optimality for nonsmooth fractional multiple objective programming abstract in this study the necessary and sufficient optimality conditions for nonsmooth fractional multiple objective optimization problems are provided our idea is based on using the properties of limiting subdifferential vectors in nonsmooth analysis and a separation theorem in convex analysis

approximate abstractions of stochastic hybrid systems we present a constructive procedure for obtaining a finite approximate abstraction of a discrete time stochastic hybrid system the procedure consists of a partition of the state space of the system and depends on a controllable parameter given proper continuity assumptions on the model the approximation errors introduced by the abstraction procedure are explicitly computed and it is shown that they can be tuned through the parameter of the partition the abstraction is interpreted as a markov set chain we show that the enforcement of certain ergodic properties on the stochastic hybrid model implies the existence of a finite abstraction with finite error in time over the concrete model and allows introducing a finite time algorithm that computes the abstraction

multiple symbol differential detection with interference suppression a multiple symbol differential detector is formulated for m ary differential phase shift keying modulation where the channel state information is unknown to the receiver the maximum likelihood decision statistic is derived for the detector and its performance is demonstrated by analysis and simulation under the gaussian assumption for the aggregate interference plus noise an exact expression for the symbol pairwise error probability is developed for m ary differential phase shift keying modulation over a diversity slow fading rayleigh channel in the presence of an interference source a simpler expression of the pairwise error probability is developed for the asymptotic case of large signal to noise ratio and small signal to interference ratio it is shown that with an increasing observation interval the performance of the differential detector over an unknown channel approaches that of optimum combining with known channel

on sufficiency and duality for generalized quasiconvex programs abstract for a nonlinear programming problem under differentiability assumptions fritz john suffcient optimality conditions are stated also some duality theorems are proved for mond weir type duals all results are given under generalized convexity assumptions

error performance of multiple symbol differential detection of psk signals transmitted over correlated rayleigh fading channels the error performance of multiple symbol differential detection of uncoded qpsk signals transmitted over correlated rayleigh fading channels is studied the optimal detector is presented along with an exact expression for the corresponding pairwise error event probability it is shown that multiple symbol differential detection is a very effective strategy for eliminating the irreducible error floor associated with a conventional differential detector in all of the cases investigated a detector with an observation interval as small as two symbols is sufficient for this purpose it is also found that the error performance of a multiple symbol differential detector is not sensitive to the mismatch between the decoding metric and the channel fading statistics

optimality and invexity in optimization problems in banach algebras spaces abstract in this paper we introduce into nonsmooth optimization theory in banach algebras a new class of mathematical programming problems which generalizes the notion of smooth kt p r invexity in fact this paper focuses on the optimality conditions for optimization problems in banach algebras regarding the generalized kt p r invexity notion and kuhn tucker points

on efficiency and duality for multiobjective variational problems abstract the concept of efficiency pareto optimum is used to formulate duality for multiobjective variational problems wolfe and mond weir type duals are formulated under generalized f convexity assumptions on the functions involved weak and strong duality theorems are proved

multiobjective symmetric duality involving cones abstract in this paper a pair of multiobjective symmetric dual programs over arbitrary cones are formulated for cone convex functions weak strong converse and self duality theorems are proved for these programs

approximately bisimilar symbolic models for nonlinear control systems control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs although these models are very powerful when dealing with physical phenomena they are less suited to describe software and hardware interfacing with the physical world for this reason there is a growing interest in describing control systems through symbolic models that are abstract descriptions of the continuous dynamics where each symbol corresponds to an aggregate of states in the continuous model since these symbolic models are of the same nature of the models used in computer science to describe software and hardware they provide a unified language to study problems of control in which software and hardware interact with the physical world furthermore the use of symbolic models enables one to leverage techniques from supervisory control and algorithms from game theory for controller synthesis purposes in this paper we show that every incrementally globally asymptotically stable nonlinear control system is approximately equivalent bisimilar to a symbolic model the approximation error is a design parameter in the construction of the symbolic model and can be rendered as small as desired furthermore if the state space of the control system is bounded the obtained symbolic model is finite for digital control systems and under the stronger assumption of incremental input to state stability symbolic models can be constructed through a suitable quantization of the inputs

approximation metrics for discrete and continuous systems established system relationships for discrete systems such as language inclusion simulation and bisimulation require system observations to be identical when interacting with the physical world modeled by continuous or hybrid systems exact relationships are restrictive and not robust in this paper we develop the first framework of system approximation that applies to both discrete and continuous systems by developing notions of approximate language inclusion approximate simulation and approximate bisimulation relations we define a hierarchy of approximation pseudo metrics between two systems that quantify the quality of the approximation and capture the established exact relationships as zero sections our approximation framework is compositional for a synchronous composition operator algorithms are developed for computing the proposed pseudo metrics both exactly and approximately the exact algorithms require the generalization of the fixed point algorithms for computing simulation and bisimulation relations or dually the solution of a static game whose cost is the so called branching distance between the systems approximations for the pseudo metrics can be obtained by considering lyapunov like functions called simulation and bisimulation functions we illustrate our approximation framework in reducing the complexity of safety verification problems for both deterministic and nondeterministic continuous systems

nonsmooth multiobjective optimization using limiting subdifferentials in this study using the properties of limiting subdifferentials in nonsmooth analysis and regarding a separation theorem some weak pareto optimality necessary and sufficient conditions for nonsmooth multiobjective optimization problems are proved

multiple symbol differential detection for mpsk space time block codes decision metric and performance analysis approximately 3 db signal to noise ratio snr loss is always paid with conventional differential space time block codes stbcs compared with coherent stbcs in this paper a multiple symbol differential detection msdd technique is proposed for m ary phase shift keying psk stbcs the new scheme can greatly narrow the 3 db performance gap by extending the observation interval for differential decoding the technique uses maximum likelihood sequence detection instead of traditional symbol by symbol detection and is carried out on the slow flat rayleigh fading channel a generalized decision metric is derived for an observation interval of arbitrary length it is shown that for a moderate number of symbols msdd provides approximately 1 5 db performance improvement over conventional differential detection in addition a closed form pairwise error probability and approximate bit error probability bep are derived for multiple symbol differential binary psk stbc results show that the theoretical bep matches simulation results well the bep is shown to converge asymptotically with the number of symbols in the observation interval to that of the differential scheme with coherent detection

minimax and symmetric duality for a class of multiobjective variational mixed integer programming problems abstract in this paper we formulate a pair of multiobjective variational mixed integer programs for arbitrary cones under the separability and partial invexity assumptions on the functions involved we establish the weak strong converse and self duality theorems related to efficient solution

differential space time modulation space time coding and modulation exploit the presence of multiple transmit antennas to improve the performance on multipath radio channels thus far most work on space time coding has assumed that perfect channel estimates are available at the receiver in certain situations however it may be difficult or costly to estimate the channel accurately in which case it is natural to consider the design of modulation techniques that do not require channel estimates at the transmitter or receiver we propose a general approach to differential modulation for multiple transmit antennas based on group codes this approach ran be applied to any number of transmit and receive antennas and any signal constellation we also derive low complexity differential receivers error bounds and modulator design criteria which we use to construct optimal differential modulation schemes for two transmit antennas these schemes can be demodulated with or without channel estimates this permits the receiver to exploit channel estimates when they are available the performance degrades by approximately 3 db when estimates are not available

higher order duality in multiobjective fractional programming with support functions abstract in this paper a new class of higher order f type i functions for a multiobjective programming problem is introduced which subsumes several known studied classes higher order mond weir and schaible type dual programs are formulated for a nondifferentiable multiobjective fractional programming problem where the objective functions and the constraints contain support functions of compact convex sets in r n weak and strong duality results are studied in both the cases assuming the involved functions to be higher order f type i a number of previously studied problems appear as special cases

controlling a class of nonlinear systems on rectangles in this paper we focus on a particular class of nonlinear affine control systems of the form xdot f x bu where the drift f is a multi affine vector field i e affine in each state component the control distribution b is constant and the control u is constrained to a convex set for such a system we first derive necessary and sufficient conditions for the existence of a multiaffine feedback control law keeping the system in a rectangular invariant we then derive sufficient conditions for driving all initial states in a rectangle through a desired facet in finite time if the control constraints are polyhedral we show that all these conditions translate to checking the feasibility of systems of linear inequalities to be satisfied by the control at the vertices of the state rectangle this work is motivated by the need to construct discrete abstractions for continuous and hybrid systems in which analysis and control tasks specified in terms of reachability of sets of states can be reduced to searches on finite graphs we show the application of our results to the problem of controlling the angular velocity of an aircraft with gas jet actuators

second order symmetric duality in nondifferentiable multiobjective programming a pair of mond weir type second order symmetric nondifferentiable multiobjective programs is formulated weak strong and converse duality theorems are established under h pseudobonvexity assumptions special cases are discussed to show that this paper extends some work appeared in this area

symbolic control of stochastic systems via approximately bisimilar finite abstractions symbolic approaches for control design construct finite state abstract models that are related to the original systems then use techniques from finite state synthesis to compute controllers satisfying specifications given in a temporal logic and finally translate the synthesized schemes back as controllers for the original systems such approaches have been successfully developed and implemented for the synthesis of controllers over non probabilistic control systems in this paper we extend the technique to probabilistic control systems modelled by controlled stochastic differential equations we show that for every stochastic control system satisfying a probabilistic variant of incremental input to state stability and for every given precision e 0 a finite state transition system can be constructed which is e approximately bisimilar to the original stochastic control system moreover we provide results relating stochastic control systems to their corresponding finite state transition systems in terms of probabilistic bisimulation relations known in the literature we demonstrate the effectiveness of the construction by synthesizing controllers for stochastic control systems over rich specifications expressed in linear temporal logic our technique enables automated correct by construction controller synthesis for stochastic control systems which are common mathematical models employed in many safety critical systems subject to structured uncertainty

pseudolinear fuzzy mappings two classes of fuzzy mappings called pseudolinear and pseudolinear fuzzy mappings are introduced by relaxing the definitions of pseudo convex and pseudo invex fuzzy mappings first some characterizations of pseudolinear and pseudolinear fuzzy mappings are obtained then characterizations of the solution sets of pseudolinear and pseudolinear fuzzy programs are derived

second order symmetric duality in multiobjective programming involving generalized cone invex functions abstract in this paper cone second order pseudo invex and strongly cone second order pseudo invex functions are defined a pair of mond weir type second order symmetric dual multiobjective programs is formulated over arbitrary cones weak strong and converse duality theorems are established under aforesaid generalized invexity assumptions a second self duality theorem is also given by assuming the functions involved to be skew symmetric

symbolic models for nonlinear control systems alternating approximate bisimulations symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states in the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating complexity in control design in fact symbolic models enable the use of well known algorithms in the context of supervisory control and algorithmic game theory for controller synthesis since the 1990s many researchers faced the problem of identifying classes of dynamical and control systems that admit symbolic models in this paper we make further progress along this research line by focusing on control systems affected by disturbances our main contribution is to show that incrementally globally asymptotically stable nonlinear control systems with disturbances admit symbolic models

on efficiency and duality for multiobjective programs abstract for a multiobjective nonlinear program which involved inequality and equality constraints wolfe mond weir and general mond weir type duals are formulated and the concept of efficiency pareto optimum is used to state some duality results under generalized f convexity assumptions

symmetric duality for minimax mixed integer programming problems with pseudo invexity in this paper we consider the pair of symmetric dual multiobjective variational mixed integer programs proposed by chen and yang x chen j yang symmetric duality for minimax multiobjective variational mixed integer programming problems with partial invexity european journal of operational research 181 2007 76 85 and extend some of their results under the assumptions of partial pseudo invexity and separability on the functions involved these results include several results available in literature as special cases

second order multiobjective symmetric duality with cone constraints abstract in this paper we formulate wolfe and mond weir type second order multiobjective symmetric dual problems over arbitrary cones weak strong and converse duality theorems are established under bonvexity pseudobonvexity assumptions this work also removes several omissions in definitions models and proofs for wolfe type problems studied in mishra 9 moreover self duality theorems for these pairs are obtained assuming the function involved to be skew symmetric

second order symmetric duality for nonlinear multiobjective mixed integer programming we formulate two pairs of second order symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones by using the concepts of efficiency and second order invexity we establish weak strong converse and self duality theorems for the dual models several known results are obtained as special cases

symmetric duality for mathematical programming in complex spaces with f convexity abstract under f convexity f concavity f pseudoconvexity f pseudoconcavity appropriate duality results for a pair of wolfe and mond weir type symmetric dual nonlinear programming problems in complex spaces are established these results are then used to develop second order f convexity f concavity second order f pseudoconvexity f pseudoconcavity and appropriate second order symmetric dual nonlinear programming problems in complex spaces

optimality and duality for multiple objective optimization under generalized type i univexity abstract in this paper we extend the classes of generalized type i vector valued functions introduced by aghezzaf and hachimi in j global optim 18 2000 91 101 to generalized univex type i vector valued functions and consider a multiple objective optimization problem involving generalized type i univex functions a number of kuhn tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution the mond weir and general mond weir type duality results are also presented

symbolic models for nonlinear control systems affected by disturbances in the last few years there has been a growing interest in the use of symbolic models for the formal verification and control design of purely continuous or hybrid systems symbolic models are abstract descriptions of continuous systems where one symbol corresponds to an aggregate of continuous states in this article we face the problem of deriving symbolic models for nonlinear control systems affected by disturbances the main contribution of this article is in proposing symbolic models that can be effectively constructed and that approximate nonlinear control systems affected by disturbances in the sense of alternating approximate bisimulation

symmetric duality for nonlinear programming problem involving η bonvex functions a pair of second order symmetric dual is formulated and corresponding duality results are established for nonlinear programming problems involving bonvex functions

second order symmetric duality for nonlinear minimax mixed integer programs abstract wolfe type second order minimax mixed integer dual programs are formulated and a symmetric duality theorem is e established under separability and bonvexity boncavity of the kernel function k x y mond weir type symmetric duality is also discussed under weaker bonvexity assumptions moreover self duality theorems for these pairs are obtained assuming k x y to be skew symmetric

on input to state stability of stochastic retarded systems with markovian switching this note develops a razumikhin type theorem on pth moment input to state stability of hybrid stochastic retarded systems also known as stochastic retarded systems with markovian switching which is an improvement of an existing result an application to hybrid stochastic delay systems verifies the effectiveness of the improved result

mixed type duality in multiobjective programming problems two mixed type duals are introduced for multiobjective programming and for multiobjective fractional programming respectively results about weak duality strong duality and strictly reverse duality are presented under more suitable conditions

multiple symbol differential detection of mpsk a differential detection technique for mpsk multiple phase shift keying which uses a multiple symbol observation interval is presented and its performance is analyzed and simulated the technique makes use of maximum likelihood sequence estimation of the transmitted phases rather than symbol by symbol detection as in the conventional differential detection thus the performance of this multiple symbol detection scheme fills the gap between conventional two symbol observation differentially coherent detection of mpsk and ideal coherent of mpsk with differential encoding the amount of improvement gained over conventional differential detection depends on the number of phases m and the number of additional symbol intervals added to the observation what is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation the analysis and simulation results presented are for uncoded mpsk

second order symmetric duality in mathematical programming with f convexity abstract under second order f convexity f concavity and second order f pseudoconvexity f pseudoconcavity appropriate second order duality results for pair of wolfe and mond weir type second order symmetric dual nonlinear programming problems are established these second order duality results are then used to formulate wolfe type and mond weir type second order minimax mixed integer dual programs and symmetric duality theorem is established under separability and second order f convexity f concavity of the kernel function f x y second order symmetric dual fractional mixed integer programs are studied using the above programs moreover second order self duality theorems for the above pairs are obtained assuming f x y to be skew symmetric

non differentiable second order symmetric duality in mathematical programming with f convexity abstract a pair of wolfe type non differentiable second order symmetric primal and dual problems in mathematical programming is formulated the weak and strong duality theorems are then established under second order f convexity assumptions symmetric minimax mixed integer primal and dual problems are also investigated

mond weir type second order symmetric duality in non differentiable minimax mixed integer programming problems abstract a pair of mond weir type non differentiable second order symmetric minimax mixed integer primal and dual problems in mathematical programming is formulated symmetric and self duality theorems are then established under second order f pseudo convexity assumptions several known results including that of gulati and ahmad eur j oper res 101 1997 122 hou and yang j math anal appl 255 2001 491 and mond and schechter bull aust math soc 53 1996 177 as well as others are obtained as special cases

non differentiable higher order symmetric duality in mathematical programming with generalized invexity a pair of non differentiable higher order symmetric dual model in mathematical programming is formulated the weak and strong duality theorems are established under higher order invexity assumption symmetric minimax mixed integer primal and dual problems are also investigated

establishing convexity of polynomial lyapunov functions and their sublevel sets there has been renewed interest in the use of polynomial and homogeneous polynomial lyapunov functions for addressing stability and performance issues in systems and control theory however no condition is yet available to establish the convexity of these functions and the convexity of their sublevel sets properties that can be useful in many applications in this paper new conditions for establishing these convexity properties are proposed which can be handled through convex linear matrix inequalities optimizations by means of sum of squares relaxations

symmetric duality for minimax nonlinear mixed integer programming abstract a pair of symmetric dual minimax integer programming problems is formulated and an appropriate duality theorem is established under the pseudoconvexity pseudoconcavity assumption on the kernel function k x y this model removes certain inconsistencies in an earlier model and helps to study self duality as well

infinite semi infinite problems to characterize the optimality of nonlinear optimization problems considering a generic nonlinear programming problem nlpp this paper provides a family of linear infinite problems lips or linear semi infinite problems lsips and establishes the connection between optimality in the respective nlpp and that in the provided lips lsips

a unified performance analysis framework for differential detection in mimo rayleigh fading channels in this paper a unified framework for the analysis of differential detection dd schemes in time variant multiple input multiple output rayleigh fading channels is provided the present results are very general in that they apply to transmission with differential phase shift keying unitary differential space time modulation dstm and block dstm and reception with conventional dd cdd multiple symbol dd msdd decision feedback dd dfdd and differentially coherent detection cd new result for general quadratic forms of gaussian random variables are derived which allows us to obtain elegant closed form expressions for the pairwise error probabilities peps of the dominant error events of the considered detectors furthermore it is shown that a unified treatment of all considered detectors is possible with a properly defined effective signal to noise ratio esnr and a useful connection between msdd and minimum mean squared error mmse interpolation is established interesting novel results obtained from this analysis include i dstm constellations designed for cdd and cd are also optimum for msdd and dfdd ii the error floor entailed by msdd and dfdd in time variant fading decreases exponentially with the observation window size n and iii in time variant fading with effective normalized fading bandwidth bh efft msdd with n rarr infin suffers only from an snr loss of 1 2bh efft compared to cd whereas dfdd suffers from a diversity loss of 1 2bh efft

effects of non identical rayleigh fading on differential unitary space time modulation non identical fading distribution in a multiple input multiple output mimo channel including unequal average channel gains and fade rates often occurs when antennas are not co located in this paper we present an analytical study of the effects of non identical rayleigh fading on the error performance of differential unitary space time modulation dustm the fading processes for different transmit receive antenna pairs are assumed to be independent and time variant we find that the maximum likelihood ml differential detector of dustm over such channels is involved except for differential cyclic group codes the conventional detector is proved to be asymptotically optimal in the limit of high signal to noise ratio snr over static fading channels applying the distribution of quadratic forms of gaussian vectors we then derive closed form expressions for the exact error probabilities of two specific unitary classes namely cyclic group codes and orthogonal codes simple and useful asymptotic bounds on error probabilities are also obtained our analysis leads to the following general findings 1 equal power allocation is asymptotically optimal and 2 non identical channel gain distribution degrades the error performance finally we also introduce a water filling based power allocation to exploit the transmit non identical fading statistics

mixed symmetric duality in non differentiable multiobjective mathematical programming two mixed symmetric dual models for a class of non differentiable multiobjective nonlinear programming problems with multiple arguments are introduced in this paper these two mixed symmetric dual models unify the four existing multiobjective symmetric dual models in the literature weak and strong duality theorems are established for these models under some mild assumptions of generalized convexity several special cases are also obtained

double differential space time block coding for time selective fading channels most existing space time coding schemes assume time invariant fading channels and offer antenna diversity gains relying on accurate channel estimates at the receiver other single differential space time block coding schemes forego channel estimation but are less effective in rapidly fading environments based on a diagonal unitary matrix group a novel double differential space time block coding approach is derived in this paper for time selective fading channels without estimating the channels at the receiver information symbols are recovered with antenna diversity gains regardless of frequency offsets the resulting transceiver has very low complexity and is applicable to an arbitrary number of transmit and receive antennas approximately optimal space time codes are also designed to minimize bit error rate system performance is evaluated both analytically and with simulations

approximately bisimilar symbolic models for randomly switched stochastic systems in the past few years there has been a growing interest in the use of symbolic models for control systems the main reason is the possibility to leverage algorithmic techniques over symbolic models to synthesize controllers that are valid for the concrete control systems such controllers can enforce complex logical specifications that are otherwise hard if not impossible to establish on the concrete models with classical control techniques examples of such specifications include those expressible via linear temporal logic or as automata on infinite strings a relevant goal in this research line is in the identification of classes of systems that admit symbolic models in particular continuous time systems with stochastic or hybrid dynamics have been only recently considered due to their rather general and complex dynamics in this work we make progress in this direction by enlarging the class of stochastic hybrid systems admitting finite symbolic models specifically we show that randomly switched stochastic systems satisfying some incremental stability assumption admit such models

differential unitary space time modulation we present a framework for differential modulation with multiple antennas across a continuously fading channel where neither the transmitter nor the receiver knows the fading coefficients the framework can be seen as a natural extension of standard differential phase shift keying commonly used in single antenna unknown channel systems we show how our differential framework links the unknown channel system with a known channel system and we develop performance design criteria as a special ease we introduce a class of diagonal signals where only one antenna is active at any time and demonstrate how these signals may be used to achieve full transmitter diversity and low probability of error

reachability and control synthesis for piecewise affine hybrid systems on simplices in this paper we consider the synthesis of control laws for piecewise affine hybrid systems on simplices the construction is based on the solution to the control to facet problem at the continuous level and on dynamic programming at the discrete level the construction is given as an explicit algorithm using only linear algebra and reach set computations for automata no numerical integration is required the method is conservative in that it may fail to find a control law where one exists but one cannot hope for a sharp algorithm for control synthesis since reachability for piecewise affine hybrid systems is undecidable

approximations of stochastic hybrid systems this paper develops a notion of approximation for a class of stochastic hybrid systems that includes as special cases both jump linear stochastic systems and linear stochastic hybrid automata our approximation framework is based on the recently developed notion of the so called stochastic simulation functions these lyapunov like functions can be used to rigorously quantify the distance or error between a system and its approximate abstraction for the class of jump linear stochastic systems and linear stochastic hybrid automata we show that the computation of stochastic simulation functions can be cast as a tractable linear matrix inequality problem this enables us to compute the modeling error incurred by abstracting some of the continuous dynamics or by neglecting the influence of stochastic noise or even the influence of stochastic discrete jumps

maximum likelihood differential detection of uncoded and trellis coded amplitude phase modulation over awgn and fading channels spl minus metrics and performance this paper derives metrics for maximum likelihood differential detection of uncoded and trellis coded mpsk and qam transmitted over rayleigh and rician fading channels receiver structures based on these metrics are proposed and their error probability performance analyzed and or simulated the results represent a generalization of the notion of multiple symbol differential detection previously introduced by the authors for mpsk over an awgn to the fading channel and other modulations for the coded cases ideal interleaving deinterleaving is assumed and furthermore the presence or absence of channel state information an interesting side result is that for a constant envelope modulation transmitted over a fading channel with unknown but rapidly varying phase error the other extreme to the slowly varying phase error case normally assumed for differential detection under certain practical assumptions it is shown that the optimum receiver is of the limiter discriminator type

stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple lyapunov functions this paper presents a general framework for analyzing stability of nonlinear switched systems by combining the method of multiple lyapunov functions with a suitably adapted comparison principle in the context of stability in terms of two measures for deterministic switched systems this leads to a unification of representative existing results and an improvement upon the current scope of the method of multiple lyapunov functions for switched systems perturbed by white noise we develop new results which may be viewed as natural stochastic counterparts of the deterministic ones in particular we study stability of deterministic and stochastic switched systems under average dwell time switching