technical communique differential geometric condition for feedback complete linearization of stochastic nonlinear system necessary and sufficient condition is obtained for the feedback complete linearization problem for stochastic nonlinear systems

bilateral locally testable languages we give an algebraic characterization of a new variety of languages that will be called bilateral locally testable languages and denoted as blt given k 0 the membership of a word x to a blt k bt language can be decided by means of exploring the segments of length k of x as well as considering the order of appearance of those segments when we scan the prefixes and the suffixes of x in this paper we also characterize the syntactic semigroup of blt languages in terms of the equations of the variety they belong to as well as in terms of the join of two previously studied varieties

on constructing constrained control lyapunov functions for linear systems this works considers the problem of control of linear systems with input constraints the notion of control lyapunov functions clfs is first generalized and relaxed to define a constrained control lyapunov function cclf and a constructive procedure for cclf is subsequently presented

on locally reversible languages there exist several works that study the class of reversible languages defined as the union closure of 0 reversible languages their properties and suitable representations in this work we define and study the class of locally reversible languages defined as the union closure of k reversible languages we characterize the class and prove that it is a local positive variety of formal languages we also extend the definition of quasi reversible automata to deal with locally reversible languages and propose a polynomial algorithm to obtain for any given locally k reversible language a quasi k reversible automaton

a framework for robustness analysis of constrained finite receding horizon control a framework for robustness analysis of input constrained finite receding horizon control is presented under the assumption of quadratic upper bounds on the finite horizon costs we derive sufficient conditions for robust stability of the standard discrete time linear quadratic receding horizon control formulation this is achieved by recasting conditions for nominal and robust stability as an implication between quadratic forms lending itself to s procedure tools which are used to convert robustness questions to tractable convex conditions robustness with respect to plant model mismatch as well as for state measurement error is shown to reduce to the feasibility of linear matrix inequalities simple examples demonstrate the approach

percolation of arbitrary words in 0 1 mathbb n let g be a possibly directed locally finite graph with countably infinite vertex set v let x v be an i i d family of random variables with p x 1 1 p x 0 p finally let 1 2 be a generic element of 0 1 n such a is called a word we say that the word is seen from the vertex if there exists a self avoiding path 1 2 on g starting at and such that x i i for i 1 the traditional problem in site percolation is whether p 1 1 1 is seen from 0 so called ab percolation occurs if p 1 0 1 0 1 0 is seen from 0 here we investigate a whether p all words are seen from 0 for a fixed and b whether p all words are seen from some 1 we show that both answers are positive if g z d or even z d with all edges oriented in the positive direction when d is sufficiently large we show that on the oriented z 3 the answer to a is negative but we do not know the answer to b on z 3 various graphs g are constructed almost all of them trees for which the set of words which can be seen from a given or from some is large even though it is w p 1 not the set of all words

global predictive regulation of null controllable input saturated linear systems a predictive regulator is described for stabilizing linear plants subject to polyhedral input constraints while the asymptotic stability of general linear plants is ensured subject to a set membership condition on the initial state global asymptotic and semiglobal exponential regulation is achieved for input saturated plants which are asymptotically null controllable with bounded inputs the design knobs of the regulator can be chosen off line so as to compromise between nonconservative regulation performance and computational complexity and an online optimization problem of prequantifiable numerical burden results

nonlinear stochastic receding horizon control stability robustness and monte carlo methods for control approximation this work considers the stability of nonlinear stochastic receding horizon control when the optimal controller is only computed approximately a number of general classes of controller approximation error are analysed including deterministic and probabilistic errors and even controller sample and hold errors in each case it is shown that the controller approximation errors do not accumulate even over an infinite time frame and the process converges exponentially fast to a small neighbourhood of the origin in addition to this analysis an approximation method for receding horizon optimal control is proposed based on monte carlo simulation this method is derived via the feynman kac formula which gives a stochastic interpretation for the solution of a hamilton jacobi bellman equation associated with the true optimal controller it is shown and it is a prime motivation for this study that this particular controller approximation method practically stabilises the underlying nonlinear process

robust controller design for stochastic nonlinear systems via convex optimization this paper presents a new nonlinear control design framework called convex optimization based stochastic steady state tracking error minimization cvstem for a class of ito stochastic nonlinear systems including stochastic lagrangian systems this state feedback controller design involves the use of multiple state dependent coefficient sdc models of a nonlinear system equation and computes its controller parameters by solving a convex optimization problem in order to minimize an upper bound of the steady state tracking error this problem is shown to be equivalent to the original nonlinear optimization problem of minimizing the upper bound the exponential stability and robustness properties due to the state dependent riccati inequality are proven using stochastic contraction analysis discrete time stochastic incremental contraction analysis with respect to a state and time dependent metric is also presented along with its explicit connection to continuous time contraction analysis a result of simulation is used to validate the superiority of the proposed controller compared to a known nonlinear controller a pid controller and an h infinity controller

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

brief a receding horizon approach to the nonlinear h control problem the receding horizon rh methodology is extended to the design of a robust controller of h type for nonlinear systems using the nonlinear analogue of the fake h algebraic riccati equation we derive an inverse optimality result for the rh schemes for which increasing the horizon causes a decrease of the optimal cost function this inverse optimality result shows that the input output map of the closed loop system obtained with the rh control law has a bounded l 2 gain robustness properties of the nonlinear h control law in face of dynamic input uncertainty are considered

constrained stochastic lqc a tractable approach despite the celebrated success of dynamic programming for optimizing quadratic cost functions over linear systems such an approach is limited by its inability to tractably deal with even simple constraints in this paper we present an alternative approach based on results from robust optimization to solve the stochastic linear quadratic control slqc problem in the unconstrained case the problem may be formulated as a semidefinite optimization problem sdp we show that we can reduce this sdp to optimization of a convex function over a scalar variable followed by matrix multiplication in the current state thus yielding an approach that is amenable to closed loop control and analogous to the riccati equation in our framework we also consider a tight second order cone socp approximation to the sdp that can be solved much more efficiently when the problem has additional constraints both the sdp and socp are tractable in the presence of control and state space constraints moreover compared to the riccati approach they provide much greater control over the stochastic behavior of the cost function when the noise in the system is distributed normally

approximating grammar probabilities solution of a conjecture it is proved that the production probabilities of a probabilistic context free grammar may be obtained as the limit of the estimates inferred from an increasing sequence of randomly drawn samples from the language generated by the grammar

the equivalence between infinite horizon optimal control of stochastic systems with exponential of integral performance index and stochastic differential games a new method based on the theory of large deviations from the invariant measure is introduced for the analysis of stochastic systems with an infinite horizon exponential of integral performance index it is shown that the infinite horizon optimal exponential of integral stochastic control problem is equivalent to a stationary stochastic differential game for an auxiliary system as an application of the developed technique the infinite horizon risk sensitive lqg problem is analyzed for both the completely observed and partially observed case

polynomial time identification of very simple grammars from positive data this paper concerns a subclass of simple deterministic grammars called very simple grammars and studies the problem of identifying the subclass in the limit from positive data the class of very simple languages forms a proper subclass of simple deterministic languages and is incomparable to the class of regular languages this class of languages is also known as the class of left szilard languages of context free grammars after providing some properties of very simple languages we show that the class of very simple grammars is polynomial time identifiable in the limit from positive data in the following sense that is we show that there effectively exists an algorithm that given a target very simple grammar g over alphabet identifies a very simple grammar g equivalent to g in the limit from positive data satisfying the property that the time for updating a conjecture is bounded by o m and the total number of prediction errors made by the algorithm is bounded by o n where n is the size of g m max n 1 3 and n is the total length of all positive data provided

generalized terminal state constraint for model predictive control a terminal state equality constraint for model predictive control mpc laws is investigated where the terminal state input pair is not fixed a priori but it is a free variable in the optimization the approach named generalized terminal state constraint can be used for both tracking mpc i e when the objective is to track a given steady state and economic mpc i e when the objective is to minimize a cost function which does not necessarily attains its minimum at a steady state it is shown that the proposed technique provides in general a larger feasibility set with respect to the existing approaches given the same prediction horizon moreover a new receding horizon strategy is introduced exploiting the generalized terminal state constraint under mild assumptions the new strategy is guaranteed to converge in finite time with arbitrarily good accuracy to an mpc law with an optimally chosen terminal state constraint while still enjoying a larger feasibility set the features of the new technique are illustrated by an inverted pendulum example in both the tracking and the economic contexts

lyapunov based model predictive control of stochastic nonlinear systems in this work we design a lyapunov based model predictive controller lmpc for nonlinear systems subject to stochastic uncertainty the lmpc design provides an explicitly characterized region from where stability can be probabilistically obtained the key idea is to use stochastic lyapunov based feedback controllers with well characterized stabilization in probability to design constraints in the lmpc that allow the inheritance of the stability properties by the lmpc the application of the proposed lmpc method is illustrated using a nonlinear chemical process system example

learning in varieties of the form v li from positive data grammatical inference and finite semigroup theory are continuously developing nevertheless it seems that they are not interacting too much we propose in this paper an inference method for languages that belong to varieties of the form v li many well known families of languages like locally testable reversible dot depth one etc are of that form the method unifies existing algorithms for inference of some of those families and can be applied to some others that had not been inferred yet it uses a result about the cascade product in which one of the factors is a transducer and the second is the automaton obtained by inferring the base case of the family using the transduction of the sample as input

stabilization of nonlinear systems with state and control constraints using lyapunov based predictive control this work considers the problem of stabilization of nonlinear systems subject to state and control constraints for cases where the state constraints need to be enforced at all times hard constraints and where they can be relaxed for some time soft constraints we propose a lyapunov based predictive control design that guarantees stabilization and state and input constraint satisfaction for all times from an explicitly characterized set of initial conditions an auxiliary lyapunov based analytical bounded control design is used to characterize the stability region of the predictive controller and also provide a feasible initial guess to the optimization problem in the predictive controller formulation for the case when the state constraints are soft we propose a switched predictive control strategy that reduces the time during which state constraints are violated driving the states into the state and input constraints feasibility region of the lyapunov based predictive controller we demonstrate the application of the lyapunov based predictive controller designs through a chemical process example

output feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance abstract we address the class of stochastic output feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori this problem is analogous to deterministic disturbance attenuation problems we first design a controller which guarantees that the solutions converge in probability to a residual set proportional to the unknown bound on the covariance then for the case of a vanishing noise vector field we design an adaptive controller which besides global stability in probability guarantees regulation of the state of the plant to zero with probability one

stabilization in probability of nonlinear stochastic systems with guaranteed region of attraction and target set we deal with nonlinear dynamical systems consisting of a linear nominal part perturbed by model uncertainties nonlinearities and both additive and multiplicative random noise modeled as a wiener process in particular we study the problem of finding suitable measurement feedback control laws such that the resulting closed loop system is stable in some probabilistic sense to this aim we introduce a new notion of stabilization in probability which is the natural counterpart of the classical concept of regional stabilization for deterministic nonlinear dynamical systems and stands as an intermediate notion between local and global stabilization in probability this notion requires that given a target set a trajectory starting from some compact region of the state space containing the target remains forever inside some larger compact set eventually enters any given neighborhood of the target in finite time and remains thereinafter all these events being guaranteed with some probability we give a lyapunov based sufficient condition for achieving stability in probability and a separation result which splits the control design into a state feedback problem and a filtering problem finally we point out constructive procedures for solving the state feedback and filtering problem with arbitrarily large region of attraction and arbitrarily small target for a wide class of nonlinear systems which at least include feedback linearizable systems the generality of the result is promising for applications to other classes of stochastic nonlinear systems in the deterministic case our results recover classical stabilization results for nonlinear systems

receding horizon control of nonlinear systems the receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems the method is especially useful for the control of slow nonlinear systems such as chemical batch processes where it is possible to solve sequentially open loop fixed horizon optimal control problems online the method has been shown to yield a stable closed loop system when applied to time invariant or time varying linear systems it is shown that the method also yields a stable closed loop system when applied to nonlinear systems

stochastic receding horizon control of constrained linear systems with state and control multiplicative noise we develop a receding horizon control approach to stochastic linear systems with control and state multiplicative noise that also contain constraints our receding horizon formulation is based upon an on line optimization that utilizes open loop plus linear feedback and is solved as a semi definite programming problem we also provide a characterization of stability performance and constraint satisfaction properties of the receding horizon controlled system under a specific choice of terminal weight and terminal constraint a simple numerical example is used to illustrate the approach

percolation and disorder resistance in cellular automata we rigorously prove a form of disorder resistance for a class of one dimensional cellular automaton rules including some that arise as boundary dynamics of two dimensional solidification rules specifically when started from a random initial seed on an interval of length l with probability tending to one as l the evolution is a replicator that is a region of space time of density one is filled with a spatially and temporally periodic pattern punctuated by a finite set of other finite patterns repeated at a fractal set of locations on the other hand the same rules exhibit provably more complex evolution from some seeds while from other seeds their behavior is apparently chaotic a principal tool is a new variant of percolation theory in the context of additive cellular automata from random initial states

robust receding horizon control of constrained nonlinear systems we present a method for the construction of a robust dual mode receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error the controller is dual mode in a neighborhood of the origin the control action is generated by a linear feedback controller designed for the linearized system outside this neighborhood receding horizon control is employed existing receding horizon controllers for nonlinear continuous time systems which are guaranteed to stabilize the nonlinear system to which they are applied require the exact solution at every instant of an optimal control problem with terminal equality constraints these requirements are considerably relaxed in the dual mode receding horizon controller presented in this paper stability is achieved by imposing a terminal inequality rather than an equality constraint only approximate minimization is required a variable time horizon is permitted robustness is achieved by employing conservative state and stability constraint sets thereby permitting a margin of error the resultant dual mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear constrained systems

lyapunov like techniques for stochastic stability the purpose of this paper is to study the stabilizability problem for control stochastic nonlinear systems driven by a wiener process sufficient conditions for the existence of stabilizing feedback laws that are smooth except possibly at the equilibrium point of the system are provided by means of stochastic lyapunov like techniques the notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced and the stabilization by means of dynamic controllers is studied

risk sensitive control and dynamic games for partially observed discrete time nonlinear systems solves a finite horizon partially observed risk sensitive stochastic optimal control problem for discrete time nonlinear systems and obtains small noise and small risk limits the small noise limit is interpreted as a deterministic partially observed dynamic game and new insights into the optimal solution of such game problems are obtained both the risk sensitive stochastic control problem and the deterministic dynamic game problem are solved using information states dynamic programming and associated separated policies a certainty equivalence principle is also discussed the authors results have implications for the nonlinear robust stabilization problem the small risk limit is a standard partially observed risk neutral stochastic optimal control problem

convexity and convex approximations of discrete time stochastic control problems with constraints we investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time we consider minimization of an expected value cost subject to probabilistic constraints we study the convexity of a finite horizon optimization problem in the case where the control policies are affine functions of the disturbance input we propose an expectation based method for the convex approximation of probabilistic constraints with polytopic constraint function and a linear matrix inequality lmi method for the convex approximation of probabilistic constraints with ellipsoidal constraint function finally we introduce a class of convex expectation type constraints that provide tractable approximations of the so called integrated chance constraints performance of these methods and of existing convex approximation methods for probabilistic constraints is compared on a numerical example

brief nonlinear model predictive control with polytopic invariant sets ellipsoidal invariant sets have been widely used as target sets in model predictive control mpc these sets can be computed by constructing appropriate linear difference inclusions together with additional constraints to ensure that the ellipsoid lies within a given inclusion polytope the choice of inclusion polytope has a significant effect on the size of the target ellipsoid but the optimal inclusion polytope cannot in general be computed systematically this paper shows that use of polytopic invariant sets overcomes this difficulty allowing larger stabilizable sets without loss of performance in the interests of online efficiency consideration is focused on interpolation based mpc

biprefix codes inverse semigroups and syntactic monoids of injective automata abstract we prove for injective automata an analogue of pin s result 1978 that any finite monoid divides the syntactic monoid of p for some finite prefix code p pin s result for arbitrary automata is strengthened in that we show divides can be replaced by is a subsemigroup of we give some conditions sufficient to guarantee that if a syntactic monoid is inverse then the automaton is injective a direct proof is given of reutenaur s result 1979 1981 that if the language recognized by an injective automaton is a subsemigroup then it is of the form b for some biprefix code b

lipschitz embeddings of random sequences we develop a new multi scale framework flexible enough to solve a number of problems involving embedding random sequences into random sequences grimmett et al random str algorithm 37 1 85 99 2010 asked whether there exists an increasing m lipschitz embedding from one i i d bernoulli sequence into an independent copy with positive probability we give a positive answer for large enough m a closely related problem is to show that two independent poisson processes on mathbb r are roughly isometric or quasi isometric our approach also applies in this case answering a conjecture of szegedy and of peled ann appl probab 20 462 494 2010 our theorem also gives a new proof to winkler s compatible sequences problem our approach does not explicitly depend on the particular geometry of the problems and we believe it will be applicable to a range of multi scale and random embedding problems

a sufficient condition to polynomially compute a minimum separating dfa the computation of a minimal separating automaton msa for regular languages has been studied from many different points of view from synthesis of automata or grammatical inference to the minimization of incompletely specified machines or compositional verification in the general case the problem is np complete but this drawback does not prevent the problem from having a real application in the above mentioned fields in this paper we propose a sufficient condition that guarantees that the computation of the msa can be carried out with polynomial time complexity

learning local languages and their application to dna sequence analysis this paper presents an efficient algorithm for learning in the limit a special type of regular languages called strictly locally testable languages from positive data and its application to identifying the protein spl alpha chain region in amino acid sequences first we present a linear time algorithm that given a strictly locally testable language learns its deterministic finite state automaton in the limit from only positive data this provides one with a practical and efficient method for learning a specific concept domain of sequence analysis we then describe several experimental results using the learning algorithm developed above following a theoretical observation which strongly suggests that a certain type of amino acid sequences can be expressed by a locally testable language we apply the learning algorithm to identifying the protein spl alpha chain region in amino acid sequences for hemoglobin experimental scores show an overall success rate of 95 correct identification for positive data and 96 for negative data

existence and computation of infinite horizon model predictive control with active steady state input constraints this note addresses the existence and implementation of the infinite horizon controller for the case of active steady state input constraints this case is important because in many practical applications controllers are required to operate at the boundary of the feasible region for instance in order to maximize global economic objectives for this case the usual finite horizon parameterizations with terminal cost cannot be applied and optimal solutions are not generally available we propose here an iterative algorithm that generates two finite horizon approximations to the true infinite horizon problem where the solution to one of the approximations yields an upper bound on the true optimum while the other approximation yields a lower bound we show convergence of both bounding approximations to the optimal solution as the horizon length in the approximations is increased we outline a procedure based on this result to provide a solution to the infinite horizon problem that is exact to within any user specified tolerance finally we present an example that includes a comparison between optimal and suboptimal controllers

model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints abstract robust predictive control handles constrained systems that are subject to stochastic uncertainty but propagating the effects of uncertainty over a prediction horizon can be computationally expensive and conservative this paper overcomes these issues through an augmented autonomous prediction formulation and provides a method of handling probabilistic constraints and ensuring closed loop stability through the use of an extension of the concept of invariance namely invariance with probability p

phase transition in dependent percolation in this paper we discuss two different models of dependent percolation on the graph 2 these models can be thought of as percolation in a random environment they were inspired by the work of mccoy and wu 7 8 on the ising model in a random environment as well as other models of particle systems in a random environment 9 5 6 3 we show that both models of dependent percolation exhibit phase transitions this proves a version of stability for percolation on 2 and proves a conjecture of jonasson mossel and peres 4 who proved a similar result on 3

output feedback lyapunov based predictive control of stochastic nonlinear systems this paper considers the problem of output feedback control of stochastic nonlinear systems a predictive controller is designed for which stability and feasibility in a probabilistic sense are guaranteed from an explicitly characterized region of attraction the controller s performance is characterized by its risk of allowing destabilizing system behavior since the controller design relies on certain convergence properties of the state observer a compatible stochastic high gain type observer design is also presented finally simulation results illustrating the efficacy of the design are presented

lattice embeddings in percolation does there exist a lipschitz injection of d into the open set of a site percolation process on d if the percolation parameter p is sufficiently close to 1 we prove a negative answer when d d and also when d 2 if the lipschitz constant m is required to be 1 earlier work of dirr dondl grimmett holroyd and scheutzow yields a positive answer for d d and m 2 as a result the above question is answered for all d d and m our proof in the case d d uses tucker s lemma from topological combinatorics together with the aforementioned result for d d one application is an affirmative answer to a question of peled concerning embeddings of random patterns in two and more dimensions

corner percolation on ℤ2 and the square root of 17 we consider a four vertex model introduced by balint toth a dependent bond percolation model on 2 in which every edge is present with probability 1 2 and each vertex has exactly two incident edges perpendicular to each other we prove that all components are finite cycles almost surely but the expected diameter of the cycle containing the origin is infinite moreover we derive the following critical exponents the tail probability diameter of the cycle of the origin n n and the expectation mathbb e length of a typical cycle with diameter n n with gamma 5 sqrt 17 4 0 219 ldots and delta sqrt 17 1 4 1 28 ldots the value of comes from a singular sixth order ode while the relation 3 2 corresponds to the fact that the scaling limit of the natural height function in the model is the additive brownian motion whose level sets have hausdorff dimension 3 2 we also include many open problems for example on the conformal invariance of certain linear entropy models

right and left locally testable languages the aim of this paper is to give a denition as well as an algebraic characterization of two new varieties of languages that will be referred to as right respectively left locally testable languages and denoted as rlt resp llt both families strictly contain the class of locally testable languages given k 0 the membership of a word x to a rlt k rt language can be decided by means of exploring the prex and sux of length k 1o fx and the segments of length k as well as considering the order of appearance of those segments when we scan the prexes of x membership of x to a k lt can be decided in a similar way but we have to change the word prexes for suxes in the above description in this paper we also show that s is a syntactic semigroup of a k rt resp k lt language if and only if the local subsemigroups of s are idempotents and right resp left repetition free c 2000 elsevier science b v all rights reserved

phase transitions on nonamenable graphs we survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph most attention is devoted to transitive graphs and trees

identification of birfsa languages the task of identifying a language from a set of its words is not an easy one for instance it is not feasible to identify regular languages in the general case therefore looking for subclasses of regular languages that can be identified in this framework is an interesting problem one of the most classical identifiable classes is the class of reversible languages introduced by d angluin also called bideterministic languages as they can be represented by deterministic automata dfa whose reverse is also deterministic residual finite state automata rfsa on the other hand is a class of non deterministic automata that shares some properties with dfa in particular dfa are rfsa and rfsa can be much smaller we study here learnability of the class of languages that can be represented by birfsa rfsa whose reverse are rfsa we prove that this class is not identifiable in general but we present two subclasses that are learnable the second one being identifiable in polynomial time

brief paper on receding horizon feedback control receding horizon feedback control rhfc was originally introduced as an easy method for designing stable state feedback controllers for linear systems here those results are generalized to the control of nonlinear autonomous systems and we develop a performance index which is minimized by the rhfc inverse optimal control problem previous results for linear systems have shown that desirable nonlinear controllers can be developed by making the rhfc horizon distance a function of the state that functional dependence was implicit and difficult to implement on line here we develop similar controllers for which the horizon distance is an easily computed explicit function of the state

inference of k testable languages in the strict sense and application to syntactic pattern recognition the inductive inference of the class of k testable languages in the strict sense k tssl is considered a k tssl is essentially defined by a finite set of substrings of length k that are permitted to appear in the strings of the language given a positive sample r of strings of an unknown language a deterministic finite state automation that recognizes the smallest k tssl containing r is obtained the inferred automation is shown to have a number of transitions bounded by o m where m is the number of substrings defining this k tssl and the inference algorithm works in o kn log m where n is the sum of the lengths of all the strings in r the proposed methods are illustrated through syntactic pattern recognition experiments in which a number of strings generated by ten given source non k tssl grammars are used to infer ten k tssl stochastic automata which are further used to classify new strings generated by the same source grammars the results of these experiments are consistent with the theory and show the ability of stochastic k tssls to approach other classes of regular languages

min max control of constrained uncertain discrete time linear systems for discrete time uncertain linear systems with constraints on inputs and states we develop an approach to determine state feedback controllers based on a min max control formulation robustness is achieved against additive norm bounded input disturbances and or polyhedral parametric uncertainties in the state space matrices we show that the finite horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs when the optimal control law is implemented in a receding horizon scheme only a piecewise affine function needs to be evaluated on line at each time step the technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state space

over testable languages abstract in this paper we give a combinatorial description of the languages that are both locally and piecewise testable we call such languages over testable the locally testable semigroups were discovered in the study of finite automata the definition of locally testable semigroup is similar to that of locally testable language if we consider words over the alphabet which is the set of all elements of a semigroup s then such a word determines an element of s the product of the letters of the word a semigroup s is locally testable if whenever two words over the alphabet s have the same factors of a fixed length k and the same prefix and suffix of length k 1 then the products of the letters of these words are equal a natural extension of locally testable semigroups is obtained by dropping the condition about the prefix and suffix we call such semigroups strongly locally testable we prove in this paper that the family of strongly locally testable semigroups is exactly the intersection of the variety of locally idempotent and commutative semigroups and that of j trivial semigroups in particular a language is over testable if and only if its syntactic semigroup is strongly locally testable we use this algebraic characterization to derive a simple family of generators for the variety of over testable languages

polluted bootstrap percolation with threshold two in all dimensions in the polluted bootstrap percolation model the vertices of a graph are independently declared initially occupied with probability p or closed with probability q at subsequent steps a vertex becomes occupied if it is not closed and it has at least r occupied neighbors on the cubic lattice mathbb z d of dimension d ge 3 with threshold r 2 we prove that the final density of occupied sites converges to 1 as p and q both approach 0 regardless of their relative scaling our result partially resolves a conjecture of morris and contrasts with the d 2 case where gravner and mcdonald proved that the critical parameter is q p 2

dependent percolation in two dimensions for a natural number k define an oriented site percolation on 2 as follows let xi yj be independent random variables with values uniformly distributed in 1 k declare a site i j 2closed if xi yj and open otherwise peter winkler conjectured some years ago that if k 4 then with positive probability there is an infinite oriented path starting at the origin all of whose sites are open i e there is an infinite path p i0 j0 i1 j1 such that 0 i0 i1 0 j0 j1 and each site in jn is open rather surprisingly this conjecture is still open in fact it is not known whether the conjecture holds for any value of k in this note we shall prove the weaker result that the corresponding assertion holds in the unoriented case if k 4 then the probability that there is an infinite path that starts at the origin and consists only of open sites is positive furthermore we shall show that our method can be applied to a wide variety of distributions of xi and yj independently peter winkler 14 has recently proved a variety of similar assertions by different methods

branching random walk with exponentially decreasing steps and stochastically self similar measures we consider a branching random walk on r whose step size decreases by a fixed factor 0 1 2 the limit measure is almost surely a s absolutely continuous with respect to the lebesgue measure but for pisot 1 it is a s singular 2 for all a 5 1 2 the support of the measure is a s the closure of its interior 3 for pisot 1 the support of the measure is fractured it is a s disconnected and the components of the complement are not isolated on both sides

lipschitz embeddings of random fields we consider the problem of embedding one i i d collection of bernoulli random variables indexed by mathbb z d into an independent copy in an injective m lipschitz manner for the case d 1 it was shown in basu and sly probab theory relat fields 159 721 775 2014 to be possible almost surely for sufficiently large m in this paper we provide a multi scale argument extending this result to higher dimensions

stochastic model predictive control of lpv systems via scenario optimization a stochastic receding horizon control approach for constrained linear parameter varying discrete time systems is proposed in this paper it is assumed that the time varying parameters have stochastic nature and that the system s matrices are bounded but otherwise arbitrary nonlinear functions of these parameters no specific assumption on the statistics of the parameters is required by using a randomization approach a scenario based finite horizon optimal control problem is formulated where only a finite number m of sampled predicted parameter trajectories scenarios are considered this problem is convex and its solution is a priori guaranteed to be probabilistically robust up to a user defined probability level p the p level is linked to m by an analytic relationship which establishes a tradeoff between computational complexity and robustness of the solution then a receding horizon strategy is presented involving the iterated solution of a scenario based finite horizon control problem at each time step our key result is to show that the state trajectories of the controlled system reach a terminal positively invariant set in finite time either deterministically or with probability no smaller than p the features of the approach are illustrated by a numerical example

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

on the compatibility of binary sequences an ordered pair of semi infinite binary sequences is said to be compatible if there is a way of removing a certain number possibly infinite of ones from and zeroes from that would map both sequences to the same semi infinite sequence this notion was introduced by peter winkler who also posed the following question and being independent i i d bernoulli sequences with parameters p and p respectively does there exist p p so that the set of compatible pairs has positive measure it is known that this does not happen for p and p very close to in the positive direction we construct for any 0 a deterministic binary sequence whose set of zeroes has hausdorff dimension larger than 1 and such that p is compatible 0 for p small enough where p stands for the product bernoulli measure with parameter p 2014 wiley periodicals inc

backstepping controller design for nonlinear stochastic systems under a risk sensitive cost criterion this paper develops a methodology for recursive construction of optimal and near optimal controllers for strict feedback stochastic nonlinear systems under a risk sensitive cost function criterion the design procedure follows the integrator backstepping methodology and the controllers obtained guarantee any desired achievable level of long term average cost for a given risk sensitivity parameter theta furthermore they lead to closed loop system trajectories that are bounded in probability and in some cases asymptotically stable in the large these results also generalize to nonlinear systems with strongly stabilizable zero dynamics a numerical example included in the paper illustrates the analytical results

receding horizon control of nonlinear systems without differentiability of the optimal value function abstract in this paper we show that receding horizon control when applied to a class of nonlinear systems has stabilizing properties our assumptions are necessarily fairly strong because they guarantee implicity that a smooth stabilizing feedback can be constructed this is an extension of our previous results which require the finite horizon value function to be continuously differentiable and therefore applies to a more restricted class of system continuous differentiability of the value function is replaced by local lipschitz continuity dini derivatives and a generalization of the invariance principle are employed to establish stability