fine hierarchy of regular ω languages by applying descriptive set theory we get several facts on the fine structure of regular languages considered by k wagner we present quite different shorter proofs for main his results and get new results our description of the fine structure is new very clear and automata free we prove also a closure property of the fine structure under boolean operations our results demonstrate deep interconnections between descriptive set theory and theory of languages

technical communique adaptive ilc for a class of discrete time systems with iteration varying trajectory and random initial condition in this work we present a discrete time adaptive iterative learning control ailc scheme to deal with systems with time varying parametric uncertainties using the analogy between the discrete time axis and the iterative learning axis the new adaptive ilc can incorporate a recursive least squares rls algorithm hence the learning gain can be tuned iteratively along the learning axis and pointwisely along the time axis when the initial states are random and the reference trajectory is iteration varying the new ailc can achieve the pointwise convergence over a finite time interval asymptotically along the iterative learning axis

d split sequences and derived equivalences abstract in this paper we introduce the so called d split sequences and show that each d split sequence gives rise to a derived equivalence via a tilting module in particular we obtain derived equivalences from auslander reiten sequences via bb tilting modules or from n almost split sequences via n bb tilting modules and auslander reiten triangles further we recover n almost split sequences from n bb tilting modules over n auslander algebras

the greatest fixed points and rational omega tree languages abstract rational omega tree languages are defined by extending the notion of rational or regular expressions for languages and their properties are investigated they are characterized by means of greatest fixed points of certain functions and are shown to be precisely the omega tree languages recognized by rabin s special automata a simple normal form for rational omega tree languages is also presented

author s reply to comments on nonlinear repetitive control our paper ghosh and paden nonlinear repetitive control ieee trans automat contr vol 45 p 949 54 2000 proves theorem 1 which establishes conditions for the stability of the nonlinear repetitive control system and proposition 2 which goes on to establish bounds on the steady state error signals these are correct as stated as they apply to repetitive controllers with a finite number of oscillators in their internal model an issue correctly raised in the commentary lucibello comments on nonlinear repetitive control ieee trans automat contr vol 48 p 1470 1 2003 is that the conditions of proposition 2 might be difficult to meet when the number of oscillators is large this observation does not challenge the veracity of the proposition but is certainly insightful in our introductory comments of section 11 we attempt and fail to make a qualitative connection to the pure time delay type repetitive control the following statement is incorrect and should be deleted from our paper this justifies the fact that in the limit n spl rarr spl infin the above model of the repetitive controller works as well as the ideal model in achieving perfect tracking for typical reference signals

discrete time adaptive iterative learning control for high order nonlinear systems with unknown control directions an adaptive iterative learning control method is proposed for a class of nonlinear strict feedback discrete time systems with random initial conditions and iteration varying desired trajectories an n step ahead predictor approach is employed to estimate the future states in the control design discrete nussbaum gain method is utilised to deal with the lack of a priori knowledge of control directions the proposed control algorithm guarantees the boundedness of all the signals in the controlled system the tracking error converges to zero asymptotically along the iterative learning axis except for beginning states affected by random initial conditions the effectiveness of the proposed control scheme is verified through numerical simulation

iterative learning control synthesis based on 2 d system theory an algorithm is presented for iterative learning of the control input for a linear discrete time multivariable system necessary and sufficient conditions are stated for convergence of the proposed algorithm the algorithm synthesis and analysis are based on two dimensional 2 d system theory a numerical example is given

on d type and p type ilc designs and anticipatory approach many schemes of iterative learning control ilc have been developed for continuous time non linear dynamic systems to improve tracking performance two schemes d type and p type have been the bases for many ilc designs recently the anticipatory ilc scheme has been introduced on the basis of a different approach wang 1998a 1999 in this paper these basic schemes are compared from both analysis and implementation view points the anticipatory ilc scheme is designed on the basis of a causal pair of the action taken and its resulting state variables this approach has the anticipatory characteristics of the d type ilc and the simplicity for implementation of p type ilcs a sampled data ilc scheme is presented as another form of this anticipatory ilc scheme furthermore control device saturation is taken into account and tracking error convergence results are established with proofs the convergence results are also provided in the presence of uncertainties disturbances and measurement noises ex

a survey on iterative learning control for nonlinear systems in this article we review the recent advances in iterative learning control ilc for nonlinear dynamic systems in the research field of ilc two categories of system nonlinearities are considered namely the global lipschitz continuous glc functions and local lipschitz continuous llc functions ilc for glc systems is widely studied and analysed using contraction mapping approach and the focus of recent exploration moves to application problems though a number of theoretical issues remain open ilc for llc systems is currently a hot area and the recent research focuses on ilc design and analysis by means of lyapunov approach the objectives of this article are to introduce recent development and advances in nonlinear ilc schemes highlight their effectiveness and limitations as well as discuss the directions for further exploration of nonlinear ilc

towards a language theory for infinite n free pomsets n free or series parallel pomsets are a model for the behavior of modularly constructed concurrent systems the investigation of recognizable languages of finite n free pomsets was initiated by lodaya and weil who extended the theorems by kleene and by myhill and nerode on recognizable word languages to this setting in this paper we extend lodaya and weil s results in several aspects a we consider the relation of recognizable sets to monadic second order logic in order to generalize buchi s theorem b we prove our results and extensions of results by lodaya and weil for sets of infinite n free pomsets and c we investigate first order axiomatizable starfree and aperiodic sets of infinite n free pomsets and prove results in the spirit of mcnaughton and papert s and schutzenberger s theorems for finite words

adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances a novel function approximator is constructed by combining a fuzzy logic system with a fourier series expansion in order to model unknown periodically disturbed system functions then an adaptive backstepping tracking control scheme is developed where the dynamic surface control approach is used to solve the problem of explosion of complexity in the backstepping design procedure and the time varying parameter dependent integral lyapunov function is used to analyze the stability of the closed loop system the semiglobal uniform ultimate boundedness of all closed loop signals is guaranteed and the tracking error is proved to converge to a small residual set around the origin two simulation examples are provided to illustrate the effectiveness of the control scheme designed in this paper

the hausdorff kuratowski hierarchy of ω regular languages and a hierarchy of muller automata given a finite alphabet we give a simple characterization of those g subsets of which are deterministic regular i e accepted by buchi automata over and then characterize the regular languages in terms of these rational g sets our characterization yields a hierarchy of regular languages similar to the classical difference hierarchy of hausdorff and kuratowski for 03 sets i e the class of sets which are both f and g we then prove that the hausdorff kuratowski difference hierarchy of 03 when restricted to regular languages coincides with our hierarchy we obtain this by showing that if an regular language k can be separated from another regular language l by the union of alternate differences of a decreasing sequence of g sets of length n then there is a decreasing sequence of length n of rational g sets such that the union of alternate differences separates k from l our results not only generalize a result of landweber 1969 but also yield an effective procedure for determining the complexity of a given muller automaton we also show that our hierarchy does not collapse thus giving a fine classification of regular languages and of muller automata

initial shift issues on discrete time iterative learning control with system relative degree this paper deals with the initial shift problem that arises from discrete time iterative learning control a unified learning scheme is considered for a class of nonlinear systems with well defined relative degree which adopts the error data with anticipation in time and provides wider freedom for the updating law formation the sufficient convergence condition is derived to enable the system to possess asymptotic tracking capability and the converged output trajectory can be assessed by the initial condition the tracking performance is improved further by the introduction of initial rectifying action and the complete tracking is achieved over a specified interval

a note on ω regular languages abstract this paper is a continuation of the work by landweber 5 to clarify the relationship between classes of languages accepted by finite automata we study their properties in the topological framework introduced by boasson and nivat 1 we characterize the classes in terms of borel hierarchy and show some interrelation of them

wadge hierarchy of omega context free languages abstract the main result of this paper is that the length of the wadge hierarchy of omega context free languages is greater than the cantor ordinal e 0 and the same result holds for the conciliating wadge hierarchy defined by duparc j symbolic logic to appear of infinitary context free languages studied by beauquier ph d thesis universite paris 7 1984 in the course of our proof we get results on the wadge hierarchy of iterated counter languages which we define as an extension of classical finitary iterated counter languages to languages

alternating finite automata on ω words abstract alternating finite automata on words are introduced as an extension of nondeterministic finite automata which process infinite sequences of symbols the classes of languages defined by alternating finite automata are investigated and characterized under four types of acceptance conditions it is shown that for one type of acceptance condition alternation increases the power in comparison with nondeterminism and for other three acceptance conditions nondeterministic finite automata on words have the same power as alternating ones

on omega context free languages which are borel sets of infinite rank this paper is a continuation of the study of topological properties of omega context free languages cfl we proved in topological properties of omega context free languages theoretical computer science 262 1 2 2001 669 697 that the class of cfl exhausts the finite ranks of the borel hierarchy and in borel hierarchy and omega context free languages theoretical computer science to appear that there exist some cfl which are analytic but non borel sets we prove here that there exist some omega context free languages which are borel sets of infinite but not finite rank giving additional answer to questions of lescow and thomas logical specifications of infinite computations in a decade of concurrency j w de bakker et al eds springer lncs 803 1994 583 621

pseudo rational input output maps and their realizations a fractional representation approach to infinite dimensional systems this paper studies matrix fractional representation for impulse responses of a certain class of infinite dimensional linear systems which contains in particular delay differential systems such impulse responses are called pseudo rational in this paper this fractional representation is effectively used to derive concrete function space models from the abstract shift realizations given a fractional representation q 1 p a standard observable realization analogous to fuhrmann realizations for finite dimensional systems is associated to it a new notion of coprimeness called approximate left coprimeness is introduced and it is shown that the standard observable realization associated to the representation q 1 p is canonical if and only if q and p are approximately left coprime some examples are discussed to illustrate the relationships among various coprimeness concepts that have appeared in the literature

robust iterative learning control for a class of nonlinear systems a novel nonlinear control scheme robust iterative learning control rilc is developed in this paper the new robust ilc system provides a general framework targeting at synthesizing learning control and robust control methods with the help of lyapunov s direct method thereafter being able to handle more general classes of nonlinear uncertain systems in the proposed control scheme learning control and variable structure control are made to function in a complementary manner the nonlinear learning control strategy is applied directly to the structured system uncertainties which can be separated and expressed as products of unknown state independent functions and known state dependent functions for non structured system uncertainties associated with known bounding functions as the only a priori knowledge variable structure control vsc strategy is applied to ensure the global asymptotic stability in addition important issues regarding the objective trajectory categories resetting condition derivative signal requirement and their relationships have been made clear in this paper

characterization of ω regular languages by first order formulas abstract first order formulas are used to specify various ways of acceptance of languages by deterministic finite automata and we study the relationship between the arithmetic hierarchy of the formulas in prenex normal form and the topological hierarchy of the accepted languages among other things it is proved that the languages accepted by finite automata under the accepting conditions specified by 1 type formulas are precisely open regular languages those accepted under the conditions specified by 2 type formulas coincide with the regular languages which are denumerable unions of closed sets and that as long as the accepting conditions are specified by first order formulas the accepted languages remain to be regular

two dimensional model and algorithm analysis for a class of iterative learning control systems the iterative learning control system ilcs has attracted considerable research interest in recent years however the theoretical results on some fundamental properties of the ilcs have not yet been established one of the common drawbacks shared by current approaches is lack of a suitable mathematical model which can clearly describe both the dynamics of the control system itself and the behaviour of the learning process as well in this paper a class of iterative learning control systems is analysed from the point of view of two dimensional 2 d system theory the 2 d model for a class of ilcs is established in the form of roessor s model based on which a general type of learning controller is proposed analysis of the 2 d error equation shows that the 2 d asymptotic stability of the 2 d model guarantees the learning convergence of an ilcs design criteria for a learning controller is also suggested the learning gain matrices are obtained from a recursive 2 d identifier using the input and output

partial tilting modules over m replicated algebras abstract let a be a hereditary algebra over an algebraically closed field k and a m be the m replicated algebra of a given an a m module t we denote by t the number of non isomorphic indecomposable summands of t in this paper we prove that a partial tilting a m module t is a tilting a m module if and only if t a m and that every partial tilting a m module has complements as an application we deduce that the tilting quiver k a m of a m is connected moreover we investigate the number of complements to almost tilting modules over duplicated algebras

brief iterative learning control with initial rectifying action this paper addresses the initial shift problem in iterative learning control with system relative degree the tracking error caused by nonzero initial shift is detected when applying a conventional learning algorithm finite initial rectifying action is introduced in the learning algorithm and is shown effective in the improvement of tracking performance in particular robustness with respect to variable initial shifts the uniform convergence of the output trajectory to a desired one jointed smoothly with a specified transient trajectory from the starting position is ensured in the presence of fixed initial shift

relationships between internal and external stability for infinite dimensional systems with applications to a servo problem a study is made of the relationships among various stability motions for a class of infinite dimensional systems which contains a class of systems not covered by existing methods e g those having infinitely many unstable poles it is proved that internal l sup 2 stability and exponential stability are equivalent and internal stability implies h sup infinity stability several necessary and sufficient conditions for internal stability are derived in particular under certain conditions a canonical realization is internally stable if it is externally stable these results are applied to the servo problem involving this class of systems it is shown that i an internal model is necessary for tracking ii an internal model along with closed loop stability implies tracking a typical example called a repetitive control system is discussed to illustrate the results

endomorphism algebras of tilting modules over m replicated algebras abstract let a be a finite dimensional hereditary algebra over an algebraically closed field k and let a m be the m replicated algebra of a in this paper we investigate the structure properties of the endomorphism algebras of tilting modules of a m and prove that all the endomorphism algebras of tilting modules of a m can be realized as the iterated endomorphism algebras of bb tilting modules that is for each pair of basic tilting a m modules t 1 and t 2 there exists a series of finite dimensional algebras 0 1 s which are the endomorphism algebras of some basic tilting a m modules and for each i there is a bb tilting i module m i such that 0 end a m t 1 i end i 1 m i 1 for 1 i s and end a m t 2 end s m s

stabilization of approximately feedback linearizable systems using singular perturbation we consider a stabilization problem of approximately feedback linearizable systems we introduce a perturbation parameter by applying high gain feedback and use both the feedback linearization method and the singular perturbation method for the controller design through this we can overcome the rigorous conditions of the feedback linearization method and can reduce the dimension of the slow model of the singularly perturbed system

a regular characterization of graph languages definable monadic second order logic abstract the class of monadic second order definable graph languages is the smallest class containing certain elementary graph languages and closed under the boolean set operations and under projections this holds for many restricted types of graphs

borel hierarchy and omega context free languages we give in this paper additional answers to questions of lescow and thomas a decade of concurrency lecture notes in computer science vol 803 springer berlin 1994 pp 583 621 proving topological properties of omega context free languages cfl which extend those of o finkel theoret comput sci 262 1 2 2001 669 697 there exist some cfl which are non borel sets and one cannot decide whether an cfl is a borel set we give also an answer to a question of niwinski problem on powers posed in the proceedings of the workshop logics and recognizable sets 1990 and of simonnet automates et th orie descriptive ph d thesis universit paris 7 1992 about powers of finitary languages giving an example of a finitary context free language l such that l is not a borel set then we prove some recursive analogues to preceding properties in particular one cannot decide whether an cfl is an arithmetical set finally we extend some results to context free sets of infinite trees

repetitive control system a new type servo system for periodic exogenous signals a control scheme called repetitive control is proposed in which the controlled variables follow periodic reference commands a high accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period l into the closed loop system sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small gain theorem and the stability theorem for time lag systems synthesis algorithms are presented by both the state space approach and the factorization approach in the former approach the technique of the kalman filter and perfect regulation is utilized while coprime factorization over the matrix ring of proper stable rational functions and the solution of the hankel norm approximation are used in the latter one

x automata on ω words abstract for any storage type x the languages accepted by x automata are investigated six accepting conditions including those introduced by landweber are compared for x automata the inclusions between the corresponding six families of languages are essentially the same as for finite state automata apart from unrestricted automata also real time and deterministic automata are considered the main tools for this investigation are 1 a characterization of the languages accepted by x automata in terms of inverse x transductions of finite state languages and 2 the existence of topological upper bounds on some of the families of accepted languages independent of the storage type x

brief paper stability analysis of discrete time iterative learning control systems with interval uncertainty this paper presents a stability analysis of the iterative learning control ilc problem for discrete time systems when the plant markov parameters are subject to interval uncertainty using the so called super vector approach to ilc vertex impulse response matrices are employed to develop sufficient conditions for both asymptotic stability and monotonic convergence of the ilc process it is shown that the stability of such interval ilc systems can be determined by checking the stability of the system using only the vertex points of the interval markov parameters

repetitive control of hamiltonian systems based on variational symmetry this paper is concerned with repetitive control of hamiltonian systems which is based on iterative learning control utilizing the variational symmetry of those systems variational symmetry allows us to obtain an algorithm to solve a certain class of optimal control problems in a repetitive control framework therefore the proposed method can deal with not only trajectory tracking control problems but also optimal trajectory generation problems never before considered in a repetitive control framework a convergence analysis of this algorithm is also discussed furthermore some numerical simulations demonstrate the effectiveness of the proposed method

brief adaptive robust iterative learning control with dead zone scheme an adaptive robust iterative learning control method based on a new dead zone scheme is presented for the control of nonlinear uncertain systems the new dead zone scheme ceases both learning and adaptation whenever the previous iteration error enters a pre specified error bound in the sequel enhances the robustness of the control system and meanwhile achieves arbitrary tracking accuracy for guaranteed stability it is indicated that the system will converge to the error bound within finite iterations and stay inside it and that the boundedness of the system signals for any iteration is ensured no finite escape time iterative learning control ilc and adaptive robust control are synthesized to achieve a new control paradigm the iterative learning control strategy is applied directly to deal with structured system uncertainties unknown time functions which are invariant over iterations the adaptive robust control strategy is used to handle non periodic system uncertainties associated with partially known bounding functions where the unknown parameters in the upper bounding functions are estimated with adaptation by integrating learning adaptation robust control and the new dead zone scheme using lyapunov s direct method the proposed scheme is able to handle fairly broad classes of nonlinear uncertain systems

the three subfamilies of rational ω languages closed under ω transduction abstract the transductions defined by gire as bimorphisms coincide with the compositions of non erasing morphisms and inverse non erasing morphisms we prove that there are exactly three subfamilies of rational languages which are closed under transduction the family of rational adherences the family of rational languages whose complementary is deterministic and the whole family of rational languages

language theoretical representations of ω languages abstract in this paper we give language theoretical representations for some classes of languages defined by finite automata the classes considered in this paper are proved to be the classes of languages represented as f f pf or p p where p and p are prefix free regular languages and f and f are prefix free finite languages

automata on infinite objects and their applications to logic and programming abstract we introduce various types of automata top down automata and bottom up automata on infinite trees we study the power of determinstic and nondeterministic tree automata and prove that deterministic and non deterministic bottom up tree automata accept the same infinite tree sets we establish a relationship between tree automata logic programs recursive program schemes and the monadic second order theory of the tree we prove that the equivalence of two rational logic programs is decidable

distributed system transfer functions of exponential order o is a real number we construct a transfer function algebra of fractions viz f o for modelling possibly unstable distributed systems such that i fcirc in f o is holomorphic in re s o i e is o stable iff fcirc is o exponentially stable and ii we allow delay in the direct input output transmission of the system this algebra is a a restriction of the algebra b o developed by callier and desoer 1978 1980 a b an extension of the algebra of proper rational functions such that the exponential order properties of the latter transfer functions of lumped systems are maintained the algebra f o can be used for modelling and feedback system design it is shown that standard semigroup systems are better modelled by a transfer function in f o rather than b o

accepting conditions for automata on ω languages abstract in this paper we study the languages accepted by finite automata under a new type of accepting conditions which are based on whether the automaton enters all of its accepting states infinitely many times or not we investigate the classes of languages defined thereby in relation to other well known subclasses of the class of regular languages

a combinatorial approach to the theory of ω automata a combinatorial lemma is proved and used here to derive new results on automata and to give simpler proofs of known ones in particular we reprove mcnaughton s fundamental theorem characterizing the regular sequence sets without having to construct a sophisticated automaton the theorem is obtained by coding the behaviour of automata in a second order language and a simple application of the lemma in close analogy now referring to a first order language a theory of counter free automata is developed it is shown that these automata are appropriate for characterizing the star free sequence sets finally the lemma is applied in mathematical logic here new normal form theorems and also decidability results are proved for the first order and the monadic second order theory of certain structures over the ordering of natural numbers

nonlinear repetitive control repetitive controllers are generally applied to reject periodic disturbances and to track periodic reference signals with a known period their design is based on the internal model principle proposed by francis and wonham 1975 this paper describes a new finite dimensional siso repetitive controller for two different classes of nonlinear plants simulation results show asymptotic tracking of the periodic reference signal by the proposed repetitive controller in closed loop up to the nth harmonic frequency a proof of robustness of the repetitive control system to small nonlinearities like actuator nonlinearities is provided

adaptive learning control of nonlinear systems by output error feedback this paper addresses the problem of designing an output error feedback control for single input single output nonlinear systems with uncertain smooth output dependent nonlinearities whose local lipschitz constants are known the considered systems are required to be observable minimum phase with known relative degree and known high frequency gain sign linear systems are included the reference output signal is assumed to be smooth and periodic with known period by developing in fourier series expansion a suitable periodic input reference signal an output error feedback adaptive learning control is designed which ldquolearnsrdquo the input reference signal by identifying its fourier coefficients bounded closed loop signals and exponential tracking of both input and output reference signals are obtained when the fourier series expansion is finite while arbitrary small tracking errors are exponentially achieved otherwise the resulting control is not model based is independent of the system order and depends only on the relative degree the reference signal period and the high frequency gain sign

defining an m cluster category we show that a certain orbit category considered by keller encodes the combinatorics of the m clusters of fomin and reading in a fashion similar to the way the cluster category of buan marsh reineke reiten and todorov encodes the combinatorics of the clusters of fomin and zelevinsky this allows us to give type uniform proofs of certain results of fomin and reading in the simply laced cases

generalized automata on infinite trees and muller mcnaughton s theorem abstract we introduce various types of top down and bottom up generalized automata on infinite trees we study the power of deterministic and nondeterministic generalized tree automata and prove that deterministic and nondeterministic bottom up automata accept the same class we prove also that nondeterministic top down and bottom up generalized automata have the same power we give various characterizations of the monadic second order theory of the tree in terms of tree automata and tree grammars we consider different types of extensions of muller mcnaughton s theorem but unfortunately not all the extensions of it are possible

nonlinear control via approximate input output linearization the ball and beam example approximate input output linearization of nonlinear systems which fail to have a well defined relative degree is studied for such systems a method for constructing approximate systems that are input output linearizable is provided the analysis presented is motivated through its application to a common undergraduate control laboratory experiment the ball and beam where it is shown to be more effective for trajectory tracking than the standard jacobian linearization

syntactic study of recognizable parts of infinite words resume cet article est le deuxieme volet d une etude concernant l extension de la theorie des varietes de eilenberg aux mots infinis a chaque variete de semigroupes v on associe trois classes de parties reconnaissables de mots infinis v v et v s les deux premieres liees a la nature des automates ont fait l object d une etude anterieure le present article est consacre a la classe v s nous montrons qu elle est liee a la syntaxe des parties est decidable avec v et peut se preter a d agreables descriptions comme dans le cas des parties localement testables ou testables par morceaux

robust discrete time iterative learning control for nonlinear systems with varying initial state shifts this note is concerned with the robust discrete time iterative learning control ilc design for nonlinear systems with varying initial state shifts a two gain ilc law is considered using a 2d analysis approach sufficient conditions are derived to guarantee both convergence of the learning process for fixed initial condition and boundedness of the tracking error for variable initial condition it is shown that the error data with anticipation in time can well handle the varying initial state shifts in discrete time ilc

analysis of iterative learning control for a class of nonlinear discrete time systems abstract an output feedback iterative learning control scheme is proposed for a class of nonlinear discrete time systems in the presence of direct transmission from system inputs to outputs the convergence condition of the iterative learning control scheme is analyzed the effectiveness of suggested discrete time iterative learning control algorithm is demonstrated with a single link robotic manipulator as the illustrative example 1997 elsevier science ltd

a sequence of finite dimensional controllers for repetitive control of positive real systems in this paper we analyze the performance of positive real plants coupled with a progressively increasing number of harmonic oscillators we prove that as the number of oscillators tends to infinity thus covering the all frequency range the steady state output weakly converges to the periodic signal to be tracked on the basis of this result we next show that under a suitable constraint on the signal to be tracked strong convergence is actually achieved

topological characterizations of infinite tree languages abstract in this paper we define several types of acceptance of finite automata for infinite trees and study the topological properties of the tree languages accepted thereby as a consequence we show that the two classes of tree languages accepted by nondeterministic tree automata in the following two types of acceptance coincide 1 1 an infinite tree is accepted iff there is a run for such that on each path an accepting state is contained 2 2 an infinite tree is accepted iff every run for contains an accepting state

a discrete time learning control algorithm for a class of linear time invariant systems a discretized version of the d type learning control algorithm is presented for a mimo linear discrete time system a necessary and sufficient condition for uniform convergence of the proposed learning algorithm is presented then we prove that the same condition is sufficient for the global robustness of the proposed learning algorithm to state disturbances measurement noise at the output and reinitialization error are present at each iteration a numerical example is given to illustrate the results

infinite word languages and continuous mappings abstract languages with infinite words have often been studied as subsets of a topological space the topology used for this purpose was always the natural topology of sequences this paper suggests that another topology may be more useful it is obtained by taking lim w as the derived set of w the resulting topological space is shown to be completely regular strongly zero dimensional and not normal the languages appearing in the theory of automata are shown to be closely related to functionally closed sets continuous inverse images of the set 0 as a consequence a number of known results can be expressed and proved in terms of continuous mappings

various hierarchies of wω regular sets barua 1992 studied a hierarchy rn n 1 2 3 where rn is a class of regular sets which are decomposed into n rational g sets forming a decreasing sequence on the other hand kaminski 1985 defined a hierarchy bm m 1 2 3 where bm is a class of regular sets which are decomposed into 2m rational g sets not necessarily forming a decreasing sequence we prove that r2n bn in spite of the difference of defining conditions

brief robust learning control for a class of nonlinear systems with periodic and aperiodic uncertainties this paper addresses the robust learning control problem for a class of nonlinear systems with structured periodic and unstructured aperiodic uncertainties a recursive technique is proposed which extends the backstepping idea to the robust repetitive learning control systems a learning evaluation function instead of a lyapunov function is formulated as a guideline for derivation of the control strategy which guarantees the asymptotic stability of the tracking system a design example is given

adaptive tracking for periodically time varying and nonlinearly parameterized systems using multilayer neural networks this brief addresses the problem of designing adaptive neural network tracking control for a class of strict feedback systems with unknown time varying disturbances of known periods which nonlinearly appear in unknown functions multilayer neural network mnn and fourier series expansion fse are combined into a novel approximator to model each uncertainty in systems dynamic surface control dsc approach and integral type lyapunov function ilf technique are combined to design the control algorithm the ultimate uniform boundedness of all closed loop signals is guaranteed the tracking error is proved to converge to a small residual set around the origin two simulation examples are provided to illustrate the feasibility of control scheme proposed in this brief

a list of arithmetical structures complete with respect to the first order definability a structure with base set n is complete with respect to the first order definability in the class of arithmetical structures if and only if the operations are definable in it a list of such structures is presented although structures with pascal s triangles modulo n are preferred a little an effort was made to collect as many simply formulated results as possible

newton method based iterative learning control for discrete non linear systems significant progress has been achieved in terms of both theory and industrial applications of iterative learning control ilc in the past decade however the techniques of solving non linear ilc problems are still under development the main result of this paper is a novel non linear ilc algorithm that utilizes the capability of the newton method by setting up links between non linear ilc problems and non linear multivariable equations the newton method is introduced into the ilc framework the implementation of the new algorithm allows one to decompose a nonlinear ilc problem into a sequence of linear time varying ilc problems simulations on a discrete non linear system and a manipulator model display its advantages conditions for its semi local convergence are analysed links of ilc with existing non linear topics are pointed out as ways to construct new non linear ilc schemes potential improvements are discussed for future work

topological properties of omega context free languages abstract this paper is a study of topological properties of omega context free languages cfl we first extend some decidability results for the deterministic ones dcfl proving that one can decide whether an dcfl is in a given borel class or in the wadge class of a given regular language we prove that cfl exhaust the hierarchy of borel sets of finite rank and that one cannot decide the borel class of an cfl giving an answer to a question of lescow and thomas a decade of concurrency springer lecture notes in computer science vol 803 springer berlin 1994 pp 583 621 we give also a partial answer to a question of simmonet automates et theorie descriptive ph d thesis universite paris 7 march 1992 about omega powers of finitary languages we show that buchi landweber s theorem cannot be extended to even closed cfl in a gale stewart game with a closed cfl winning set one cannot decide which player has a winning strategy from the proof of topological properties we derive some arithmetical properties of cfl

a new fuzzy logic learning control scheme for repetitive trajectory tracking problems in this paper we consider repeatable tracking control tasks using a new control approach pd type fuzzy logic learning control fllc fllc integrates two main control strategies fuzzy logic control as the basic control part and learning control as the refinement part the new fllc is constructed by simply adding an iterative learning mechanism to a fuzzy pd controller the incorporation of the learning function into fuzzy pd controllers ensures exact tracking because it completely nullifies the effects of reference signal and periodic disturbances on the tracking error through the rigorous proof based on energy function and functional analysis we show that the proposed fllc system achieves the following novel properties 1 the tracking error sequence converges uniformly to zero 2 learning control sequence converges to the desired control profile almost everywhere

a composite energy function based learning control approach for nonlinear systems with time varying parametric uncertainties a new learning control approach is developed in this note to address a class of nonlinear systems with time varying parametric uncertainties the concept of composite energy function cef which provides the system information along both time and learning repetition horizons is introduced in the analysis of learning control cef consists of two parts the first part is a standard lyapunov function which is used to access system behavior along time horizon during each learning cycle the second part is an l sup 2 norm of parametric learning errors which reflects the variation of the system status when the control system is updated on the basis of learning cycles the proposed learning control algorithm achieves asymptotical convergence along a learning repetition horizon at the same time the boundedness and pointwise convergence of the tracking error along time horizon is guaranteed the proposed learning control strategy is applicable to quite general classes of nonlinear systems without requiring the global lipschitz continuity condition and zero relative degree condition

iterative learning control design based on composite energy function with input saturation in this work an iterative learning control scheme is designed for a class of nonlinear uncertain systems with input saturation the analysis of convergence in the iteration domain is based on composite energy function which consists of both input and state information along the time and iteration axes through rigorous analysis the learning convergence in the iteration domain can be guaranteed under the input saturation provided the desired trajectory is realizable within the saturation bound

a hierarchy of sets of infinite trees a hierarchy of sets of infinite valued trees is introduced which has no counterpart in the theory of sets of infinite strings languages as a consequence we obtain that for sets of infinite trees an analogue of mcnaughton s fundamental theorem on languages does not hold

finite acceptance of infinite words abstract in this paper we consider the following two types of finite acceptance of infinite words by finite automata an infinite word is accepted if and only if there is a run on input for which 1 1 an accepting state is visited at least once or 2 2 an accepting state is visited at least once but only finitely often the resulting classes of regular languages are characterized by language theoretic means and they are positioned into the known hierarchies of regular languages