asymptotic fuzzy tracking control for a class of stochastic strict feedback systems this paper presents an asymptotic tracking control design method for stochastic strict feedback systems via fuzzy logic systems in the existing results stochastic controls are usually limited to be bounded in probability however how to realize the asymptotic tracking control for stochastic strict feedback systems remains a control dilemma this paper achieves the asymptotic tracking control by proposing a novel gain suppressing inequality approach specifically the three part construction is performed to achieve such control objective for stochastic systems first the novel gain suppressing inequality technique is developed to lay the foundation for carrying out the lyapunov stability analysis second the developed inequality technique is integrated with each step of the backstepping based adaptive control design procedure third analyses are provided to realize the asymptotic tracking control of stochastic strict feedback systems

stabilization by means of state space depending switching rules abstract in this paper we consider switched systems defined by a pair of linear systems x a 1 x x a 2 x such that there exists a neutrally stable linear combination of the matrices a 1 a 2 under an additional assumption we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense the result is illustrated by some simulations and examples

on a definition of random sequences with respect to conditional probability we study a universal martin lof test with respect to a computable probability on a product space then we define random sequences with respect to a conditional probability by using a section of the set of random points of product space we show that 1 our definition is consistent with fubini s theorem and 2 it is equivalent to the relative notion of randomness under a condition this is an extension of lambalgen s theorem 1987 to a correlated probability

on a common quadratic lyapunov function for widely distant systems a sufficient condition concerning the construction of a common quadratic lyapunov function for widely distant linear systems is presented the condition is set on a mutual relation matrix whose size is just equal to the number of the coefficient matrices

a new control method for state constrained nonlinear switched systems with application to chemical process this paper presents a new control method for a class of nonlinear switched systems in strict feedback form with a state constraint in the proposed approach a nonlinear mapping is first introduced to transform the problem of controlling the switched system with state constraint to a new problem of regulating the transformed system without a constraint by using the backstepping technique the designed state feedback controller ensures that the corresponding closed loop system is asymptotically stable without violation of the constraint and that all closed loop signals keep bounded furthermore we explore the use of a coordinate transformation to deal with an asymmetric state constraint as a generalised approach in the end an application example on a chemical process is shown to demonstrate the efficacy of the obtained results

combinatorial lower bound arguments for deterministic and nondeterministic turing machines on introduit de nouvelles techniques combinatoires pour etablir des bornes inferieures quadratiques des machines de turing deterministes et non deterministes a une bande

stability of switched linear discrete time descriptor systems a new commutation condition in this article we study stability of switched linear discrete time descriptor systems under the assumption that all subsystems are stable and there is no impulse occurring at the switching instants we establish a new pairwise commutation condition under which the switched system is stable it turns out that the condition is a natural and important extension to the existing commutation conditions and it can be applied in discretised continuous time switched systems in a straightforward manner finally we also show that when the proposed commutation condition holds there exists a common quadratic lyapunov function for the subsystems

blind identification of an autoregressive system using a nonlinear dynamical approach the problem of identifying an autoregressive ar system with arbitrary driven noise is considered here using an abstract dynamical system to represent both chaotic and stochastic processes in a unified framework a dynamic based complexity measure called phase space volume psv which has its origins in chaos theory can be applied to identify an ar model in chaotic as well as stochastic noise environments it is shown that the psv of the output signal of an inverse filter applied to identify an ar model is always larger than the psv of the input signal of the ar model therefore by minimizing the psv of the inverse filter output one can estimate the coefficients and the order of the ar system a major advantage of this minimum phase space volume mpsv identification technique is that it works like a universal estimator that does not require precise statistical information about the ar input signal because the theoretical psv is so difficult to compute two approximations of psv are also considered the e psv and nearest neighbor psv both approximations are shown to approach the ideal psv asymptotically the identification performance based on these two approximations are evaluated using monte carlo simulations both approximations are found to generate relatively good results in identifying an ar system in various noise environments including chaotic non gaussian and colored noise

stability results for switched controller systems there are many practical control problems where the control action is determined by switching among a given set of control laws this paper presents necessary and sufficient conditions to test for quadratic stabilizability and for robust stabilizability with a quadratic storage function for switched controller systems algorithms which can be used to construct appropriately stabilizing control laws are also presented

control of nonlinear systems with output tracking error constraints and its application to magnetic bearings a constructive method is presented to design controllers that force the output of nonlinear systems in a strict feedback form to track a bounded and sufficiently smooth reference trajectory asymptotically under a suitable condition on the initial output tracking error the proposed controllers guarantee the output tracking error within a symmetric or an asymmetric pre specified limit range and boundedness of all signals of the closed loop system a transformation is introduced to take care of the output tracking error constraint smooth and or p times differentiable step functions are proposed and incorporated in the output tracking error transformation to overcome difficulties due to the asymmetric limit range on the output tracking error as a result there are no switchings in the proposed controllers despite the asymmetric limit range the proposed control design is then applied to design a tracking controller for active magnetic bearings as an illustrating application

homogeneous observers iterative design and global stabilization of high order nonlinear systems by smooth output feedback we study the problem of global stabilization by smooth output feedback for a class of n dimensional homogeneous systems whose jacobian linearization is neither controllable nor observable a new output feedback control scheme is proposed for the explicit design of both homogeneous observers and controllers while the smooth state feedback control law is constructed based on the tool of adding a power integrator the observer design is new and carried out by developing a machinery which makes it possible to assign the observer gains one by one in an iterative manner such design philosophy is fundamentally different from that of the traditional luenberger observer in which the observer gain is determined by observability in the case of linear systems our design method provides not only a new insight but also an alternative solution to the output feedback stabilization problem for a class of high order nonhomogeneous systems we further show how the proposed design method with an appropriate modification can still achieve global output feedback stabilization examples and simulations are given to demonstrate the main features and effectiveness of the proposed output feedback control schemes

upcrossing inequalities for stationary sequences and applications for arrays s i j 1 i j of random variables that are stationary in an appropriate sense we show that the fluctuations of the process s 1 n n 1 can be bounded in terms of a measure of the mean subadditivity of the process s i j 1 i j we derive universal upcrossing inequalities with exponential decay for kingman s subadditive ergodic theorem the shannon macmillan breiman theorem and for the convergence of the kolmogorov complexity of a stationary sample

an lmi approach for h analysis and control of discrete time piecewise affine systems in this paper we investigate some analysis and control problems for discrete time hybrid systems in the piece wise affine form by using arguments from the dissipativity theory for non linear systems we show that h x analysis and synthesis problems can be formulated and solved via linear matrix inequalities by taking into account the switching structure of the considered system in this paper we address the generalized problem of controlling hybrid systems whose switching structure does not depend only on the state but also on the control input

on stability l2 gain and h control for switched systems this paper addresses the issues of stability l 2 gain analysis and h control for switched systems via multiple lyapunov function methods a concept of general lyapunov like functions is presented a necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized lyapunov like functions which enables derivation of improved stability tests an l 2 gain characterization and a design method for stabilizing switching laws a solution to the h control problem for switched systems is also provided

output feedback robust mpc with one free control move for the linear polytopic uncertain system with bounded disturbance in this paper a previous approach for the robust model predictive control mpc for a linear polytopic uncertain system is extended to the case with bounded disturbance and unmeasurable state the controller on line optimizes a free control move followed by an output feedback control law based on the pre specified state estimator a key technique for this controller is an appropriate formulation of the estimation error bound which accounts for recursive feasibility of the optimization problem the quadratic boundedness qb of the augmented state is guaranteed by the proposed approach a numerical example is given to illustrate the effectiveness of the proposed controller

distortion program size complexity with respect to a fidelity criterion and rate distortion function a novel concept of distortion kolmogorov chaitin complexity is proposed bearing analogy to ordinary kolmogorov chaitin complexity that represents the information content of a single message distortion kolmogorov chaitin complexity can be regarded as the amount of information about a single message that must be conveyed in order to reproduce it with a bounded distortion this explanation is justified by the properties of distortion kolmogorov chaitin complexity and the equivalences between distortion kolmogorov chaitin complexity and the rate distortion function which are analogous to those between ordinary kolmogorov chaitin complexity and the shannon entropy some implications for universal almost sure data compression are also discussed

almost sure stability of markov jump linear systems with deterministic switching the technical note studies a class of linear systems whose piecewise constant dynamic matrix is subject to both stochastic jumps governed by a markov chain and deterministic switches these systems will be dubbed switching dynamics markov jump linear systems sd mjls sufficient conditions for exponential almost sure stability eas stability are established under either hard or average constraints on the dwell time between switching instants the proof relies on easy to check norm contractivity conditions and the ergodic law of large numbers

kolmogorov s contributions to information theory and algorithmic complexity briefly information theory says a random object x p x has complexity entropy h xp x log p x with the attendant interpretation that h bits are sufficient to describe x on the average algorithmic complexity says an object x has a complexity k x equal to the length of the shortest binary program that describes x it is a beautiful fact that these ideas are much the same in fact it is roughly true that ek x h moreover if we let pu x pr u prints x be the probability that a given computer u prints x when given a random program it can be shown that log 1 pu x k x for all x thus establishing a vital link between the universal probability measure pu and the universal complexity k more on this later the relationship of these ideas to probability theory was summed up in kolmogorov s 1983 paper which was based on his 1970 talk in nice perhaps only

stability and stabilization of switched linear systems with mode dependent average dwell time in this paper the stability and stabilization problems for a class of switched linear systems with mode dependent average dwell time mdadt are investigated in both continuous time and discrete time contexts the proposed switching law is more applicable in practice than the average dwell time adt switching in which each mode in the underlying system has its own adt the stability criteria for switched systems with mdadt in nonlinear setting are firstly derived by which the conditions for stability and stabilization for linear systems are also presented a numerical example is given to show the validity and potential of the developed techniques

stability analysis of switched systems using variational principles an introduction many natural and artificial systems and processes encompass several modes of operation with a different dynamical behavior in each mode switched systems provide a suitable mathematical model for such processes and their stability analysis is important for both theoretical and practical reasons we review a specific approach for stability analysis based on using variational principles to characterize the most unstable solution of the switched system we also discuss a link between the variational approach and the stability analysis of switched systems using lie algebraic considerations both approaches require the use of sophisticated tools from many different fields of applied mathematics the purpose of this paper is to provide an accessible and self contained review of these topics emphasizing the intuitive and geometric underlying ideas

output feedback control of switched nonlinear systems using multiple lyapunov functions abstract this work presents a hybrid nonlinear control methodology for a broad class of switched nonlinear systems with input constraints the key feature of the proposed methodology is the integrated synthesis via multiple lyapunov functions of lower level bounded nonlinear feedback controllers together with upper level switching laws that orchestrate the transitions between the constituent modes and their respective controllers both the state and output feedback control problems are addressed under the assumption of availability of full state measurements a family of bounded nonlinear state feedback controllers are initially designed to enforce asymptotic stability for the individual closed loop modes and provide an explicit characterization of the corresponding stability region for each mode a set of switching laws are then designed to track the evolution of the state and orchestrate switching between the stability regions of the constituent modes in a way that guarantees asymptotic stability of the overall switched closed loop system when complete state measurements are unavailable a family of output feedback controllers are synthesized using a combination of bounded state feedback controllers high gain observers and appropriate saturation filters to enforce asymptotic stability for the individual closed loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain a different set of switching rules based on the evolution of the state estimates generated by the observers is designed to orchestrate stabilizing transitions between the output feedback stability regions of the constituent modes the differences between the state and output feedback switching strategies and their implications for the switching logic are discussed and a chemical process example is used to demonstrate the proposed approach

non stochastic infinite and finite sequences abstract combining outcomes of coin tossing and transducer algorithms it is possible to generate with probability close to 1 very pathological sequences for which computable probabilistic forecasting is impossible these sequences are not random with respect to any reasonable probability distribution a natural consequence from the definition of such sequences is that each simple measure of the set of all such sequences is equal to 0 it was kolmogorov s and levin s idea to estimate the probability of generating of such sequences in the combinations of probabilistic and algorithmic processes 8 14 21 we collect several results in this direction for infinite sequences and asymptotic results for finite sequences including estimation of space and time of losing randomness for time bounded forecasting systems a correction to 22

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

barrier lyapunov functions for the output tracking control of constrained nonlinear switched systems abstract in this paper we investigate the output tracking control problem of constrained nonlinear switched systems in lower triangular form first when all the states are subjected to constraints we employ a barrier lyapunov function blf which grows to infinity whenever its arguments approach some finite limits to prevent the states from violating the constraints based on the simultaneous domination assumption we design a continuous feedback controller for the switched system which guarantees that asymptotic output tracking is achieved without transgression of the constraints and all closed loop signals remain bounded provided that the initial states are feasible then we further consider the case of asymmetric time varying output constraints by constructing an appropriate blf finally the effectiveness of the proposed results is demonstrated with a numerical example

brief paper h estimation for discrete time piecewise homogeneous markov jump linear systems this paper concerns the problem of h estimation for a class of markov jump linear systems mjls with time varying transition probabilities tps in discrete time domain the time varying character of tps is considered to be finite piecewise homogeneous and the variations in the finite set are considered to be of two types arbitrary variation and stochastic variation respectively the latter means that the variation is subject to a higher level transition probability matrix the mode dependent and variation dependent h filter is designed such that the resulting closed loop systems are stochastically stable and have a guaranteed h filtering error performance index using the idea in the recent studies of partially unknown tps for the traditional mjls with homogeneous tps a generalized framework covering the two kinds of variations is proposed a numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results

entropic measures markov information sources and complexity the concept of entropy plays a major part in communication theory the shannon entropy is a measure of uncertainty with respect to a priori probability distribution in algorithmic information theory the information content of a message is measured in terms of the size in bits of the smallest program for computing that message this paper discusses the classical entropy and entropy rate for discrete or continuous markov sources with finite or continuous alphabets and their relations to program size complexity and algorithmic probability the accent is on ideas constructions and results no proofs will be given

state unilateral tracking control of positive switched systems via designing a switching law abstractthis paper focuses on the model reference state unilateral tracking control problem of positive switched systems the state unilateral tracking means that the state always keeps in the same direction of the reference objective either above or below this feature makes unilateral tracking play a role of avoiding the overshoot via the dual design of both the controller and the switching signal the state unilateral tracking control problem with l1 gain performance for positive switched systems is solved through adopting multiple linear co positive lyapunov functions technique the design method is applicable to the case that the unilateral tracking control problem is unsolvable for any subsystem of a positive switched system moreover two techniques are presented in order to deal with the state unilateral tracking problem finally a practical example demonstrates the validity of the presented result

parameter dependent h filter design for lpv systems and an autopilot application abstract this paper considers the design problem of parameter dependent h filters for linear parameter varying lpv systems whose parameters are measurable conditions for existence of parameter dependent lyapunov function are proposed via parametrical linear matrix inequality lmi constraints based on the solutions to the lmis an algorithm for the gain matrices of lpv filter is presented the design method is applied to a missile system to demonstrate the effectiveness

approximate robust dynamic programming and robustly stable mpc we present a technique for approximate robust dynamic programming that is suitable for linearly constrained polytopic systems with piecewise affine cost functions the approximation method uses polyhedral representations of the cost to go function and feasible set and can considerably reduce the computational burden compared to recently proposed methods for exact robust dynamic programming bemporad a borrelli f morari m 2003 min max control of constrained uncertain discrete time linear systems ieee transactions on automatic control 48 9 1600 1606 diehl m bjornberg j 2004 robust dynamic programming for min max model predictive control of constrained uncertain systems ieee transactions on automatic control 49 12 2253 2257 we show how to apply the method to robust mpc and give conditions that guarantee closed loop stability we finish by applying the method to a state constrained tutorial example a parking car with uncertain mass

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 strong ergodic theorem for densities generalized shannon mcmillan breiman theorem let xi x2 be a stationary process with probability densities f x1 x2 xn with respect to lebesgue measure or with respect to a markov measure with a stationary transition measure it is shown that the sequence of relative entropy densities 1 n log f xi x2 x0 converges almost surely this long conjectured result extends the l convergence obtained by moy perez and kieffer and generalizes the shannon mcmillanbreiman theorem to nondiscrete processes the heart of the proof is a new martingale inequality which shows that logarithms of densities are l dominated

a fast ellipsoidal mpc scheme for discrete time polytopic linear parameter varying systems this paper proposes a fast ellipsoidal model predictive control mpc strategy to address feedback regulation problems for constrained polytopic linear parameter varying lpv systems subject to bounded disturbances in order to deal with the specific non convex structure of the state prediction tubes arising in lpv contexts a new convexification procedure is proposed and based on the off line computation of a sequence of inner ellipsoidal approximations of exact one step controllable sets a computationally low demanding mpc algorithm is presented comparisons with state of the art mpc control algorithms for lpv systems are reported in a final numerical example where several methods are contrasted in terms of achievable domains of attraction control performance numerical burdens and memory requirements

stability and l2 gain analysis for switched delay systems a delay dependent method in this paper we study stability and l 2 gain for a class of switched systems with time varying delays sufficient conditions for exponential stability and weighted l 2 gain are developed for a class of switching signals with average dwell time these conditions are delay dependent and are given in the form of linear matrix inequalities lmis as a special case of such switching signals we can obtain exponential stability and normal l 2 gain under arbitrary switching signals the state decay estimate is explicitly given two examples illustrate the effectiveness and applicability of the proposed method

finite time stabilisation of a class of switched nonlinear systems with state constraints abstractthis paper investigates the finite time stabilisation for a class of switched nonlinear systems with state constraints some power orders of the system are allowed to be ratios of positive even integers over odd integers a barrier lyapunov function is introduced to guarantee that the state constraint is not violated at any time using the convex combination method and a recursive design approach a state dependent switching law and state feedback controllers of individual subsystems are constructed such that the closed loop system is finite time stable without violation of the state constraint two examples are provided to show the effectiveness of the proposed method

dissipativity based sliding mode control of switched stochastic systems this technical brief is concerned with dissipativity analysis and dissipativity based sliding mode control smc of continuous time switched stochastic systems firstly a sufficient condition is proposed to guarantee the mean square exponential stability and strict dissipativity for the switched stochastic system then an integral type sliding surface function is designed for establishing a sliding mode dynamics which can be formulated by a switched stochastic system with an external disturbance uncertainty dissipativity analysis and synthesis are both investigated for the sliding mode dynamics and consequently sufficient conditions are derived which pave the way for solving the dissipativity analysis and control problems moreover a smc law is synthesized to drive the system trajectories onto the predefined sliding surface in a finite time finally the efficiency of the theoretical findings is demonstrated by an illustrative example

h_ infty control of switched nonlinear systems in p normal form using multiple lyapunov functions the problem of h control of switched nonlinear systems in p normal form is investigated in this technical note where the solvability of the h control problem for individual subsystems is unnecessary using the generalized multiple lyapunov functions method and the adding a power integrator technique we design a switching law and construct continuous state feedback controllers of subsystems explicitly by a recursive design algorithm to produce global asymptotical stability and a prescribed h performance level multiple lyapunov functions are exploited to reduce the conservativeness caused by adoption of a common lyapunov function for all subsystems which is usually required when applying the backstepping like recursive design scheme an example is provided to demonstrate the effectiveness of the proposed design method

stability of systems with controller failure and time varying delay this paper studies the stability for a class of systems with time varying delay subject to controller failure it explores under what conditions of controller failure the system is still exponentially stable the concept of controller failure frequency is introduced first the delay system with failed controller is modelled as a class of switched delay systems next based on two lemmas developed in this paper and the piecewise lyapunov functional method sufficient conditions are provided to guarantee the exponential stability of the system when controller failure occurs which is in terms of the solvability of a set of linear matrix inequalities lmis finally an example of a networked control system is given to illustrate the effectiveness of the proposed method

brief an efficient off line formulation of robust model predictive control using linear matrix inequalities the practicality of model predictive control mpc is partially limited by its ability to solve optimization problems in real time moreover on line computational demand for synthesizing a robust mpc algorithm will likely grow significantly with the problem size in this paper we use the concept of an asymptotically stable invariant ellipsoid to develop a robust constrained mpc algorithm which gives a sequence of explicit control laws corresponding to a sequence of asymptotically stable invariant ellipsoids constructed off line one within another in state space this off line approach can address a broad class of model uncertainty descriptions with guaranteed robust stability of the closed loop system and substantial reduction of the on line mpc computation the controller design is illustrated with two examples

brief paper backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings this paper is concerned with the global stabilization problem for switched nonlinear systems in lower triangular form under arbitrary switchings two classes of state feedback controllers and a common lyapunov function clf are simultaneously constructed by backstepping the first class uses the common state feedback controller which is independent of switching signals the other class utilizes individual state feedback controllers for the subsystems as an extension of the designed method the global stabilization problem under arbitrary switchings for switched nonlinear systems in nested lower triangular form is also studied an example is given to show the effectiveness of the proposed method

quasi min max mpc algorithms for lpv systems in this paper a new model predictive controller mpc is developed for polytopic linear parameter varying lpv systems we adopt the paradigm used in gain scheduling and assume that the time varying parameters are measured on line but their future behavior is uncertain and contained in a given polytope at each sampling time optimal control action is computed by minimizing the upper bound on the quasi worst case value of an infinite horizon quadratic objective function subject to constraints on inputs and outputs the mpc algorithm is called quasi because the first stage cost can be computed without any uncertainty this allows the inclusion of the first move u k k separately from the rest of the control moves governed by a feedback law and is shown to reduce conservatism and improve feasibility characteristics with respect to input and output constraints proposed optimization problems are solved by semi definite programming involving linear matrix inequalities it is shown that closed loop stability is guaranteed by the feasibility of the linear matrix inequalities a numerical example demonstrates the unique features of the mpc design

stability analysis and control synthesis for switched systems a switched lyapunov function approach this paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete time domain the approach followed in this paper looks at the existence of a switched quadratic lyapunov function to check asymptotic stability of the switched system under consideration two different linear matrix inequality based conditions allow to check the existence of such a lyapunov function the first one is classical while the second is new and uses a slack variable which makes it useful for design problems these two conditions are proved to be equivalent for stability analysis investigating the static output feedback control problem we show that the second condition is in this case less conservative the reduction of the conservatism is illustrated by a numerical evaluation

constrained rhc for lpv systems with bounded rates of parameter variations this paper studies a stabilization problem of polytopically uncertain linear parameter varying systems with input constraints and bounded rates of parameter variations in the framework of finite receding horizon control rhc a system containing parameter uncertainties is modified into a system with parameter incremental uncertainties within each horizon for the system modified in this manner a robust rhc is designed by solving an optimization problem at each time instant based on the feasibility of the problem and the optimality of its solution the closed loop system stability is guaranteed a numerical example is included to illustrate the validity of the results

analysis and synthesis of markov jump linear systems with time varying delays and partially known transition probabilities in this note the stability analysis and stabilization problems for a class of discrete time markov jump linear systems with partially known transition probabilities and time varying delays are investigated the time delay is considered to be time varying and has a lower and upper bounds the transition probabilities of the mode jumps are considered to be partially known which relax the traditional assumption in markov jump systems that all of them must be completely known a priori following the recent study on the class of systems a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality lmi formulation and the design of the stabilizing controller is further given a numerical example is used to illustrate the developed theory

minimum description length induction bayesianism and kolmogorov complexity the relationship between the bayesian approach and the minimum description length approach is established we sharpen and clarify the general modeling principles minimum description length mdl and minimum message length mml abstracted as the ideal mdl principle and defined from bayes s rule by means of kolmogorov complexity the basic condition under which the ideal principle should be applied is encapsulated as the fundamental inequality which in broad terms states that the principle is valid when the data are random relative to every contemplated hypothesis and also these hypotheses are random relative to the universal prior the ideal principle states that the prior probability associated with the hypothesis should be given by the algorithmic universal probability and the sum of the log universal probability of the model plus the log of the probability of the data given the model should be minimized if we restrict the model class to finite sets then application of the ideal principle turns into kolmogorov s minimal sufficient statistic in general we show that data compression is almost always the best strategy both in model selection and prediction

bayesianism an algorithmic analysis abstract the bayesian program in statistics starts from the assumption that an individual can always ascribe a definite probability to any event it will be demonstrated that this assumption is incompatible with the natural requirement that the individual s subjective probability distribution should be computable we shall construct a probabilistic algorithm producing with probability extremely close to 1 an infinite binary sequence which is not random with respect to any computable probability distribution we use dawid s notion of randomness computable calibration but the results hold for other widely known notions of randomness as well since the bayesian knows the algorithm he must believe that this sequence will be noncalibrable on the other hand it seems that the bayesian must believe that the sequence is random with respect to his own probability distribution we hope that the discussion of this apparent paradox will clarify the foundations of bayesian statistics we analyse also the time of computation and the place of losing randomness we show that we need only polynomial time and space to demonstrate non calibration effects on finite sequences

minimum complexity density estimation the authors introduce an index of resolvability that is proved to bound the rate of convergence of minimum complexity density estimators as well as the information theoretic redundancy of the corresponding total description length the results on the index of resolvability demonstrate the statistical effectiveness of the minimum description length principle as a method of inference the minimum complexity estimator converges to true density nearly as fast as an estimator based on prior knowledge of the true subclass of densities interpretations and basic properties of minimum complexity estimators are discussed some regression and classification problems that can be examined from the minimum description length framework are considered

kolmogorov s structure functions and model selection in 1974 kolmogorov proposed a nonprobabilistic approach to statistics and model selection let data be finite binary strings and models be finite sets of binary strings consider model classes consisting of models of given maximal kolmogorov complexity the structure function of the given data expresses the relation between the complexity level constraint on a model class and the least log cardinality of a model in the class containing the data we show that the structure function determines all stochastic properties of the data for every constrained model class it determines the individual best fitting model in the class irrespective of whether the true model is in the model class considered or not in this setting this happens with certainty rather than with high probability as is in the classical case we precisely quantify the goodness of fit of an individual model with respect to individual data we show that within the obvious constraints every graph is realized by the structure function of some data we determine the un computability properties of the various functions contemplated and of the algorithmic minimal sufficient statistic

finite valued feedback laws and piecewise classical solutions abstract often in engineering literature we find control systems in which the open loop inputs are piecewise constant and take values in a finite set such open loop inputs cause the system to have fairly regular solutions on the other hand when acting in closed loop feedback laws taking values in a finite set may not be reinterpreted as open loop inputs of the considered type in fact pathological behaviours such as the accumulation of discontinuities may appear zeno phenomenon we give some conditions which can be used as tools for building finite valued feedback laws not causing such pathological behaviours

output feedback robust mpc for lpv system with polytopic model parametric uncertainty and bounded disturbance abstractthe output feedback robust model predictive control mpc for the linear parameter varying lpv system with norm bounded disturbance is addressed where the model parametric matrices are only known to be bounded within a polytope the previous techniques of norm bounding technique quadratic boundedness qb dynamic output feedback and ellipsoid true state bound tsb refreshment formula for guaranteeing recursive feasibility are fused into the newly proposed approaches in the notion of qb the full lyapunov matrix is applied for the first time in this context the single step dynamic output feedback robust mpc where the infinite horizon control moves are parameterised as a dynamic output feedback law is the main topic of this paper while the multi step method is also suggested in order to strictly guarantee the physical constraints the outer bound of the true state replaces the true state itself so tightness of this bound has a major effect on the control performance in order to ti

technical communique improving off line approach to robust mpc based on nominal performance cost this paper gives two alternative off line synthesis approaches to robust model predictive control rmpc for systems with polytopic description in each approach a sequence of explicit control laws that correspond to a sequence of nested asymptotically invariant ellipsoids are constructed off line in order to accommodate a wider class of systems nominal performance cost is chosen to substitute the worst case one in an existing technique in the design of control law for a larger ellipsoid the second approach further incorporates the knowledge of control laws associated with all smaller ellipsoids so as to further improve feasibility and optimality the effectiveness of the alternative approaches is illustrated by a simulation example

does snooping help one of the most efficient way of improving the performance of learning algorithms is snooping i e using some information about the data to be predicted for choosing the parameters of the learning algorithm or the learning algorithm itself allowing different degrees of snooping makes it possible to attain a better performance lossp x of a prediction strategy p on the given data set x we study the snooping curves lx infk p lossp x where k p is the kolmogorov complexity of the prediction strategy p we prove that every non increasing function can be approximated with arbitrary precision by some snooping function lx our framework is that of on line prediction for simplicity we assume that sequences x are binary

h bumpless transfer for switched lpv systems and its application in this paper the approach of the control bumps limitation is generalised and applied to the problem of h bumpless transfer for a class of switched linear parameter varying lpv systems the h

minimum complexity pursuit for universal compressed sensing the nascent field of compressed sensing is founded on the fact that high dimensional signals with simple structure can be recovered accurately from just a small number of randomized samples several specific kinds of structures have been explored in the literature from sparsity and group sparsity to low rankness however two fundamental questions have been left unanswered what are the general abstract meanings of structure and simplicity do there exist universal algorithms for recovering such simple structured objects from fewer samples than their ambient dimension in this paper we address these two questions using algorithmic information theory tools such as the kolmogorov complexity we provide a unified definition of structure and simplicity leveraging this new definition we develop and analyze an abstract algorithm for signal recovery motivated by occam s razor minimum complexity pursuit mcp requires approximately 2 randomized samples to recover a signal of complexity and ambient dimension n we also discuss the performance of the mcp in the presence of measurement noise and with approximately simple signals

brief paper design of switching sequences for controllability realization of switched linear systems in this paper we study the problem of designing switching sequences for controllability of switched linear systems each controllable state set of designed switching sequences coincides with the controllable subspace both aperiodic and periodic switching sequences are considered for the aperiodic case a new approach is proposed to construct switching sequences and the number of switchings involved in each designed switching sequence is shown to be upper bounded by d d d 1 1 here d is the dimension of the controllable subspace d email protected i 1 m where a i b i are subsystems for the periodic case we show that the controllable subspace can be realized within d switching periods

bibo stability of linear switching systems in this paper we show that for linear switching systems of the form x sub n 1 a sub n x sub n u sub n 1 where the matrices a sub n are chosen arbitrarily from a given set of matrices bounded input bounded output stability implies uniform exponential stability

brief paper control of nonlinear systems with time varying output constraints this paper presents control design for strict feedback nonlinear systems with time varying output constraints an asymmetric time varying barrier lyapunov function blf is employed to ensure constraint satisfaction by allowing the barriers to vary with the desired trajectory in time the initial condition requirements are relaxed through a change of tracking error coordinates we eliminate the explicit dependence of the blf on time thereby simplifying the analysis of constraint satisfaction we show that asymptotic output tracking is achieved without violation of the output constraint and also quantify the transient performance bound as a function of time that converges to zero to handle parametric model uncertainty we present an adaptive controller that ensures constraint satisfaction during the transient phase of online parameter adaptation the performance of the proposed control is illustrated through a simulation example

an ellipsoidal off line mpc scheme for uncertain polytopic discrete time systems an off line model predictive control mpc method based on ellipsoidal calculus and viability theory is described in order to address control problems in the presence of state and input constraints for uncertain polytopic linear plants subject to persistent disturbances in order to reduce the computational burdens and conservativeness of traditional polytopic mpc schemes the present approach carries out off line most of the computations and it makes use of closed loop predictions to improve the control performance this is done by recursively pre computing suitable ellipsoidal inner approximations of the exact controllable sets and solving on line a simple and numerically low demanding optimization problem subject to a set membership constraint comparisons with three other recent off line mpc approaches are also provided in the final example