stochastic system controller synthesis for reachability specifications encoded by random sets we consider a reach avoid specification for a stochastic hybrid dynamical system defined as reaching a goal set at some finite time while avoiding an unsafe set at all previous times in contrast with earlier works which consider the target and avoid sets as deterministic we consider these sets to be probabilistic an optimal control policy is derived which maximizes the reach avoid probability special structure on the stochastic sets is exploited to make the computation tractable for large space dimensions

linear codes with covering radius 2 and other new covering codes infinite families of linear binary codes with covering radius r 2 and minimum distance d 3 and d 4 are given using the constructed codes with d 3 r 2 families of covering codes with r 2 are obtained the parameters of many constructed codes with r

control synthesis for stochastic systems given automata specifications defined by stochastic sets abstract the problem of control synthesis to maximize the probability of satisfying automata specifications for systems with uncertainty is addressed two types of uncertainty are considered stochasticity in the dynamical system and in the sets defining the specifications we model the uncertain dynamical sets as stochastic set processes we show that the optimal control policy can be computed by solving a reachability problem for a hybrid stochastic system which evolves on product state spaces of the automaton stochastic sets and the dynamical system we derive an approximation to the stochastic set processes to alleviate the complexity of reachability computation a case study illustrates the framework and the solution approach

global regularity and formation of singularities of solutions to first order quasilinear hyperbolic systems for the cauchy problem for strictly hyperbolic systems with general eigenvalues we obtain existence of global smooth solutions under certain conditions on the composition of the eigenvalues and the initial data on the other hand we give a sufficient condition which guarantees that singularities of the solution must occur in a finite time and describe certain applications the present paper includes the corresponding results in earlier papers by several authors as special cases

blow up of periodic solutions to linearly degenerate quasilinear hyperbolic systems an example is given to show that for the cauchy problem of n n homogeneous linearly degenerate quasilinear hyperbolic systems with periodic initial data when n 2 c1 solutions may blow up in a finite time no matter how small and smooth the initial data are

further results on k t subnormal covering codes the concept of k t subnormal covering codes is discussed generalizing some of the earlier results in a similar way k t normal covering codes are defined using the results including some new constructions upper bounds for covering codes are improved it is shown how simulated annealing can be used to find acceptable partitions for codes

blow up of solutions to the initial boundary value problem for quasilinear hyperbolic systems of conservation laws abstract this work is a continuation of our previous work z q shao d x kong y c li shock reflection for general quasilinear hyperbolic systems of conservation laws nonlinear anal 66 1 2007 93 124 in the present paper we study the global structure instability of the self similar solution u u x t containing shocks contact discontinuities and at least one rarefaction wave of the initial boundary riemann problem for general n n quasilinear hyperbolic systems of conservation laws on the quarter plane t x t 0 x 0 we prove the nonexistence of global piecewise c 1 solution to a class of the mixed initial boundary value problem for general n n quasilinear hyperbolic systems of conservation laws on the quarter plane t x t 0 x 0 our result indicates that the kind of riemann solution u u x t mentioned above is globally structurally unstable as an application of our result we consider the model proposed by aw and rascle a aw m rascle resurrection of second order models of traffic flow siam j appl math 60 2000 916 938 describing traffic flow on a road network following the work of garavello and piccoli m garavello b piccoli traffic flow on a road network using the aw rascle model comm partial differential equations 31 2 2006 243 275 we prove the nonexistence of global piecewise c 1 solution containing one rarefaction wave of the initial boundary value problem for this model

formation of singularities for certain hyperbolic systems in one space dimension we study the development of singularities of classical solutions of quasilinear strictly hyperbolic systems in one space dimension the systems are supposed to be in the diagonal form but we do not impose restrictions on the size of the initial data and in some cases we can replace the genuine nonlinearity by weaker conditions

short codes with a given covering radius the covering radius r of a code is the maximum distance from any vector in the space containing the code to the nearest codeword the authors introduce a new function l m r called the length function which equals the smallest length of a binary code of codimension m and covering radius r they investigate basic properties of the length function projective geometries over larger fields are used to construct families of codes which improve significantly the upper bound for l m 2 obtained by amalgamation of hamming codes general methods are developed for ruling out the existence of codes of covering radius 2 with a given codimension and length resulting in lower bounds for l m 2 a table is presented which gives the best results now known for l m r with m

on the breakdown of solutions to n n quasilinear hyperbolic systems we shall be concerned with the development of singularities of the c1 solutions of the quasilinear n n hyperbolic system ut a u ux 0 in one space dimension generalizing a nonlinearity condition introduced by maccamy and mizel arch rat mech anal 25 1967 299 320 in this paper we prove some results of blow up for the first order derivatives without restrictions on the size of the initial data

constructions of nonlinear covering codes constructions of nonlinear covering codes are given using any nonlinear starting code of covering radius r spl ges 2 these constructions form an infinite family of codes with the same covering radius a nonlinear code is treated as a union of cosets of a linear code new infinite families of nonlinear covering codes are obtained concepts of r l objects r l partitions and r l length are described for nonlinear codes

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

analysis of singularities for one dimensional quasilinear hyperbolic systems using the method of new characteristic coordinates and the singularity theory of smooth mappings in this paper we analyze the long time behavior of smooth solutions for one dimensional quasilinear hyperbolic systems give a complete description of the solutions close to blow up points and provide some sharp estimates on the blow up rate of singularities

singularities of solutions for first order quasilinear hyperbolic systems in this paper the existence of global smooth solutions and the formation of singularities of solutions for strictly hyperbolic systems with general eigenvalues are discussed for the cauchy problem with essentially periodic small initial data or nonperiodic initial data a result of klainerman and majda is thus extended to the general case

blow up of periodic solutions to reducible quasilinear hyperbolic systems under general assumption we prove that the smooth solution to reducible quasilinear hyperbolic system with periodic initial data in general develop singularities in finite time provided that the total variation on one period of the initial data is small

global entropy solutions to weakly nonlinear gas dynamics abstract entropy weak solutions with bounded periodic initial data are considered for the system of weakly nonlinear gas dynamics through a modified glimm scheme an approximate solution sequence is constructed and then a priori estimates are provided with the methods of approximate characteristics and approximate conservation laws which gives not only the existence and uniqueness but also the uniform total variation bounds for the entropy solutions

verification of discrete time stochastic hybrid systems a stochastic reach avoid decision problem we present a dynamic programming based solution to a probabilistic reach avoid problem for a controlled discrete time stochastic hybrid system we address two distinct interpretations of the reach avoid problem via stochastic optimal control in the first case a sum multiplicative cost function is introduced along with a corresponding dynamic recursion which quantifies the probability of hitting a target set at some point during a finite time horizon while avoiding an unsafe set during each time step preceding the target hitting time in the second case we introduce a multiplicative cost function and a dynamic recursion which quantifies the probability of hitting a target set at the terminal time while avoiding an unsafe set during the preceding time steps in each case optimal reach while avoid control policies are derived as the solution to an optimal control problem via dynamic programming computational examples motivated by two practical problems in the management of fisheries and finance are provided

probabilistic reachability and safety for controlled discrete time stochastic hybrid systems in this work probabilistic reachability over a finite horizon is investigated for a class of discrete time stochastic hybrid systems with control inputs a suitable embedding of the reachability problem in a stochastic control framework reveals that it is amenable to two complementary interpretations leading to dual algorithms for reachability computations in particular the set of initial conditions providing a certain probabilistic guarantee that the system will keep evolving within a desired safe region of the state space is characterized in terms of a value function and maximally safe markov policies are determined via dynamic programming these results are of interest not only for safety analysis and design but also for solving those regulation and stabilization problems that can be reinterpreted as safety problems the temperature regulation problem presented in the paper as a case study is one such case

global structure instability of riemann solutions for general quasilinear hyperbolic systems of conservation laws in the presence of a boundary abstract this work is a continuation of our previous work z q shao d x kong y c li shock reflection for general quasilinear hyperbolic systems of conservation laws nonlinear anal tma 66 1 2007 93 124 in this paper we study the global structure instability of the riemann solution u u x t containing shocks at least one rarefaction wave for general n n quasilinear hyperbolic systems of conservation laws in the presence of a boundary we prove the nonexistence of global piecewise c 1 solution to a class of the mixed initial boundary value problem for general n n quasilinear hyperbolic systems of conservation laws on the quarter plane our result indicates that this kind of riemann solution u u x t mentioned above for general n n quasilinear hyperbolic systems of conservation laws in the presence of a boundary is globally structurally unstable some applications to quasilinear hyperbolic systems of conservation laws arising from physics and mechanics are also given

constructions and families of covering codes and saturated sets of points in projective geometry in davydov 1990 constructions of linear binary covering codes were considered in the present paper constructions and techniques of the earlier paper are developed and modified for q ary linear nonbinary covering codes q spl ges 3 and new constructions are proposed the described constructions design an infinite family of codes with covering radius r based on a starting code of the same covering radius for arbitrary r spl ges 2 q spl ges 3 new infinite families of nonbinary covering codes with good parameters are obtained with the help of an iterative process when constructed codes are the starting codes for the following steps the table of upper bounds on the length function for codes with q 3 r 2 3 and codimension up to 24 is given the author proposes to use saturated sets of points in projective geometries over finite fields as parity check matrices of starting codes new saturated sets are obtained

long time existence of entropy solutions to the one dimensional non isentropic euler equations with periodic initial data the non isentropic euler system with periodic initial data in mathbb r 1 is studied by analyzing wave interactions in a framework of specially chosen riemann invariants generalizing glimm s functionals and applying the method of approximate conservation laws and approximate characteristics an mathcal o varepsilon 2 lower bound is established for the life span of the entropy solutions with initial data that possess varepsilon variation in each period

formation of singularities in the motion of plane curves under hyperbolic mean curvature flow abstract this paper concerns the hyperbolic mean curvature flow hmcf for plane curves a quasilinear wave equation is derived and studied for the motion of plane curves under the hmcf based on this we investigate the formation of singularities in the motion of these curves in particular we prove that the motion under the hmcf of periodic plane curves with small variation on one period and small initial velocity in general blows up and singularities develop in finite time some blowup results have been obtained and the estimates on the life span of the solutions are given

a new construction for covering codes a novel method for constructing normal binary nonlinear covering codes is presented the construction improves several upper bounds on k n r the minimum cardinality of a binary code of length n and covering radius r