fair derivations in context free grammars this paper connects between notions of pure formal language theory and nondeterministic programming the notion of a fair derivation in a context free grammar is defined whereby for every variable appearing infinitely often in sentential forms of an infinite derivation each of its rules is used infinitely often a context free language is fairly generated if it has a grammar all of whose fair derivations are finite it is proved that a context free grammar is fairly terminating iff it is non expansive

the m calculus as an assertion language for fairness arguments abstract various principles of proof have been proposed to reason about fairness this paper addresses for the first time the question in what formalism such fairness arguments can be couched to wit we prove that park s monotone first order calculus augmented with constants for all recursive ordinals can serve as an assertion language for proving fair termination of do loops in particular the weakest precondition for fair termination of a loop w r t some postcondition is definable in it the relevance of this result to proving eventualities in the temporal logic formalism of manna and pnuelis in foundations of computer science iv part 2 math centre tracts vol 159 math centrum amsterdam 1983 is discussed

a survey of adaptive fuzzy controllers nonlinearities and classifications adaptive fuzzy controllers afcs i e fuzzy controllers using heuristic expert knowledge and equipped with adaption ability are widely used in the industry in the present days as they are capable of dealing with ill formulated nonlinear systems where exact mathematical formulas are not known or partially described nonlinear systems afcs have been widely deployed to control many nonlinear systems with different types of critical nonlinearities over the last two decades many different approaches toward adaptive fuzzy control have been reported in this paper we recapitulate the latest research works related to afcs and provide an up to date survey on the latest development made in adaptive fuzzy control theory and applications based on different types of fuzzy systems considered and nonlinearities associated with the nonlinear system to be controlled we categorize the different approaches based on different types of nonlinearities and consider basic nonlinear systems nonlinear systems with external disturbances nonlinear systems with some special type of nonlinearities nonaffine nonlinear systems and strict feedback nonlinear systems it turns out that many existing methods are subject to various limitations and none of them is capable of controlling a general nonlinear systems hence it is still an open problem to design and develop a universal afc for a general class of nonlinear systems

adaptive fuzzy output feedback control for mimo switched nonlinear systems with prescribed performances abstract this paper proposes an adaptive fuzzy output feedback control approach for a class of uncertain multiple input and multiple output mimo switched nonlinear systems with prescribed performance and immeasurable states in this research fuzzy logic systems are used to identify the unknown nonlinear functions a fuzzy switched state observer is established to observe the unmeasured states based on backstepping technique and the prescribed performance theory a new adaptive fuzzy control method with prescribed performance is developed it is proved that the proposed control approach can ensure that all the signals of the resulting closed loop system are bounded and the tracking errors are within the prescribed performance bounds for all times simulation studies illustrate the effectiveness of the proposed approach

nonsingular terminal sliding mode control of robot manipulators using fuzzy wavelet networks this paper presents an adaptive nonsingular terminal sliding mode ntsm tracking control design for robotic systems using fuzzy wavelet networks compared with linear hyperplane based sliding control terminal sliding mode controller can provide faster convergence and higher precision control therefore a terminal sliding controller combined with the fuzzy wavelet network which can accurately approximate unknown dynamics of robotic systems by using an adaptive learning algorithm is an attractive control approach for robots in addition the proposed learning algorithm can on line tune parameters of dilation and translation of fuzzy wavelet basis functions and hidden to output weights therefore a robust control law is used to eliminate uncertainties including the inevitable approximation errors resulted from the finite number of fuzzy wavelet basis functions the proposed controller requires no prior knowledge about the dynamics of the robot and no off line learning phase moreover both tracking performance and stability of the closed loop robotic system can be guaranteed by lyapunov theory finally the effectiveness of the fuzzy wavelet network based control approach is illustrated through comparative simulations on a six link robot manipulator

infinite trees markings and well foundedness abstract a necessary and sufficient condition for a given marked tree to have no infinite paths satisfying a given formula is presented the formulas are taken from a language introduced by harel covering a wide scale of properties of infinite paths including most of the known notions of fairness this condition underlies a proof rule for proving that a nondeterministic program has no infinite computations satisfying a given formula interpreted over state sequences we also show two different forms of seemingly more natural necessary and sufficient conditions to be inadequate

robust impedance control of robot manipulators using differential equations as universal approximator abstractthis paper presents a robust impedance controller for robot manipulators using function approximation techniques fat recently some fat based robust impedance control approaches have been presented using fourier series expansion or legendre polynomials for uncertainty estimation however the dimensions of regressor matrices in these approaches are relatively large this problem becomes hypersensitive especially for higher degree of freedom robot manipulators in this paper a simpler and less computational fat based robust controller is presented without considering discontinuous nonlinearities it is assumed that the lumped uncertainty can be modeled by a linear differential equation with unknown coefficients then using stone weierstrass theorem it is verified that these differential equations are universal approximators the advantage of proposed controller in comparison with previous related works is reducing the dimensions of regressor matrices simulation results on a puma560 robot man

probabilistic termination versus fair termination note abstract in this note we show that probabilistic termination of concurrent programs is in many cases much simpler than the fair one for a wide class of definitions of probabilistic termination we may express termination by 0 2 arithmetic formula whereas the fair termination can be expressed only by second order arithmetic formula proof of fair termination usually needs induction on recursive ordinals but proof of probabilistic termination has the complexity equivalent to that of deterministic program termination

adaptive fuzzy terminal sliding mode control for a class of mimo uncertain nonlinear systems this paper presents a new adaptive terminal sliding mode tracking control design for a class of nonlinear systems using fuzzy logic system the terminal sliding mode control tsm was developed to provide faster convergence and higher precision control than the linear hyperplane based sliding control however the original tsm encountered singularity problem with discontinuous control action moreover a prior knowledge about the plant to be controlled is required the proposed controller combines a continuous non singular tsm with an adaptive learning algorithm and fuzzy logic system to estimate the dynamics of the controlled plant so that closed loop stability and finite time convergence of tracking errors can be guaranteed the performance of the proposed control strategy is evaluated through the control of a two link rigid robotic manipulator finally the effectiveness of the proposed scheme is demonstrated through the control of the ankle and knee movements in paraplegic subjects using functional electrical stimulation simulation and experimental results verify that the proposed control strategy can achieve favorable control performance with regard to system parameter variations and external disturbances 2011 elsevier b v all rights reserved

adaptive fuzzy control of a class of mimo nonlinear systems this paper presents two indirect adaptive fuzzy control schemes for a class of uncertain continuous time multi input multi output nonlinear dynamic systems within these schemes fuzzy systems are employed to approximate the plant s unknown nonlinear functions and robustifying control terms are used to compensate for approximation errors by using a regularized matrix inverse a stable well defined adaptive controller is firstly investigated then in order to obtain an adaptive controller not depending upon any parameter initialization conditions and to relax the requirement of bounding parameter values a second adaptive controller is proposed all parameter adaptive laws and robustifying control terms are derived based on lyapunov stability analysis so that under appropriate assumptions semi global stability and asymptotic convergence to zero of tracking errors can be guaranteed simulations performed on a two link robot manipulator illustrate the approach and exhibit its performance

commuting and stable feedback design for switched linear systems abstract in the paper commuting and stable feedback design for switched linear systems is investigated this problem is formulated as to build up suitable state feedback controller for each subsystem such that the closed loop systems are not only asymptotically stable but also commuting each other a new concept common admissible eigenvector set caes is introduced to establish necessary sufficient conditions for commuting and stable feedback controllers for second order systems a necessary and sufficient condition is established moreover a parametrization of the caes is also obtained the motivation comes from stabilization of switched linear systems which consist of a family of lti systems and a switching law specifying the switching between them where if all the subsystems are stable and commuting each other then the total system is stable under arbitrary switching

adaptive fuzzy tracking control of nonlinear mimo systems with time varying delays this paper focuses on the problem of adaptive fuzzy tracking control for a class of nonlinear multi input and multi output mimo time delay systems in strict feedback form the time delays in the systems may be time varying based on razumikhin functional method the state feedback adaptive fuzzy tracking controllers are constructed via backstepping technique the proposed adaptive fuzzy controllers guarantee that all the signals in the closed loop system are bounded and the system s outputs converge to a small neighborhood of the reference signals three examples are used to illustrate the effectiveness of the proposed approach

a proof rule for fair termination of guarded commands we present a proof rule for fairly terminating guarded commands based on a well foundedness argument the rule is applied to several examples and proved to be sound and semantically complete w r t an operational semantics of computation trees the rule is related to another rule suggested by lehmann pnueli and stavi in proc internat colloq automata lang and programming 81 acre july 1981 by showing that the semantic completeness of the lps rule follows from the completeness or ours

observer based fuzzy adaptive control for multi input multi output nonlinear systems with a nonsymmetric control gain matrix and unknown control direction in this study we present an observer based fuzzy adaptive control scheme for a class of uncertain multi input multi output nonlinear systems with a nonsymmetric control gain matrix unknown control direction and unmeasured states in this scheme fuzzy systems are used to approximate the unknown nonlinear functions and an adaptive fuzzy state observer is designed to estimate the unmeasured states the parameter adaptive laws are designed by fuzzy basis functions rather than by its filtering and a robust control term is used to compensate for the lumped errors the proposed method solves the problem of the nonsymmetric control gain matrix and it requires no a priori knowledge of the control direction for the states that are unmeasured we prove that all of the signals in the resulting closed loop systems are bounded and that the tracking errors converge asymptotically to zero two simulation examples are used to demonstrate the effectiveness of the proposed scheme

optimal guaranteed cost sliding mode control of interval type 2 fuzzy time delay systems this paper is concerned with the optimal guaranteed cost sliding mode control problem for interval type 2 it2 takagi sugeno fuzzy systems with time varying delays and exogenous disturbances in the presence of the uncertain parameters hidden in membership functions an adaptive method is presented to handle the time varying weight coefficients reflecting the change of the uncertain parameters a new integral sliding surface is presented based on the system output by designing a novel adaptive sliding mode controller system perturbation or modeling error can be compensated and the reachability of the sliding surface can be guaranteed with the ultimate uniform boundedness of the closed loop system optimal conditions of an mathcal h 2 guaranteed cost function and an mathcal h infty performance index are established for the resulting time delay control system finally an inverted pendulum system represented by the it2 fuzzy model is applied to illustrate the advantages and effectiveness of the proposed control scheme

adaptive fuzzy hierarchical sliding mode control for the trajectory tracking of uncertain underactuated nonlinear dynamic systems the trajectory tracking of uncertain underactuated nonlinear dynamic systems is tackled by an adaptive fuzzy hierarchical sliding mode control afhsmc first one of the subsystems is assigned as the first layer sliding surface next a second layer sliding surface from the first layer sliding surface and the sliding surface of another subsystem is constructed in this paper the nth layer is supposed to be the top layer or hierarchical layer for including the sliding surfaces of all subsystems because two nonlinear system functions and the time varying external disturbance of each subsystem are supposed to be unknown different online fuzzy models are employed to approximate these nonlinear system functions and the upper bounded functions of external disturbances moreover the upper bound of uncertainties caused by these fuzzy modeling errors is estimated online based on these learning fuzzy models and the estimated upper bound of these modeling errors an afhsmc is developed the stability analysis and tracking performance of the closed loop system are verified by lyapunov stability theory finally two simulation examples including different amplitudes of external disturbance and comparison with hierarchical sliding mode control confirm the effectiveness and robustness of the proposed control

robust tracking observer based adaptive fuzzy control design for uncertain nonlinear mimo systems with time delayed states this paper addresses the problem of designing robust observer based adaptive fuzzy tracking control scheme for a class of mimo nonlinear systems with plant uncertainties time delayed uncertainties and external disturbances a fuzzy logic system fls is utilized to approximate the unknown nonlinear functions and an adaptive fuzzy observer is introduced for state estimations the proposed control law is based on indirect adaptive fuzzy control and uses two on line estimations this allows for the simultaneous inclusion of identifying gains of the delayed state uncertainties and training of the weights of the fuzzy system by introducing estimated error vectors the advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with online update laws the adaptive fuzzy tracking control using variable structure vs control technique is derived based on lyapunov criterion and the riccati inequality to resolve system uncertainties time delayed uncertainties and external disturbances this is done in such a way that all states of the system are bounded and the h tracking performance is achieved finally a two connected inverted pendulums on carts system liu et al 2011 29 is used for simulation purposes and some comparisons are given to illustrate the validity and effectiveness of the proposed method

interpretations of recursion under unbounded nondeterminacy abstract a language is constructed that supports arbitrary atomic statements composition alternatives and mutual recursion in the presence of unbounded nondeterminacy the concept of interpretation is defined axiomatically by operational means a standard interpretation is constructed which is proved to be the smallest interpretation with respect to the egli milner ordering the corresponding weakest precondition and weakest liberal precondition are characterized as smallest and largest preparator functions we characterize the interpretations which upon divergence cannot deliver unjustified meaningful values these interpretations form a spectrum that ranges from standard semantics over various forms of fair semantics to the so called friendly semantics where error is signalled only if divergence can become inevitable after finitely many steps we determine the corresponding preparator functions

adaptive control for a class of uncertain strict feedback nonlinear systems based on a generalized fuzzy hyperbolic model in this study we propose an effective method for designing an adaptive controller for a class of uncertain strict feedback nonlinear systems with unknown bounded disturbances during the controller design process all of the unknown functions are accumulated at the intermediate steps to approximate the last step in addition only one generalized fuzzy hyperbolic model is used to approximate the total unknown functions for the system thus only the actual control law needs to be implemented and one adaptive law is proposed for the overall controller design process as a result the controller design is much simpler and the computational burden is reduced greatly using lyapunov techniques we obtain the uniformly ultimately bounded stability of all the signals for the closed loop system our simulation results verified the theoretical analysis and they illustrated the superior performance of the method proposed in this study

effective transformations on infinite trees with applications to high undecidability dominoes and fairness elementary translations between various kinds of recursive trees are presented it is shown that trees of either finite or countably infinite branching can be effectively put into one one correspondence with infinitely branching trees in such a way that the infinite paths of the latter correspond to the p abiding infinite paths of the former here p can be any member of a very wide class of properties of infinite paths for many properties the converse holds too two of the applications involve a the formulation of large classes of highly undecidable variants of classical computational problems and in particular easily describable domino problems that are iii 1 1 complete and b the existence of a general method for proving termination of nondeterministic or concurrent programs under any reasonable notion of fairness

deadlock and fairness in morphisms of transition systems in order to investigate deadlock free implementations of processes a formalization is proposed in which processes are elements of transition systems morphisms of transition systems are introduced as an approximate formalization of implementation of processes a morphism f x y shows deadlock if there is an implementing process x x such that x has no transitions and that the implemented process f x y has transitions the morphism is called strict if the implementing processes x provide all transitions of the implemented processes f x strict morphisms are used to clarify the problem of a universal domain of processes in which bisimilar processes are identified to talk of fairness the alphabet of actions is structured by a family bj j j of subsets each subset bj formalizes one component process which is to be treated fairly infinitely many components are admitted a morphism f x y is said to be fair if every execution sequence in the transition system x such that set bj is enabled infinitely many times by the image sequence in y activates set bj infinitely many times for a given transition system y we construct a family of fair and deadlock free morphisms to y which is universal in a well defined sense this construction is applied to the fair communicating merge of a family of processes

adaptive fuzzy control for mimo nonlinear systems with nonsymmetric control gain matrix and unknown control direction in this paper an indirect adaptive fuzzy control scheme is developed for a class of uncertain multi input multi output nonlinear systems with nonsymmetric control gain matrix and unknown control direction the nonsymmetric control gain matrix is expressed as the sum of a symmetric matrix and a skew symmetric matrix and the symmetric matrix as well as the skew symmetric matrix is approximated by fuzzy systems by using the symmetric matrix decomposition technique the estimated symmetric matrix is decomposed into the product of one diagonal matrix and two orthogonal matrixes based on the decomposition results the adaptive fuzzy controller is developed to avoid the possible singularity problem and the parameter initialization problem a robust control term is employed to compensate for the lumped errors and a nussbaum type function is incorporated in the robust control term to deal with the unknown control direction the proposed scheme guarantees that all the signals in the resulting closed loop system are bounded and that the tracking errors converge asymptotically to zero two simulation examples are used to demonstrate the effectiveness of the proposed scheme

adaptive fuzzy control for feedback linearizable mimo nonlinear systems with prescribed performance abstract in this paper a new adaptive fuzzy control scheme with prescribed performance is developed for a class of feedback linearizable uncertain mimo nonlinear systems with unknown control direction and external disturbances the fuzzy systems are employed to approximate the unknown nonlinear functions and a nussbaum type function is applied to resolve the unknown control direction problems by using the prescribed performance bounds an adaptive fuzzy controller equipped with the nussbaum type gain function is developed the proposed design scheme guarantees that all the signals in the closed loop systems are bounded and that the tracking errors converge to a prescribed performance bounds by guaranteeing the convergence of the filtered tracking error to a predefine performance bounds two simulation examples are used to demonstrate the effectiveness of the proposed scheme

ten years of hoare s logic a survey part ii nondeterminism a survey of various results concerning the use of hoare s logic in proving correctness of nondeterministic programs is presented various proof systems together with the example proofs are given and the corresponding soundness and completeness proofs of the systems are discussed programs allowing bounded and countable nondeterminism are studied proof systems deal with partial and total correctness freedom of failure and the issue of fairness the paper is a continuation of part i by apt 1981 where various results concerning hoare s approach to proving correctness of sequential programs are presented