expansions and contractions of isotropic stochastic flows of homeomorphisms a sequence of piecewise constant approximations to rescaled isotropic homeomorphic stochastic flows is shown to converge weakly in skorohod metric to the coalescing brownian flow intermittent behavior of isotropic flows is exposed and the clustering properties of isotropic flows are studied by the means of this convergence we obtain qualitative and quantitative description of expansions and contractions of an arbitrary isotropic homeomorphic flow on large time and space scales

fundamental properties of infinite trees infinite trees naturally arise in the formalization and the study of the semantics of programming languages this paper investigates some of their combinatorial and algebraic properties that are especially relevant to semantics

the ordinal generated by an ordinal grammar is computable abstract a prefix grammar is a context free grammar whose nonterminals generate prefix free languages a prefix grammar g is an ordinal grammar if the language l g is well ordered with respect to the lexicographic ordering it is known that from a finite system of parametric fixed point equations over ordinals one can construct an ordinal grammar g such that the lexicographic order of g is isomorphic with the least solution of the system if this solution is well ordered in this paper we show that given an ordinal grammar one can compute the cantor normal form of the order type of the lexicographic order of its language yielding that least solutions of fixed point equation systems defining algebraic ordinals are effectively computable and thus their isomorphism problem is also decidable

a numerically robust state space approach to stable predictive control strategies recent work with predictive control strategies has shown that the stable gpc sgpc approach has significant computational and numerical advantages however sgpc is cast in the transfer function framework which limits its application here we develop a means of extending the results to state space models and show that improved numerical conditioning can be obtained for many stable predictive control strategies

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

model predictive control of continuous time nonlinear systems with piecewise constant control a new model predictive control mpc algorithm for nonlinear systems is presented the plant under control the state and control constraints and the performance index to be minimized are described in continuous time while the manipulated variables are allowed to change at fixed and uniformly distributed sampling times in so doing the optimization is performed with respect to sequences as in discrete time nonlinear mpc but the continuous time evolution of the system is considered as in continuous time nonlinear mpc

a polynomial algorithm for deciding bisimilarity of normed context free processes the previous best upper bound on the complexity of deciding bisimilarity between normed context free processes due to huynh and tian is that the problem lies in the second level of the polynomial hierarchy their algorithm guesses a proof of equivalence and validates this proof in polynomial time using oracles freely answering questions which are in np in this paper we improve on this result by presenting a polynomial time algorithm which solves this problem as a corollary we have a polynomial algorithm for the equivalence problem for simple context free grammars

robust model predictive control with integral sliding mode in continuous time sampled data nonlinear systems this paper proposes a control strategy for nonlinear constrained continuous time uncertain systems which combines robust model predictive control mpc with sliding mode control smc in particular the so called integral smc approach is used to produce a control action aimed to reduce the difference between the nominal predicted dynamics of the closed loop system and the actual one in this way the mpc strategy can be designed on a system with a reduced uncertainty in order to prove the stability of the overall control scheme some general regional input to state practical stability results for continuous time systems are proved

moving horizon control of linear systems with input saturation and plant uncertainty part 1 robustness we present a moving horizon feedback system based on constrained optimal control algorithms for linear plants with input saturation the system is a non conventional sampled data system its sampling periods vary from sampling instant to sampling instant and the control during the sampling time is not constant but determined by the solution of an open loop optimal control problem this is a two part paper in this part we show that the proposed moving horizon control system is robustly stable whether the state of the plant is measurable or not in the second part we show that the proposed moving horizon control system is capable of following a class of reference inputs and suppressing a class of disturbances experimental results show that the behaviour of the moving horizon control system is superior to that resulting from some alternative control laws

lebesgue approximation model predictive control of nonlinear sampled data systems this article studies discrete time implementation of model predictive control mpc algorithms in continuous time nonlinear sampled data systems we present a discrete time and aperiodic nonlinear mpc algorithm to stabilize continuous time nonlinear dynamics based on the lebesgue approximation model lam in this lam based mpc lampc the sampling instants are triggered by a self triggered scheme and the predicted states and transition time instants in the optimal control problem are calculated in an aperiodic manner subject to the lam sufficient conditions are derived on feasibility and stability of the resulting closed loop systems according to these conditions the parameters in lampc are designed with the guarantee of exclusion of zeno behavior meanwhile it is shown that the periodic task model is a special case in our framework with appropriate choice of the parameters in the lam simulation results indicate that lampc can dynamically adjust the computation periods and has the potential to reduce the computational costs compared with periodic approaches

ccs expressions finite state processes and three problems of equivalence abstract we examine the computational complexity of testing finite state processes for equivalence in milner s calculus of communicating systems ccs the equivalence problems in ccs are presented as refinements of the familiar problem of testing whether two nondeterministic finite automata nfa are equivalent i e accept the same language three notions of equivalence proposed for ccs are investigated namely observational equivalence strong observational equivalence and failure equivalence we show that observational equivalence can be tested in polynomial time as defined in ccs observational equivalence is the limit of a sequence of successively finer equivalence relations k where 1 is nondeterministic finite automaton equivalence we prove that for each fixed k deciding k is pspace complete we show that strong observational equivalence can be decided in polynomial time by reducing it to generalized partitioning a new combinatorial problem of independent interest finally we demonstrate that testing for failure equivalence is pspace complete even for a very restricted type of process

buchi context free languages we define context free grammars with buchi acceptance condition generating languages of countable words we establish several closure properties and decidability results for the class of buchi context free languages generated by these grammars we also define context free grammars with muller acceptance condition and show that there is a language generated by a grammar with muller acceptance condition which is not a buchi context free language

isotropic stochastic flows on considere les flots stochastiques isotropes dans un espace euclidien de d dimensions d 2 on relie la tendance des distances entre deux points et des vecteurs tangents a se borner ou s etendre a la dimension et a la proportion du flot solenoidal ou potentiel

a mezei wright theorem for categorical algebras the main result of this paper is a generalization of the mezei wright theorem a result on solutions of a system of fixed point equations in the typical setting one solves a system of fixed point equations in an algebra equipped with a suitable partial order there is a least element suprema of w chains exist the operations preserve the ordering and least upper bounds of w chains in this setting one solution of this kind of system is provided by least fixed points the mezei wright theorem asserts that such a solution is preserved by a continuous order preserving algebra homomorphism in several settings such as countable words or synchronization trees there is no well defined partial order but one can naturally introduce a category by considering morphisms between the elements the generalization of this paper consists in replacing ordered algebras by categorical algebras the least element is replaced by an initial element and suprema of w chains are replaced by colimits of w diagrams then the mezei wright theorem for categorical algebras is that initial solutions are preserved by continuous morphisms we establish this result for initial solutions of parametric fixed point equations one use of the theorem is to characterize an algebraic element as one that can arise as a solution of some system of fixed point equations in familiar examples an algebraic element is one that is context free regular or rational then if h a b is a continuous morphism of categorical algebras the algebraic objects in b are those isomorphic to h images of algebraic objects in a

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

intermittency of the tracer gradient the problem of stirring a passive scalar tracer by a random velocity field is considered for gaussian velocity fields with infinitely small time and space scales it is shown that the tracer gradient is concentrated in a discrete set of points the points that form a random point process independent of the initial tracer distribution a complete description of this point process is given if the initial tracer field is a random function with homogeneous increments a full statistics of the jumps is also given

a general framework to design stabilizing nonlinear model predictive controllers abstract we propose a new model predictive control mpc framework to generate feedback controls for time varying nonlinear systems with input constraints we provide a set of conditions on the design parameters that permits to verify a priori the stabilizing properties of the control strategies considered the supplied sufficient conditions for stability can also be used to analyse the stability of most previous mpc schemes the class of nonlinear systems addressed is significantly enlarged by removing the traditional assumptions on the continuity of the optimal controls and on the stabilizability of the linearized system some important classes of nonlinear systems including some nonholonomic systems can now be stabilized by mpc in addition we can exploit increased flexibility in the choice of design parameters to reduce the constraints of the optimal control problem and thereby reduce the computational effort in the optimization algorithms used to implement mpc

finite automata and ordinals abstract several definitions of automata on words indexed by ordinals have been proposed previously the first one was introduced by buchi to prove the decidability of the monadic second order theory of denumerable ordinals wojciechowski studied the properties of these automata independently of the length of the input the second definition proposed by choueka works only on words of length less than n in this paper we restrict the domain of wojciechowski automata to the domain of choueka s ones that is given n we keep only sequences for n 1 in the language defined by a wojciechowski automaton in order to prove the equivalence between choueka automata and wojciechowski automata then we obtain the closure under complementation of the class of wojciechowski s definable sets and finally we give an algorithm for determinizing wojciechowski automata

isomorphism of regular trees and words the computational complexity of the isomorphism problem for regular trees regular linear orders and regular words is analyzed a tree is regular if it is isomorphic to the prefix order on a regular language in case regular languages are represented by nfas dfas the isomorphism problem for regular trees turns out to be exptime complete resp p complete in case the input automata are acyclic nfas acyclic dfas the corresponding trees are succinctly represented finite trees and the isomorphism problem turns out to be pspace complete resp p complete a linear order is regular if it is isomorphic to the lexicographic order on a regular language a polynomial time algorithm for the isomorphism problem for regular linear orders and even regular words which generalize the latter given by dfas is presented this solves an open problem by esik and bloom similar techniques can be used to show that one can check in polynomial time whether a given regular linear order has a non trivial automorphism this improves a recent decidability result of kuske

on isotropic brownian motions this paper includes a detailed study of isotropic brownian motion on matrices and brownian flows associated with isotropic gaussian fields characteristic exponents stability asymptotic behaviour statistical equilibrium are the topics on which the main results are obtained

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

on direct products of automaton decidable theories abstract this paper is concerned with connections between two different ways to prove decidability results methods of automata theory and methods related to products of algebraic systems some basic automaton theoretic conditions on relational structures are presented which give preservation theorems for decidability under certain direct products

isomorphisms of scattered automatic linear orders abstract we prove that the isomorphism of scattered tree automatic linear orders as well as the existence of automorphisms of scattered word automatic linear orders are undecidable for the existence of automatic automorphisms of word or tree automatic linear orders we determine the exact level of undecidability in the arithmetical hierarchy

on the stabilizing property of siorhc it is shown that the stabilizing property of siorhc stabilizing i o receding horizon control holds for general stabilizable discrete time linear plants irrespective of the condition that the plant has no poles at the origin

mpc for sampled data linear systems guaranteeing constraint satisfaction in continuous time model predictive controllers mpc designed for sampled data systems can be shown to violate the constraints in continuous time a reformulation of the initial problem will guarantee constraint satisfaction throughout the intersample period polytopic inclusions of the continuous trajectory are used in this technical note to establish additional constraints leading to a linearly constrained quadratic optimization problem continuous time asymptotic stability and continuous time positive invariance are proven for the reformulated problem

stability margins of nonlinear receding horizon control via inverse optimality using the nonlinear analog of the fake riccati equation developed for linear systems we derive an inverse optimality result for several receding horizon control schemes this inverse optimality result unifies stability proofs and shows that receding horizon control possesses the stability margins of optimal control laws

heuristically enhanced feedback control of constrained discrete time linear systems recent advances in computer technology have spurred new interest in the use of feedback controllers based upon on line minimization for the control of constrained linear systems still the use of computers in the feedback loop has been hampered by the fact that the amount of time available for computation in most sampled data systems is not enough to achieve a complete solution using conventional algorithms several ad hoc techniques have been proposed but their applicability is restricted by the lack of supporting theory in this paper we present a theoretical framework to analyze the stability of the closed loop system resulting from the use of on line optimization in the feedback loop using these results we show that a suboptimal algorithm based upon the use of heuristic search techniques yields asymptotically stable systems provided that enough computation power is available to solve at each sampling interval an optimization problem considerably simpler than the original the controller presented in this paper is valuable for situations where the customary approaches of using pontryagin s minimum principle or storing a family of extremal curves are not applicable due to limitations in the computational resources available

long words the theory of concatenation and o power it is shown that for any set a the algebra of ordinal words on the alphabet a equipped with the operations of concatenation and power is axiomatized by the equationsx y z x y z x y x y x xn x n 1 indeed the algebra freely generated by a in the variety determined by these equations is the algebra of tail finite ordinal words of length on the alphabet a it is further shown that this collection of identities cannot be replaced by any finite set last a polynomial algorithm is given for recognizing when two terms denote the same tail finite ordinal word

robust model predictive control of stable linear systems a new robust model predictive control mpc algorithm is presented for stable constrained linear plants that is a direct generalization of the nominally stabilizing regulator presented by rawlings and muske model uncertainty is parametrized by a list of possible plants robust stability is achieved through the addition of constraints that prevent the sequence of optimal controller costs from increasing for the true plant asymptotic stability is demonstrated through a lyapunov argument simulation experiments demonstrate the performance of the algorithm for two example processes

robust digital model predictive control for linear uncertain systems with saturations actuator saturation constraint is inevitable in industrial process in this note we consider a discrete receding horizon control a piecewise constant robust model predictive control for a continuous time plant with actuator saturation constraint through a sampled data control approach the solution is formulated as an optimization problem subject to linear matrix inequalities a numerical example is used to demonstrate the effectiveness of the proposed design procedure

tree automatic scattered linear orders tree automatic linear orders on regular tree languages are studied it is shown that there is no tree automatic scattered linear order and therefore no tree automatic well order on the set of all finite labeled trees and that a regular tree language admits a tree automatic scattered linear order if and only if for some n no binary tree of height n can be embedded into the union of the domains of its trees hence the problem whether a given regular tree language can be ordered by a scattered linear order or a well order is decidable moreover sharp bounds for tree automatic well orders on some regular tree languages are computed by connecting tree automata with automata on ordinals the proofs use elementary techniques of automata theory

the equational theory of regular words courcelle introduced the study of regular words i e words isomorphic to frontiers of regular trees heilbrunner showed that a nonempty word is regular iff it can be generated from the singletons by the operations of concatenation omega power omega op power and the infinite family of shuffle operations we prove that the algebra of nonempty regular words on the set a equipped with these operations is freely generated by a in a variety which is axiomatizable by an infinite collection of some natural equations we also show that this variety has no finite equational basis and that its equational theory is decidable in polynomial time

receding horizon revisited an easy way to robustly stabilize an ltv system stabilization schemes are often based on infinite horizon optimization of a non singular cost functional for such schemes to make sense in a time varying context a fairly good knowledge of the system parameters at all times is a prerequisite that is a major disadvantage in adaptive implementations when applicable the receding horizon approach overcomes this difficulty as though it relies on general qualitative long term properties such as controllability it requires quantitative knowledge only of temporally local parameter values work done on receding horizon stabilization during the 1970 s focused on lq h2 optimization criteria looking for a stabilization method which carries also the robustness properties of infinite horizon h design we consider here local minimization of the l2 induced i o norm h optimization as the design objective both state and observation based feedback scheme are derived and relations to finite and infinite horizon optimization are discussed