of the finite horizon approximation problem will converge to the optimal objective value and solution of the infinite horizon problem when the time horizon goes to infinity these convergence results together with the integrality of decision variables imply the existence of a planning horizon we also develop a useful formula to calculate an upper bound on the planning horizon then by decomposition we show the existence of a planning horizon for a class of very general stochastic capacity planning problems which have complicated decision structure

backstepping based boundary observer for a class of time varying linear hyperbolic pides in this paper a luenberger type boundary observer is presented for a class of distributed parameter systems described by time varying linear hyperbolic partial integro differential equations first known limitations due to the minimum observation time for simple transport equations are restated for the considered class of systems then the backstepping method is applied to determine the unknown observer gain term by avoiding the framework of gevrey functions which is typically used for the time varying case it is shown that the backstepping method can be employed without severe limitations on the regularity of the time varying terms a modification of the underlying volterra transformation ensures that the observer error dynamics is equivalent to the behavior of a predefined exponentially stable target system the magnitude of the observer gain term can be traded for lower decay rates of the observer error after the theoretic results have been proven the effectiveness of the proposed design is demonstrated by simulation examples

solving nonstationary infinite horizon dynamic optimization problems monotonicity of optimal solutions to finite horizon dynamic optimization problems is used to prove the existence of a forecast horizon i e a long enough planning horizon that ensures that a first period optimal action for the infinite horizon and the finite horizon problem agree regardless of problem parameter changes in the tail the existence of extremal monotone optimal solutions motivates a stopping rule that is ensured to detect the minimal forecast horizon to be used in a rolling horizon procedure to exactly solve the problem

controllability for a scalar conservation law with nonlocal velocity abstract in this paper we study the state controllability and nodal profile controllability for a scalar conservation law with a nonlocal velocity that models a highly re entrant manufacturing system as encountered in semi conductor production we first prove a local state controllability result i e there exists a control that drives the solution from any given initial data to any desired final data in a certain time period provided that the initial and final data are both close to a given equilibrium 0 we also obtain a global state controllability result for the same system where there is no limitation on the distance between the initial and final data finally we prove a nodal profile controllability result i e there exists a control under which the solution starts from any initial data reaches exactly any given out flux over a fixed time period

null controllability and finite time stabilization for the heat equations with variable coefficients in space in one dimension via backstepping approach using the backstepping approach we recover the null controllability for the heat equations with variable coefficients in space in one dimension and prove that these equations can be stabilized in finite time by means of periodic time varying feedback laws to this end on the one hand we provide a new proof of the well posedness and the optimal bound with respect to damping constants for the solutions of the kernel equations this allows one to deal with variable coefficients even with a weak regularity of these coefficients on the other hand we establish the well posedness and estimates for the heat equations with a nonlocal boundary condition at one side

an interesting class of partial differential equations this paper presents an observation that under reasonable conditions many partial differential equations from mathematical physics possess three structural properties one of them can be understand as a variant of the celebrated onsager reciprocal relation in modern thermodynamics it displays a direct relation of irreversible processes to the entropy change we show that the properties imply various entropy dissipation conditions for hyperbolic relaxation problems as an application of the observation we propose an approximation method to solve relaxation problems moreover the observation is interpreted physically and verified with eight sets of systems from different fields

control of homodirectional and general heterodirectional linear coupled hyperbolic pdes research on stabilization of coupled hyperbolic pdes has been dominated by the focus on pairs of counter convecting heterodirectional transport pdes with distributed local coupling and with controls at one or both boundaries a recent extension allows stabilization using only one control for a system containing an arbitrary number of coupled transport pdes that convect at different speeds against the direction of the pde whose boundary is actuated in this paper we present a solution to the fully general case in which the number of pdes in either direction is arbitrary and where actuation is applied on only one boundary to all the pdes that convect downstream from that boundary to solve this general problem we solve as a special case the problem of control of coupled homodirectional hyperbolic linear pdes where multiple transport pdes convect in the same direction with arbitrary local coupling our approach is based on pde backstepping and yields solutions to stabilization by both full state and observer based output feedback and trajectory tracking problems

a quadratic lyapunov function for saint venant equations with arbitrary friction and space varying slope the exponential stability problem of the nonlinear saint venant equations is addressed in this paper we consider the general case where an arbitrary friction and space varying slope are both included in the system which lead to non uniform steady states an explicit quadratic lyapunov function as a weighted function of a small perturbation of the steady states is constructed then we show that by a suitable choice of boundary feedback controls that we give explicitly the local exponential stability of the nonlinear saint venant equations for the h 2 norm is guaranteed

boundary stabilization of hyperbolic balance laws with characteristic boundaries abstract this article is concerned with boundary stabilization of one dimensional linear hyperbolic systems with characteristic boundaries we assume that the systems satisfy a physically relevant structural stability condition for hyperbolic relaxation problems which describe various non equilibrium phenomena by introducing new and simple lyapunov functions the structural stability condition is used to derive stabilization results for problems with characteristic boundaries the result is illustrated with an application to the transport of neurofilaments in axons a phenomenon studied in neuroscience

stabilization of a system of n 1 coupled first order hyperbolic linear pdes with a single boundary input we solve the problem of stabilization of a class of linear first order hyperbolic systems featuring n rightward convecting transport pdes and one leftward convecting transport pde we design a controller which requires a single control input applied on the leftward convecting pde s right boundary and an observer which employs a single sensor on the same pde s left boundary we prove exponential stability of the origin of the resulting plant observer controller system in the spatial l2 sense

state and observer based feedback control of normal flow equations abstract we investigate wellposedness and stability of normal flow equations with two different control schemes the first one considers the velocity field as a control action and relies on a proportional regulator that is proved to be stable in the second one control acts on the source term and is based on an observer providing an estimate of the gradient of the normal flow solution convergence properties are demonstrated in this case numerical results are presented to show the effectiveness of the proposed approaches

on the modelling and stabilization of flows in networks of open canals in this paper we present a model for the controlled flow of a fluid through a network of canals using a coupled system of st venant equations we then generalize in a variety of ways recent results of coron d andrea novel and bastin concerning the stabilizability around equilibrium of the flow through a single channel this work is based on the theory of quasilinear hyperbolic systems and in particular on a delicate result of li ta tsien concerning the existence and decay of global classical solutions

monotone comparative statics the authors derive a necessary and sufficient condition for the solution set of an optimization problem to be monotonic in the parameters of the problem in addition they develop practical methods for checking the condition and demonstrate its applications to the classical theories of the competitive firm the monopolist the bertrand oligopolist consumer and growth theory game theory and general equilibrium analysis copyright 1994 by the econometric society

harmonic maps between surfaces and teichmuller spaces we study harmonic maps between two distinct compact riemann surfaces of the same genus our aim is to examine the role of the curvature in the relationship between energies of harmonic maps and conformal metrics on the target surface we consider the energy of the energy minimizing map between the surfaces as a function of the metrics within the conformal class of the target and solve the variational problem of minimizing this functional when we restrict the upper curvature bound and normalize the area of the metrics in doing so we show that the upper curvature bound on the normalized target metric is an obstruction in obtaining a degree 1 conformal harmonic map between distinct riemann surfaces

backstepping stabilization of a linearized ode pde rijke tube model abstract the problem of boundary stabilization of thermoacoustic oscillations in the rijke tube is investigated using the backstepping method as a first step this work only considers the full state design this system consists of a vertical tube open at both ends and a heater placed in the lower half of the tube to study this problem we consider that the mathematical model takes the form of 2 2 linear first order hyperbolic partial differential equations pdes with a point source term induced by the dirac delta distribution on the right hand side plus the coupling of an ordinary differential equation ode and control input at one boundary condition the presence of the dirac delta distribution implies that the system solution has a discontinuity on a point of the domain but is continuous everywhere else we use a coordinate transformation to rewrite the equations into a system of four transport pdes convecting in opposite directions and to translate the discontinuity to the boundary conditions then a full state feedback backstepping controller is designed to exponentially stabilize the origin however the model is non strict feedback making unfeasible the use of standard backstepping designs this issue is tackled by formulating a well posed and invertible integral transformation with volterra and fredholm terms that maps the rijke system into a target system with desirable stability properties an exact piecewise differentiable expression for the kernels of this transformation is found allowing us in turn to derive an explicit feedback control law simulation results are presented to illustrate the effectiveness of the proposed control design

a shadow simplex method for infinite linear programs we present a simplex type algorithm that is an algorithm that moves from one extreme point of the infinite dimensional feasible region to another not necessarily adjacent extreme point for solving a class of linear programs with countably infinite variables and constraints each iteration of this method can be implemented in finite time whereas the solution values converge to the optimal value as the number of iterations increases this simplex type algorithm moves to an adjacent extreme point and hence reduces to a true infinite dimensional simplex method for the important special cases of nonstationary infinite horizon deterministic and stochastic dynamic programs

local exponential h2 stabilization of 2x2 quasilinear hyperbolic systems using backstepping in this work we consider the problem of boundary stabilization for a quasilinear 2 times2 system of first order hyperbolic pdes we design a new full state feedback control law with actuation on only one end of the domain which achieves h 2 exponential stability of the closed loop system our proof uses a backstepping transformation to find new variables for which a strict lyapunov function can be constructed the kernels of the transformation are found to verify a goursat type 4 times4 system of first order hyperbolic pdes whose well posedness is shown using the method of characteristics and successive approximations once the kernels are computed the stabilizing feedback law can be explicitly constructed from them

a linear programming approach to nonstationary infinite horizon markov decision processes nonstationary infinite horizon markov decision processes mdps generalize the most well studied class of sequential decision models in operations research namely that of stationary mdps by relaxing the restrictive assumption that problem data do not change over time linear programming lp has been very successful in obtaining structural insights and devising solution methods for stationary mdps however an lp approach for nonstationary mdps is currently missing this is because the lp formulation of a nonstationary infinite horizon mdp includes countably infinite variables and constraints and research on such infinite dimensional lps has traditionally faced several hurdles for instance duality results may not hold an extreme point may not be a basic feasible solution and in the context of a simplex algorithm a pivot operation may require infinite data and computations and a sequence of improving extreme points need not converge in value to optimal in this paper we tackle these challenges a

marcum q functions and explicit kernels for stabilization of 2 2 linear hyperbolic systems with constant coefficients abstract we find the exact analytical solution to a goursat pde system governing the kernels of a backstepping based boundary control law that stabilizes a constant coefficient 2 2 system of first order hyperbolic linear pdes the solution to the goursat system is related to the solution of a simpler explicitly solvable goursat system through a suitable infinite series of powers of partial derivatives which is summed explicitly in terms of special functions including bessel functions and the generalized marcum q functions of the first order the marcum functions are common in certain applications in communications but have not appeared previously in control design problems the dependence of the explicit solutions with respect to system parameters is analyzed through several examples including the stabilization of a constant equilibrium for a quasi linear plant

sampled data boundary feedback control of 1 d linear transport pdes with non local terms abstract the paper provides results for the application of boundary feedback control with zero order hold zoh to 1 d inhomogeneous linear transport partial differential equations on bounded domains with constant velocity and non local terms it is shown that the emulation design based on the recently proposed continuous time boundary feedback designed by means of backstepping guarantees closed loop exponential stability provided that the sampling period is sufficiently small it is also shown that contrary to the parabolic case a smaller sampling period implies a faster convergence rate with no upper bound for the achieved convergence rate the obtained results provide stability estimates for the sup norm of the state and robustness with respect to perturbations of the sampling schedule is guaranteed

exponential stability of switched linear hyperbolic initial boundary value problems we consider the initial boundary value problem governed by systems of linear hyperbolic partial differential equations in the canonical diagonal form and study conditions for exponential stability when the system discontinuously switches between a finite set of modes the switching system is fairly general in that the system matrix functions as well as the boundary conditions may switch in time we show how the stability mechanism developed for classical solutions of hyperbolic initial boundary value problems can be generalized to the case in which weaker solutions become necessary due to arbitrary switching we also provide an explicit dwell time bound for guaranteeing exponential stability of the switching system when for each mode the system is exponentially stable our stability conditions only depend on the system parameters and boundary data these conditions easily generalize to switching systems in the nondiagonal form under a simple commutativity assumption we present tutorial examples to illustrate the instabilities that can result from switching

concepts of forecast and decision horizons applications to dynamic stochastic optimization problems in this paper we develop a rigorous new framework for the concepts of forecast and decision horizons these concepts are conditional in nature and in turn enable us to unify the existing concepts of strong and weak horizons moreover we are able to precisely state the questions of existence of forecast decision horizons finally we are able to further develop the theory of existence of forecast decision horizons in the discounted case and procedures to compute these horizons

on the weil petersson metric on teichmuller space teichmuller space for a compact oriented surface m without boundary is described as the quotient ji b0 where s is the space of almost complex structures on m compatible with a given orientation and 8 0 are those c diffeomorphisms homotopic to the identity there is a natural 3 0 invariant l2 riemannian structure on si which induces a riemannian structure on si 3 n infinitesimally this is the bilinear pairing suggested by andre weil the weil petersson riemannian struc ture the structure is shown to be kahler with respect to a naturally induced complex structure on s0