sharp sets of permutations abstract a set of permutations is sharp if its cardinality is the product of the distinct non zero hamming distances between pairs of permutations in the set we give a number of new results and constructions for sharp sets and groups and for the more special geometric sets and groups using a mixture of algebraic and combinatorial techniques

sharp characters of finite groups abstract if is a virtual generalized character of a finite group g with n and l g g g g 1 g g g g 1 then g dividesfl n where fl x is the monic polynomial of least degree having l as its set of roots this generalises a result of the second author for permutation characters we say that the pair g is l sharp if g f l n we characterise the l sharp pairs for various sets l sometimes under additional hypotheses and give a number of examples

sharp characters of finite groups of type 1 1 1 1 satisfying a weaker condition than sharpness is studied especially for a pair g x in that class the group structure of g o g is determinted where o g is the largest normal subgroup of g of odd order the theorem is proved by picking the sharp pairs among pairs in the class

solution and asymptotic behavior of coupled riccati equations in jump linear systems a new necessary and sufficient condition for the existence of a positive semidefinite solution of coupled riccati equations occurring in jump linear systems is derived by verifying a riccati inequality it is shown that such a solution exists in addition two numerical algorithms are given to compute it an example is given to illustrate the proposed method

optimal control of unknown parameter systems the problem is discussed of finding a cost functional for which an adaptive control law is optimal the system under consideration is a partially observed linear stochastic system with unknown parameters it is well known that an optimal finite dimensional filter for this problem can be derived when the parameters belong to a finite set since the optimal filter involves the evaluation of a finite set of a posteriori probabilities for each of the parameter values given the observations a natural adaptive control scheme is i develop the optimal linear feedback law given each parameter ii use the a posteriori probabilities to form the weighted average convex combination of the individual control policies and iii use the weighted average as the control law a quadratic cost functional is devised for which this strategy is optimal in a general case and it is shown that the probing effect identified with dual control problems is inherent in the standard linear quadratic gaussian problem with parameter uncertainty

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

stabilizing control law for hybrid models this note is concerned with the adaptive stabilizing control problem for jump markov systems a new control law is proposed based on a simple set of algebraic sufficient conditions it is shown that this approach can be used for a class of stochastic models for which the more restrictive solution proposed by caines and zhang 1992 does not apply

stabilization of jump linear gaussian systems without mode observations systems such as those subject to abrupt changes including failure or those with uncertain dynamic model or more than one possible model can be naturally modelled as jump linear jl systems because of their applications in fields such as tracking fault tolerant control manufacturing process and robots jl systems have drawn extensive attention the optimal control and stabilization problem for jl systems when the mode system model is not assumed to be directly and perfectly observed a realistic assumption in many applications is nonlinear and prohibitive both analytically and computationally because of the dual effect the main contribution of this work is the sufficient condition for stabilization for a class of adaptive controllers when the mode is not directly observed we first present the optimal controller under an assumption of a certain type of mode availability using this optimal feedback gain we derive a condition that ensures the stabilizing property for a class of adaptive cont

on sharp characters of rank 2 with rational values abstract for a finite group g and its character let l be the set of distinct values of on non identity elements of g and f l 1 denote the monic polynomial of least degree having l as its set of roots blichfeldt a theorem concerning the invariants of linear homogeneous groups with some applications to substitution groups trans amer math soc 5 1904 461 466 2 showed that f l 1 g is a rational integer cameron and kiyota sharp character of finite groups j algebra 115 1988 125 143 called the pair g l sharp if g f l 1 and posed the problem of determining all the l sharp pairs g for a given set l for several cases those problems have already been studied by many authors our purpose is to determine the sharp pairs of types 2 1 and 1 2 having non trivial center

paper evidence measures based on fuzzy information an organized body of results pertaining to the analysis of evidence when the available knowledge is pervaded with imprecision is provided the evidence theory of dempster and shafer is extended to the case of fuzzy observations and fuzzy events upper and lower possibilities of such events are derived by iterating the generation process of upper and lower probabilities as done by dempster both probabilistic and possibilistic models are developed in parallel these evidence measures are used for decision evaluation when the available knowledge is poor the classical model of decision making under uncertainty is thus extended to the case when the consequences of a decision are only roughly described and their probabilities of occurrence modeled by intervals or fuzzy numbers

optimal adaptive lqg control for systems with finite state process parameters the situation where a totally observed process y t is generated by a stochastic differential equation whose parameters evolve on a finite set 1 n according to a stochastic differential equation is considered the optimal control law is sought with respect to quadratic loss functions on y t and the control u t the auxiliary p d e technique of hijab 6 is used together with a nonlinear filter to obtain the solution whose existence depends upon that of a smooth solution to the auxiliary p d e and strong solutions to the system s d e under the given control inputs

jump linear quadratic gaussian control in continuous time the optimal quadratic control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes is addressed the systems are also subject to gaussian input and measurement noise the optimal solution for the jump linear quadratic gaussian jlqc problem is given this solution is based on a separation theorem the optimal state estimator is sample path dependent if the plant parameters are constant in each value of the underlying jumping process then the controller portion of the compensator converges to a time invariant control law however the filter portion of the optimal infinite time horizon jlqc compensator is not time invariant thus a suboptimal filter which does converge to a steady state solution under certain conditions is derived and a time invariant compensator is obtained

almost sure stabilization for feedback controls of regime switching linear systems with a hidden markov chain this work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown markov chain the control system displays continuous dynamics represented by differential equations and discrete events given by a hidden markov chain in the previous investigation on this class of problems averaging criteria were used which provides only the system behavior in some expectation sense a closer scrutiny of the system behavior necessarily requires the consideration of sample path properties different from previous work on stabilization of adaptive controlled systems with a hidden markov chain where average criteria were considered this work focuses on the almost sure stabilization or sample path stabilization of the underlying processes under simple conditions it is shown that as long as the feedback controls have linear growth in the continuous component the resulting process is regular moreover by appropriate choice of the lyapunov functions it is shown that the adaptive system is stabilizable almost surely as a by product it is also established that the controlled process is positive recurrent

tracking and identification of regime switching systems using binary sensors this work is concerned with tracking and system identification for time varying parameters the parameters are markov chains and the observations are binary valued with noise corruption to overcome the difficulties due to the limited measurement information wonham type filters are developed first then based on the filters two popular estimators namely mean squares estimator msq and maximum posterior map estimator are constructed for the mean squares estimator we derive asymptotic normality in the sense of weak convergence and in the sense of strong approximation the asymptotic normality is then used to derive error bounds when the markov chain is infrequently switching we derive error bounds for map estimators when the markovian parameters are fast varying we show that the averaged behavior of the parameter process can be derived from the stationary measure of the markov chain and that can be estimated using empirical measures upper and lower error bounds on estimation errors are also established

on the adaptive control for jump parameter systems vianonlinear filtering in this paper we first present an error analysis for the process of estimates generated by the wonham filter when it is used for the estimation of the finite set valued jump markov parameters of a random parameter linear stochastic system and further give bounds on certain functions of these estimates we then consider a certainty equivalence adaptive linear quadratic gaussian feedback control law using the estimates generated by the nonlinear filter and demonstrate the global existence of solutions to the resulting closed loop system a stochastic lyapunov analysis establishes that the certainty equivalence law stabilizes the markov jump parameter linear system in the mean square average sense the conditions for this result are that certain products of i the parameter process jump rate and ii the solution of the control riccati equation and its second derivatives should be less than certain given bounds an example is given where the controlled linear system has state dimension 2 finally the stabilizing properties of certainty equivalence laws which depend on i the maximum likelihood estimate of the parameter value and ii a modified version of this estimate are established under certain conditions

towards fuzzy differential calculus part 2 integration on fuzzy intervals abstract the problem of integrating mappings over fuzzy domains has already received some attention in the literature however there is not a unique approach but several definitions have been proposed each carrying its own meaning this paper tries to emphasize the relationships and the differences between the various points of view

incomplete conjunctive information abstract many information systems capable of handling incomplete or fuzzy information manipulate objects with single valued attributes information is then said to be disjunctive information is said to be conjunctive when pertaining to many valued attributes while a piece of incomplete disjunctive information is easily represented by means of a set of mutually exclusive possible values modeling incomplete conjunctive information theoretically leads to consider families of sets since attributes are then set valued under complete information some proposals are made in order to efficiently and rigorously represent incomplete conjunctive information and deal with query evaluation especially in the case where only upper and or lower bounds of the set of values of a many valued attribute are known applications of this approach can be expected for the processing of time intervals as well as spatial reasoning among other topics in knowledge base management

the solution of a partially observed stochastic optimal control problem in terms of predicted miss the explicit solution of a partially observed lq problem driven by a combination of a wiener process and an unobserved finite state jump markov process is given applications of the model include guidance problems where the jump markov process models evasive maneuvers acceleration values of the target or systems subject to a sequence of failures that can be modeled by a jump markov process

twofold fuzzy sets and rough sets some issues in knowledge representation abstract this paper deals with the representation of sets where the membership of some elements may be ill known rather than just a matter of degree as in a fuzzy set the notion of a twofold fuzzy set is introduced when the relevant information for determining the membership status is incomplete a twofold fuzzy set is made of a nested pair of fuzzy sets the one which gathers the elements which more or less necessarily belong and the one which gathers the elements which more or less possibly belong twofold fuzzy sets are compared from a frontal and from a semantical point of view with other proposals and particularly with the notion of a rough set recently introduced by pawlak set operations of twofold fuzzy sets are discussed and the cardinality of a twofold fuzzy set is defined twofold fuzzy relations are also introduced finally various applications of twofold fuzzy sets in knowledge representation are briefly discussed

stochastic stability of jump discrete time linear systems with markov chain in a general borel space necessary and sufficient conditions for stochastic stability ss of discrete time linear systems subject to markov jumps in the parameters are considered assuming that the markov chain takes values in a general borel space s it is shown that ss is equivalent to the spectrum radius of a bounded linear operator in a banach space being less than 1 or to the existence of a solution of a lyapunov type equation these results generalize several previous results in the literature which considered only the case of the markov chain taking values in a finite or infinite countable space

on a partially observable lqg problem for systems with markovian jumping parameters in this paper a variant of the lqg problem for systems with markovian jumping parameters is studied it is assumed that the system is partially observable in the sense that we do not have access to the jumping parameter via nonlinear filtering the problem is recast as one with complete information it is then shown that a certain averaged control is an optimal policy vis a vis a modified quadratic cost apart from its intrinsic theoretical interest this result has an important bearing on a number of different analyses related with the original quadratic cost