root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

robust model predictive control of constrained linear systems with bounded disturbances this paper provides a novel solution to the problem of robust model predictive control of constrained linear discrete time systems in the presence of bounded disturbances the optimal control problem that is solved online includes uniquely the initial state of the model employed in the problem as a decision variable the associated value function is zero in a disturbance invariant set that serves as the origin when bounded disturbances are present and permits a strong stability result namely robust exponential stability of the disturbance invariant set for the controlled system with bounded disturbances to be obtained the resultant online algorithm is a quadratic program of similar complexity to that required in conventional model predictive control

stochastic mpc framework for controlling the average constraint violation this technical note considers linear discrete time systems with additive bounded disturbances subject to hard control input bounds and a stochastic constraint on the amount of state constraint violation averaged over time the amount of violations is quantified by a loss function and the averaging can be weighted corresponding to exponential forgetting of past violations the freedom in the choice of the loss function makes this formulation highly flexible for instance probabilistic constraints or integrated chance constraints can be enforced by an appropriate choice of the loss function for the type of constraint considered we develop a recursively feasible receding horizon control scheme exploiting the averaged over time nature by explicitly taking into account the amount of past constraint violations when determining the current control input this leads to a significant reduction in conservatism as a simple extension of the proposed approach we show how time varying state constraints can be handled within our framework the computational complexity online as well as offline is comparable to existing model predictive control schemes the effectiveness of the proposed methodology is demonstrated by means of a numerical example from building climate control

collet eckmann and holder we prove that collet eckmann condition for rational functions which requires exponential expansion only along the critical orbits yields the holder regularity of fatou components this implies geometric regularity of julia sets with non hyperbolic and critically recurrent dynamics in particular polynomial collet eckmann julia sets are locally connected if connected and their hausdorff dimension is strictly less than 2 the same is true for rational collet eckmann julia sets with at least one non empty fully invariant fatou component

matching on the estimated propensity score propensity score matching estimators rosenbaum and rubin 1983 are widely used in evaluation research to estimate average treatment effects in this article we derive the large sample distribution of propensity score matching estimators our derivations take into account that the propensity score is itself estimated in a first step prior to matching we prove that first step estimation of the propensity score affects the large sample distribution of propensity score matching estimators and derive adjustments to the large sample variances of propensity score matching estimators of the average treatment effect ate and the average treatment effect on the treated atet the adjustment for the ate estimator is negative or zero in some special cases implying that matching on the estimated propensity score is more efficient than matching on the true propensity score in large samples however for the atet estimator the sign of the adjustment term depends on the data generating process and ignoring the estimation error in the propensity score may lead to confidence intervals that are either too large or too small

non uniform hyperbolicity and universal bounds for s unimodal maps an s unimodal map f is said to satisfy the collet eckmann condition if the lower lyapunov exponent at the critical value is positive if the infimum of the lyapunov exponent over all periodic points is positive then f is said to have a uniform hyperbolic structure we prove that an s unimodal map satisfies the collet eckmann condition if and only if it has a uniform hyperbolic structure the equivalence of several non uniform hyperbolicity conditions follows one consequence is that some renormalization of an s unimodal map has an absolutely continuous invariant probability measure with exponential decay of correlations if and only if the collet eckmann condition is satisfied the proof uses new universal bounds that hold for any s unimodal map without periodic attractors

robust event triggered mpc with guaranteed asymptotic bound and average sampling rate we propose a robust event triggered model predictive control mpc scheme for linear time invariant discrete time systems subject to bounded additive stochastic disturbances and hard constraints on the input and state for given probability distributions of the disturbances acting on the system we design event conditions such that the average frequency of communication between the controller and the actuator in the closed loop system attains a given value we employ tube mpc methods to guarantee robust constraint satisfaction and a robust asymptotic bound on the system state moreover we show that instead of a given periodically updated tube mpc scheme an appropriate event triggered mpc scheme can be applied with the same guarantees on constraints and region of attraction but with a reduced number of average communications

harmonic gibbs and hausdorff measures on repellers for holomorphic maps i we prove that for a simply connected domain q c c whose boundary a q is self similar there is the following dichotomy concerning the harmonic measure x on a q viewed from 0 either a q is piecewise real analytic or else o is singular with respect to the hausdorff measure a notation o i a using makarov s function 4dc t t exp c log 1 t log log log 1 t for some c c x 0 and x is absolutely continuous with respect to a notation x c so if q has fractal boundary then the boundary compression and the radial growth of j logir l j for a riemann mapping r d are as strong respectively as fast as permitted by makarov s theory we prove that c x 2a 2 x for some asymptotic variance a 2 for a sequence of weakly dependent random variables and a lyapunov characteristic exponent x this includes the case where a q is a mixing repeller in ruelle s sense for a holomorphic map f defined on its neighbourhood the case a q is a quasi circle invariant under the action of a quasi fuchsian group for a pair of isomorphic compact surface fuchsian groups and the cases of the boundary of the snowflake and more generally of carleson s fractal jordan curves this dichotomy is partially deduced from the dichotomy concerning gibbs measures for holder continuous functions on an arbitrary mixing repeller x c c for a holomorphic map either i i ak where k is the hausdorff dimension of y

brief paper stochastic tube mpc with state estimation an output feedback model predictive control mpc strategy for linear systems with additive stochastic disturbances and probabilistic constraints is proposed given the probability distributions of the disturbance input the measurement noise and the initial state estimation error the distributions of future realizations of the constrained variables are predicted using the dynamics of the plant and a linear state estimator from these distributions a set of deterministic constraints is computed for the predictions of a nominal model the constraints are incorporated in a receding horizon optimization of an expected quadratic cost which is formulated as a quadratic program the constraints are constructed so as to provide a guarantee of recursive feasibility and the closed loop system is stable in a mean square sense all uncertainties in this paper are taken to be bounded in most control applications this gives a more realistic representation of process and measurement noise than the more traditional gaussian assumption

stability analysis of quadratic mpc with a discrete input alphabet we study stability of model predictive control mpc with a quadratic cost function for lti systems with a discrete input alphabet since this kind of systems may present a steady state error the focus is on practical stability i e ultimate boundedness of solutions to derive sufficient conditions for practical stability and characterize the ultimately invariant set we analyze the one step horizon solution and adapt tools used for convex mpc formulations

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

brief constrained receding horizon predictive control for nonlinear systems the paper concerns the receding horizon predictive control of constrained nonlinear systems and presents an algorithm which relies on the online solution of a simple linear program lp use is made of a finite control horizon in conjunction with a terminal inequality constraint and a predicted cost that includes a terminal penalty term the optimization procedure is based on predictions made by linearized incremental models at points of a given seed trajectory and the effects of linearization error are taken into account to give a bound on the predicted tracking error the algorithm is posed in the form of an lp and the proper selection of the terminal penalty term of the predicted cost guarantees the asymptotic stability the results of the paper are illustrated by means of a simple example

equi normalization and exact scaling dynamics in homothetic tube model predictive control this paper develops an equi normalization process in order to verify the existence of and characterize the minimal robust positively invariant set generated by a number of a priori but suitably selected linear inequalities it also develops the exact scaling dynamics associated with this set the paper then proposes an improved homothetic tube model predictive control synthesis for linear systems subject to additive disturbances and polytopic constraints

local control lyapunov functions for constrained linear discrete time systems the minkowski algebra approach this technical note utilizes minkowski algebra of convex sets to characterize a family of local control lyapunov functions for constrained linear discrete time systems local control lyapunov functions are induced by parametrized contractive invariant sets underlying contractive invariant sets belong to a family of minkowski decomposable convex sets and are in fact parametrized by a basic shape set and linear transformations of system matrices and a set of design matrices corresponding local control lyapunov functions can be detected by solving a single tractable convex optimization problem which in case of polyhedral constraints reduces to a single linear program the a priori complexity estimate of the characterized local control lyapunov function is provided for some practically relevant cases an illustrative example and relevant numerical experience are also reported

simple least squares estimator for treatment effects using propensity score residuals summary propensity score matching is widely used to control covariates when analysing the effects of a nonrandomized binary treatment however it requires several arbitrary decisions such as how many matched subjects to use and how to choose them in this paper a simple least squares estimator is proposed where the treatment and possibly the response variable is replaced by the propensity score residual the proposed estimator controls covariates semiparametrically if the propensity score function is correctly specified furthermore it is numerically stable and relatively easy to use compared with alternatives such as matching regression imputation weighting and doubly robust estimators the proposed estimator also has a simple valid asymptotic variance estimator that works well in small samples the least squares estimator is extended to multiple treatments and noncontinuously distributed responses a simulation study demonstrates that it has lower mean squared error than its competitors

switched systems with average dwell time computation of the robust positive invariant set abstract in this paper computational results of robust positive invariant rpi sets for switched systems with amplitude bounded persistent additive disturbance and average dwell time adt switching are developed towards this end new idea for facilitating the analysis of the adt switching signal is conceptualized by a series of predefined stages and sufficient conditions for the existence of an adt rpi set of the considered systems are established by utilizing the structure characteristics at each stage of the adt switching signal an exact computational algorithm of the adt rpi set of the considered system is developed the effectiveness of the proposed algorithms are illustrated by a numerical example

constraint admissible state sets for switched systems with average dwell time abstract the exact computational problem of constrained admissible average dwell time caadt contractive set and caadt invariant set for discrete time switched systems with and without persistent amplitude bounded additive disturbance is investigated in this paper the considered switching signal satisfies average dwell time adt and is discussed in terms of stage which is both length based and sequence based for the first time two more general criteria are established for checking the existence of the average dwell time adt contractive set and the adt invariant set of the considered system by assuming the value of stage length is taken from an arbitrary finite set a detailed discussion is included to identify a proper value for stage length by taking the computational complexity and the conservatism of the designed finite step computational algorithms of the caadt contractive set and the caadt invariant set into consideration some characteristics of the admissible caadt contractive set and caadt invariant set are derived an illustrative example illustrates the effectiveness of the developed results

equilibrium states of weakly hyperbolic one dimensional maps for holder potentials there is a wealth of results in the literature on the thermodynamic formalism for potentials that are in some sense hyperbolic we show that for a sufficiently regular one dimensional map satisfying a weak hyperbolicity assumption every holder continuous potential is hyperbolic a sample consequence is the absence of phase transitions the pressure function is real analytic on the space of holder continuous functions another consequence is that every holder continuous potential has a unique equilibrium state and that this measure has exponential decay of correlations

nice inducing schemes and the thermodynamics of rational maps we study the thermodynamic formalism of a complex rational map f of degree at least two viewed as a dynamical system acting on the riemann sphere more precisely for a real parameter t we study the existence of equilibrium states of f for the potential t rm ln left f prime right and the analytic dependence on t of the corresponding pressure function we give a fairly complete description of the thermodynamic formalism for a large class of rational maps including well known classes of non uniformly hyperbolic rational maps such as topological collet eckmann maps and much beyond in fact our results apply to all non renormalizable polynomials without indifferent periodic points to infinitely renormalizable quadratic polynomials with a priori bounds and all quadratic polynomials with real coefficients as an application for these maps we describe the dimension spectrum for lyapunov exponents and for pointwise dimensions of the measure of maximal entropy and obtain some level 1 large deviations results for polynomials as above we conclude that the integral means spectrum of the basin of attraction of infinity is real analytic at each parameter in mathbb r with at most two exceptions

efficient robust optimization for robust control with constraints this paper proposes an efficient computational technique for the optimal control of linear discrete time systems subject to bounded disturbances with mixed linear constraints on the states and inputs the problem of computing an optimal state feedback control policy given the current state is non convex a recent breakthrough has been the application of robust optimization techniques to reparameterize this problem as a convex program while the reparameterized problem is theoretically tractable the number of variables is quadratic in the number of stages or horizon length n and has no apparent exploitable structure leading to computational time of mathcal o n 6 per iteration of an interior point method we focus on the case when the disturbance set is norm bounded or the linear map of a hypercube and the cost function involves the minimization of a quadratic cost here we make use of state variables to regain a sparse problem structure that is related to the structure of the original problem that is the policy optimization problem may be decomposed into a set of coupled finite horizon control problems this decomposition can then be formulated as a highly structured quadratic program solvable by primal dual interior point methods in which each iteration requires mathcal o n 3 time this cubic iteration time can be guaranteed using a riccati based block factorization technique which is standard in discrete time optimal control numerical results are presented using a standard sparse primal dual interior point solver that illustrate the efficiency of this approach

robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks this paper presents a neural network approach to robust model predictive control mpc for constrained discrete time nonlinear systems with unmodeled dynamics affected by bounded uncertainties the exact nonlinear model of underlying process is not precisely known but a partially known nominal model is available this partially known nonlinear model is first decomposed to an affine term plus an unknown high order term via jacobian linearization the linearization residue combined with unmodeled dynamics is then modeled using an extreme learning machine via supervised learning the minimax methodology is exploited to deal with bounded uncertainties the minimax optimization problem is reformulated as a convex minimization problem and is iteratively solved by a two layer recurrent neural network the proposed neurodynamic approach to nonlinear mpc improves the computational efficiency and sheds a light for real time implementability of mpc technology simulation results are provided to substantiate the effectiveness and characteristics of the proposed approach

equivalence and topological invariance of conditions for non uniform hyperbolicity in the iteration of rational maps we show equivalence of several standard conditions for non uniform hyperbolicity of complex rational functions including the topological collet eckmann condition tce uniform hyperbolicity on periodic orbits exponential shrinking of components of pre images of small discs backward collet eckmann condition at one point positivity of the infimum of lyapunov exponents of finite invariant measures on the julia set the condition tce is stated in purely topological terms so we conclude that all these conditions are invariant under topological conjugacy for rational maps with one critical point in julia set all the conditions above are equivalent to the usual collet eckmann and backward collet eckmann conditions thus the latter ones are invariant by topological conjugacy in the unicritical setting we also prove that neither part of this stronger statement is valid in the multicritical case

computation of maximal safe sets for switching systems the problem of determining maximal safe sets and hybrid controllers is computationally intractable because of the mathematical generality of hybrid system models given the practical and theoretical relevance of the problem finding implementable procedures that could at least approximate the maximal safe set is important to this end we begin by restricting our attention to a special class of hybrid systems switching systems we exploit the structural properties of the graph describing the discrete part of a switching system to develop an efficient procedure for the computation of the safe set this procedure requires the computation of a maximal controlled invariant set we then restrict our attention to linear discrete time systems for which there is a wealth of results available in the literature for the determination of maximal controlled invariant sets however even for this class of systems the computation may not converge in a finite number of steps we then propose to compute inner approximations that are controlled invariant and for which a procedure that terminates in a finite number of steps can be obtained a tight bound on the error can be given by comparing the inner approximation with the classical outer approximation of the maximal controlled invariant set our procedure is applied to the idle speed regulation problem in engine control to demonstrate its efficiency

fekete configuration quantitative equidistribution and wandering critical orbits in non archimedean dynamics let f be a rational function of degree d 1 on the projective line over a possibly non archimedean algebraically closed field a well known process initiated by brolin considers the pullbacks of points under iterates of f and produces an important equilibrium measure we define the asymptotic fekete property of pullbacks of points which means that they mirror the equilibrium measure appropriately as application we obtain an error estimate of equidistribution of pullbacks of points for c1 test functions in terms of the proximity of wandering critical orbits to the initial points and show that the order is o sqrt kd k upto a specific exceptional set of capacity 0 of initial points which is contained in the set of superattracting periodic points and the omega limit set of wandering critical points from the julia set or the presingular domains of f as an application in arithmetic dynamics together with a dynamical diophantine approximation these estimates recover favre and rivera letelier s quantitative equidistribution in a purely local manner

inverse minimax optimality of model predictive control policies we present novel results linking model predictive control mpc and minimax optimal control theory specifically we show that for linear discrete time systems with constraints and disturbance inputs the closed loop optimal solutions of a particular class of minimax optimal control problems are a class of typical mpc policies we also present conditions which ensure that the inverse optimal mpc policies achieve a prescribed regional l2 gain from the disturbance input

one hundred years of complex dynamics holomorphic dynamics has been a key area of study for 100 years in this survey we focus on the dynamics of rational functions

brief robust receding horizon predictive control for systems with uncertain dynamics and input saturation a receding horizon predictive control method which assures stability for systems with model uncertainty and input saturation is derived by extending earlier work in two important respects i ellipsoidal invariant sets are replaced by polyhedral invariant sets and ii the constraint that the state lie in an invariant set is invoked n steps ahead the new algorithm allows for a considerable enlargement of the stabilizable set and provides extra degrees of freedom with which to improve performance

efficient estimation of average treatment effects using the estimated propensity score we are interested in estimating the average effect of a binary treatment on a scalar outcome if assignment to the treatment is exogenous or unconfounded that is independent of the potential outcomes given covariates biases associated with simple treatmentcontrol average comparisons can be removed by adjusting for differences in the covariates rosenbaum and rubin 1983 show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates although adjusting for differences in the propensity score removes all the bias this can come at the expense of efficiency as shown by hahn 1998 heckman ichimura and todd 1998 and robins mark and newey 1992 we show that weighting by the inverse of a nonparametric estimate of the propensity score rather than the true propensity score leads to an efficient estimate of the average treatment effect we provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score

the role of the propensity score in estimating dose response functions summary estimation of average treatment effects in observational studies often requires adjustment for differences in pre treatment variables if the number of pre treatment variables is large standard covariance adjustment methods are often inadequate rosenbaum rubin 1983 propose an alternative method for adjusting for pre treatment variables for the binary treatment case based on the so called propensity score here an extension of the propensity score methodology is proposed that allows for estimation of average casual effects with multi valued treatments estimation of average treatment effects in observational studies often requires adjustment for differences in pre treatment variables if the number of pre treatment variables is large and their distribution varies substantially with treatment status standard adjustment methods such as covari ance adjustment are often inadequate rosenbaum rubin 1983 1984 propose an alternative method for adjusting for pre treatment variables based on the propensity score the conditional probability of receiving the treatment given pre treatment variables they demonstrate that adjusting solely for the propensity score removes all bias associated with differences in the pre treatment variables the rosenbaum rubin proposals deal exclusively with binary valued treat ments in many cases of interest however treatments take on more than two values here an extension of the propensity score methodology is proposed that allows for estimation of average causal effects with multi valued treatments the key insight is that for estimation of average causal effects it is not necessary to divide the population into subpopulations where causal comparisons are valid as the propensity score does it is sufficient to divide the population into subpopulations where average potential outcomes can be estimated

distribution of rational maps with a preperiodic critical point let f lambda be a family of rational maps of a fixed degree with a marked critical point c lambda under a natural assumption we first prove that the hypersurfaces of parameters for which c lambda is periodic converge as a sequence of positive closed 1 1 currents to the bifurcation current attached to c and defined by demarco we then turn our attention to the parameter space of polynomials of a fixed degree d by intersecting the d 1 currents attached to each critical point of a polynomial bassaneli and berteloot obtained a positive measure mu rm bif of finite mass which is supported on the connectedness locus they showed that its support is included in the closure of the set of parameters admitting d 1 neutral cycles we show that the support of this measure is precisely the closure of the set of strictly critically finite polynomials i e of misiurewicz points

the lyapunov exponent of holomorphic maps we prove that for any polynomial map with a single critical point its lower lyapunov exponent at the critical value is negative if and only if the map has an attracting cycle similar statement holds for the exponential maps and some other complex dynamical systems we prove further that for the unicritical polynomials with positive area julia sets almost every point of the julia set has zero lyapunov exponent part of this statement generalizes as follows every point with positive upper lyapunov exponent in the julia set of an arbitrary polynomial is not a lebegue density point

improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data considerable recent interest has focused on doubly robust estimators for a population mean response in the presence of incomplete data which involve models for both the propensity score and the regression of outcome on covariates the usual doubly robust estimator may yield severely biased inferences if neither of these models is correctly specified and can exhibit nonnegligible bias if the estimated propensity score is close to zero for some observations we propose alternative doubly robust estimators that achieve comparable or improved performance relative to existing methods even with some estimated propensity scores close to zero

collet eckmann and the bifurcation measure the moduli space mathcal m d of degree d ge 2 rational maps can naturally be endowed with a measure mu text bif detecting maximal bifurcations called the bifurcation measure we prove that the support of the bifurcation measure mu text bif has positive lebesgue measure to do so we establish a general sufficient condition for the conjugacy class of a rational map to belong to the support of mu text bif and we exhibit a large set of collet eckmann rational maps which satisfy this condition as a consequence we get a set of collet eckmann rational maps of positive lebesgue measure which are approximated by hyperbolic rational maps

brief paper feedback and invariance under uncertainty via set iterates we examine discrete time control systems under non parametric disturbances sets which a given control feedback makes invariant under the disturbance are analyzed via lifting the feedback operation to the space of sets properties of being an attractor of the disturbed dynamics and being a minimal invariant set are derived from the corresponding notions of the set dynamics yielding in turn useful characterizations and error estimates for numerical algorithms which detect the minimal invariant sets concrete numerics for some examples of practical feedback rules are offered

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

worst case formulations of model predictive control for systems with bounded parameters two different predictive control formulations are developed based on minimization of the worst case quadratic cost for systems with bounded parameters the two formulations differ on the assumptions made about the future inputs in optimizing the current input one assumes open loop control while the other considers closed loop control their closed loop properties such as asymptotic stability are examined we then focus on a moving average model with an integrator and derive computationally simpler suboptimal algorithms

an approach to output feedback mpc of stochastic linear discrete time systems in this paper we propose an output feedback model predictive control mpc algorithm for linear discrete time systems affected by a possibly unbounded additive noise and subject to probabilistic constraints in case the noise distribution is unknown the probabilistic constraints on the input and state variables are reformulated by means of the chebyshev cantelli inequality the recursive feasibility is guaranteed the convergence of the state to a suitable neighbor of the origin is proved under mild assumptions and the implementation issues are thoroughly addressed two examples are discussed in detail with the aim of providing an insight into the performance achievable by the proposed control scheme

optimized robust control invariance for linear discrete time systems theoretical foundations this paper introduces the concept of optimized robust control invariance for discrete time linear time invariant systems subject to additive and bounded state disturbances a novel characterization of two families of robust control invariant sets is given the existence of a constraint admissible member of these families can be checked by solving a single and tractable convex programming problem in the generic linear convex case and a standard linear quadratic program when the constraints are polyhedral or polytopic the solution of the same optimization problem yields the corresponding feedback control law that is in general set valued a procedure for selection of a point valued nonlinear control law is provided

ultimate boundedness control for uncertain discrete time systems via set induced lyapunov functions in this note linear discrete time systems affected by both parameter and input uncertainties are considered the problem of the synthesis of a feedback control assuring that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence is investigated it is shown that the problem has a solution if and only if there exists a certain lyapunov function which does not belong to a preassigned class of functions e g the quadratic ones but it is determined by the target set in which ultimate boundedness is desired one of the advantages of this approach is that we may handle systems with control constraints no matching assumptions are made for systems with linearly constrained uncertainties it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets the resulting compensator may be implemented as a linear variable structure control

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

on robust control invariance of boolean control networks this paper investigates the robust control invariance of boolean control networks bcns via the semi tensor product of matrices firstly based on an algebraic state space representation of bcns two necessary and sufficient conditions are presented to check whether or not a given set is a robust control invariant set under a given state feedback controller secondly by defining a series of suitable sets all possible state feedback gain matrices under which a given set is a robust control invariant set are characterized an illustrative example is presented to demonstrate the obtained new results

admissible sets for slowly varying discrete time systems abstract this note describes a method to calculate admissible sets for dynamical systems with slowly varying parameters a set of initial states is said to be admissible if all state trajectories starting within this set respect safety critical constraints for all future time instances for many classes of systems the maximal admissible set mas equals the maximal robust positive invariant mrpi set therefore much of the literature focus on algorithms that produce approximations of the mrpi set however for slowly varying systems it turns out that the mas can be larger than the mrpi set a property referred to as the m proximal contraction property is defined for such systems to state sufficient conditions for sets to be admissible it is then shown that algorithm 2 produces an admissible set that is a superset of the mrpi set

large deviation principle in one dimensional dynamics we study the dynamics of smooth interval maps with non flat critical points for every such a map that is topologically exact we establish the full level 2 large deviation principle for empirical means in particular the large deviation principle holds for every non renormalizable quadratic map this includes the maps without physical measure found by hofbauer and keller and challenges the widely shared view of the large deviation principle as a refinement of laws of large numbers

low complexity polytopic invariant sets for linear systems subject to norm bounded uncertainty we propose a novel algorithm to compute low complexity polytopic robust control invariant rci sets along with the corresponding state feedback gain for linear discrete time systems subject to norm bounded uncertainty additive disturbances and state input constraints using a slack variable approach we propose new results to transform the original nonlinear problem into a convex lmi problem whilst introducing only minor conservatism in the formulation through numerical examples we illustrate that the proposed algorithm can yield improved maximal minimal volume rci set approximations in comparison with the schemes given in the literature

low temperature phase transitions in the quadratic family abstract we give the first example of a quadratic map having a phase transition after the first zero of the geometric pressure function this implies that several dimension spectra and large deviation rate functions associated to this map are not expected to be real analytic in contrast to the uniformly hyperbolic case the quadratic map we study has a non recurrent critical point so it is non uniformly hyperbolic in a strong sense

attractors and recurrence for dendrite critical polynomials we call a rational map f dendrite critical if all its recurrent critical points either belong to an invariant dendrite d or have minimal limit sets we prove that if f is a dendrite critical polynomial then for any conformal measure either for almost every point its limit set coincides with the julia set of f or for almost every point its limit set coincides with the limit set of a critical point c of f moreover if is non atomic then c can be chosen to be recurrent a corollary is that for a dendrite critical polynomial and a non atomic conformal measure the limit set of almost every point contains a critical point

robust time optimal control of constrained linear systems a version of dynamic programming which computes level sets of the value function rather than the value function set itself is used to design robust non linear controllers for linear discrete time dynamical systems subject to hard constraints on controls and states the controller stabilizes the system and steers all trajectories emanating in a prescribed set to a control invariant set in minimum time for the robust regulator problem the control invariant terminal set is a neighborhood preferably small of the origin for the robust tracking problem the control invariant terminal set is a neighborhood of the invariant set in which the tracking error is zero two non linear controllers which utilize the level sets of the value function are described the first requires the controller to solve on line a modest linear program whose dimension is approximately the same as that of the control variable the second decomposes each level set into a set of simplices a piecewise linear control law affine in each simplex is then constructed

robust model predictive control using tubes a form of feedback model predictive control mpc that overcomes disadvantages of conventional mpc but which has manageable computational complexity is presented the optimal control problem solved on line yields a tube and an associated piecewise affine control law that maintains the controlled trajectories in the tube despite uncertainty computational complexity is linear rather than exponential in horizon length asymptotic stability of the controlled system is established

min max feedback model predictive control for constrained linear systems min max feedback formulations of model predictive control are discussed both in the fixed and variable horizon contexts the control schemes the authors discuss introduce in the control optimization the notion that feedback is present in the receding horizon implementation of the control this leads to improved performance compared to standard model predictive control and resolves the feasibility difficulties that arise with the min max techniques that are documented in the literature the stabilizing properties of the methods are discussed as well as some practical implementation details

examples when nonlinear model predictive control is nonrobust we consider nominal robustness of model predictive control for discrete time nonlinear systems we show by examples that when the optimization problem involves state constraints or terminal constraints coupled with short optimization horizons the asymptotic stability of the closed loop may have absolutely no robustness that is to say it is possible for arbitrarily small disturbances to keep the closed loop strictly inside the interior of the feasibility region of the optimization problem and at the same time far from the desired set point this phenomenon does not occur when using model predictive control for linear systems with convex constraint sets we emphasize that a necessary condition for the absence of nominal robustness in nonlinear model predictive control is that the value function and feedback law are discontinuous at some point s in the interior of the feasibility region

inherent robustness properties of quasi infinite horizon nonlinear model predictive control we consider inherent robustness properties of model predictive control mpc for continuous time nonlinear systems with input constraints and terminal constraints we show that mpc with a nominal prediction model and persistent but bounded disturbances has some degree of inherent robustness when the terminal control law and the terminal penalty matrix are chosen as the linear quadratic control law and the related lyapunov matrix respectively we emphasize that the input constraint sets can be any compact set rather than convex sets and our results do not depend on the continuity of the optimal cost function or of the control law in the interior of the feasible region

on the lyapunov spectrum for rational maps we study the dimension spectrum for lyapunov exponents for rational maps on the riemann sphere

systems with persistent disturbances predictive control with restricted constraints predictive regulation of linear discrete time systems subject to unknown but bounded disturbances and to state control constraints is addressed an algorithm based on constraint restrictions is presented and its stability properties are analysed

brief doubly invariant equilibria of linear discrete time games in this paper the notion of doubly invariant di equilibrium is introduced the concept extends controlled and robustly controlled invariance notions to the context of two person dynamic games each player tries to keep the state in a region of state space independently of the actions of the rival player the paper gives existence conditions criteria and algorithms for the determination of di equilibria of linear dynamic games in discrete time two examples illustrate the results the first one is in the area of fault tolerant controller synthesis the second is an application to macroeconomics

on the role of the propensity score in efficient semiparametric estimation of average treatment effects in this paper the role of the propensity score in the efficient estimation of average treatment effects is examined under the assumption that the treatment is ignorable given some observed characteristics it is shown that the propensity score is ancillary for estimation of the average treatment effects the propensity score is not ancillary for estimation of average treatment effects on the treated it is suggested that the marginal value of the propensity score lies entirely in the dimension reduction efficient semiparametric estimators of average treatment effects and average treatment effects on the treated are shown to take the form of relevant sample averages of the data completed by the nonparametric imputation method it is shown that the projection on the propensity score is not necessary for efficient semiparametric estimation of average treatment effects on the treated even if the propensity score is known an application to the experimental data reveals that conditioning on the propensity score may even result in a loss of efficiency

a one step approach to computing a polytopic robust positively invariant set a procedure and theoretical results are presented for the problem of determining a minimal robust positively invariant rpi set for a linear discrete time system subject to unknown bounded disturbances the procedure computes via the solving of a single lp a polytopic rpi set that is minimal with respect to the family of rpi sets generated from a finite number of inequalities with pre defined normal vectors

the explicit linear quadratic regulator for constrained systems we present a technique to compute the explicit state feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints we show that this closed form solution is piecewise linear and continuous as a practical consequence of the result constrained linear quadratic regulation becomes attractive also for systems with high sampling rates as on line quadratic programming solvers are no more required for the implementation

brief a polytopic game we consider a discrete time linear dynamic game in state space form where the actions of two players are confined to belong to prescribed convex polytopes at all times each player has a home set a polyhedral domain in state space and should devise a cooperative or a non cooperative strategy contingent on the known initial state to reach her own home set in a finite number of steps and stay there irrespective of the action taken by the opponent players act independently on the basis of the state at each time using feedback strategies purpose of the analysis is to classify the set of initial states into winning sets and draw sets for each player and prescribe strategies able to implement the kind of invariance home sets should enjoy in the paper necessary and sufficient conditions for the existence of invariant sets with the above properties are derived these conditions and the relative strategies are characterized in terms of linear programming problems that provide a straightforward algorithmic solution to the game

efficient robust predictive control predictive constrained control of time varying and or uncertain linear systems has been effected through the use of ellipsoidal invariant sets kothare et al 1996 linear matrix inequalities lmis have been used to design a state dependent state feedback law that maintains the state vector inside invariant feasible sets for the purposes of prediction however at each time instant the state feedback law is assumed constant in addition due to the large number of lmis involved online computation becomes intractable for anything other than small dimensional systems here we propose an approach that deploys a fixed state feedback law but introduces extra degrees of freedom through the use of perturbations on the fixed state feedback law the problem is so formulated that all demanding computations can be performed offline leaving only a simple optimization problem to be solved online over and above the very significant reduction in computational cost the extra degrees of freedom allow for better performance and wider applicability

parameterized robust control invariant sets for linear systems theoretical advances and computational remarks we characterize a family of parametrized robust control invariant sets for linear discrete time systems subject to additive but bounded state disturbances the existence of a member of the introduced family of parametrized robust control invariant sets can be verified by solving a tractable convex optimization problem in the linear convex case which reduces to the standard linear or convex quadratic programme in the linear polytopic case the developed method can also be utilized to detect and obtain an implicit representation of local control lyapunov functions in the linear convex case from the solution of a single and tractable convex optimization problem the offered method permits for the computation of polytopic robust control invariant sets and local control lyapunov functions of indirectly controlled and limited complexity in the linear polytopic case

invariant approximations of the minimal robust positively invariant set this note provides results on approximating the minimal robust positively invariant mrpi set also known as the 0 reachable set of an asymptotically stable discrete time linear time invariant system it is assumed that the disturbance is bounded persistent and acts additively on the state and that the constraints on the disturbance are polyhedral results are given that allow for the computation of a robust positively invariant outer approximation of the mrpi set conditions are also given that allow one to a priori specify the accuracy of this approximation

constrained stabilization with an assigned initial condition set the problem of stabilizing a linear discrete time system with control constraints is considered necessary and sufficient conditions are given for the existence of a state feedback controller which drives the state to the origin asymptotically from every initial state in an assigned compact polyhedral set these conditions can be checked via linear programming it is shown that when the problem has a solution a polyhedral function can be formed which turns out to be a lyapunov function if a proper nonlinear feedback controller is applied two procedures are presented for the construction of the lyapunov function the first is based on the property that the stabilizing feedback compensator exists if and only if for every initial condition chosen on a vertex of the set there exists an open loop control driving the state to its interior the second procedure is based on the construction of the controllability regions to the given polyhedral set this procedure can also be applied to systems with parameter u

cooperative distributed stochastic mpc for systems with state estimation and coupled probabilistic constraints a cooperative distributed stochastic model predictive control cdsmpc algorithm is given for multiple dynamically decoupled subsystems with additive stochastic disturbances and coupled probabilistic constraints for which states are not measurable cooperation between subsystems is promoted by a scheme in which a local subsystem designs hypothetical plans for others in some cooperating set and considers the weighted costs of these subsystems in its objective to achieve satisfaction of coupled probabilistic constraints in a distributed way only one subsystem is permitted to optimize at each time step in addition by using a lifting technique and the probabilistic information on additive disturbances measurement noise and the state estimation error a set of deterministic constraints is constructed for the predictions of nominal models recursive feasibility with respect to both local and coupled probabilistic constraints is guaranteed and stability for any choice of update sequence and any structure of cooperation is ensured numerical examples illustrate the efficacy of the proposed algorithm

h infinity set membership observer design for discrete time lpv systems this paper presents a new set membership observer design method for discrete time linear parameter varying systems the real process is assumed to be perturbed by unknown but bounded disturbances

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

homothetic tube model predictive control the robust model predictive control for constrained linear discrete time systems is solved through the development of a homothetic tube model predictive control synthesis method the method employs several novel features including a more general parameterization of the state and control tubes based on homothety and invariance a more flexible form of the terminal constraint set and a relaxation of the controlled dynamics of the sets that define the state and control tubes under natural assumptions the proposed method is computationally efficient and it induces strong system theoretic properties

harmonic measure and expansion on the boundary of the connectedness locus the paper develops a technique for proving properties that are typical in the boundary of the connectedness locus with respect to the harmonic measure a typical expansion condition along the critical orbit is proved this condition implies a number of properties including the collet eckmann condition hausdorff dimension less than 2 for the julia set and the radial continuity in the parameter space of the hausdorff dimensions of totally disconnected julia sets

convex liftings based robust control design this paper presents a new approach for control design of constrained linear systems affected by bounded additive disturbances and polytopic uncertainties this method hinges on so called convex liftings which emulate control lyapunov function by providing a constructive framework for optimization based control implementation it will be shown that this method can guarantee the recursive feasibility and robust stability finally a numerical example will be presented to illustrate this method

brief paper constrained linear systems with hard constraints and disturbances an extended command governor with large domain of attraction this paper considers a nonlinear feedback control policy that is an extension of those provided by command governors and reference governors as in these control approaches it applies to discrete time linear systems with hard constraints and set bounded disturbances the control policy retains the main properties of traditional governors such as straightforward direct implementation and finite settling time response to arbitrarily specified set points its principal advantage over traditional governors is a significantly larger domain of attraction that may compete in size with those obtained by dynamic programming connections to model predictive control are made numerical examples illustrate advantageous features of the proposed approach