unknown time varying input delay compensation for uncertain nonlinear systems abstract a tracking controller is developed for a class of uncertain nonlinear systems subject to unknown time varying input delay and additive disturbances a novel filtered error signal is designed using the past states in a finite integral over a constant estimated delay interval the maximum tolerable error between unknown time varying delay and a constant estimate of the delay is determined to establish uniformly ultimately bounded convergence of the tracking error to the origin the controller development is based on an approach which uses lyapunov krasovskii functionals to analyze the effects of unknown sufficiently slowly time varying input delays a stability analysis is provided to prove ultimate boundedness of the tracking error signals numerical simulation results illustrate the performance of the developed robust controller

equivalence of linear time delay systems the question of characterizing those time delay systems which are equivalent up to bicausal transformations to a delay free system is a natural and fundamental problem which has been raised since the early 1980s surprisingly this problem remains largely open despite that some partial answers have been provided this technical note tackles this problem for linear systems with constant time delays and gives necessary and sufficient conditions to eliminate whenever is possible or to reduce the number of time delays and a constructive way to get the corresponding bicausal change of coordinates

control of an unstable reaction diffusion pde with long input delay abstract a smith predictor like design for compensation of arbitrarily long input delays is available for general controllable possibly unstable lti finite dimensional systems such a design has not been proposed previously for problems where the plant is a pde we present a design and stability analysis for a prototype problem where the plant is a reaction diffusion parabolic pde with boundary control the plant has an arbitrary number of unstable eigenvalues and arbitrarily long delay with an unbounded input operator the predictor based feedback design extends fairly routinely within the framework of infinite dimensional backstepping however the stability analysis contains interesting features that do not arise in predictor problems when the plant is an ode the unbounded character of the input operator requires that the stability be characterized in terms of the h 1 rather than the usual l 2 norm of the actuator state the analysis involves an interesting structure of interconnected pdes of parabolic and first order hyperbolic types where the feedback gain kernel for the undelayed problem becomes an initial condition in a pde arising in the compensator design for the problem with input delay space and time variables swap their roles in an interesting manner throughout the analysis

technical communique h optimal terminal control for linear systems with delayed states and controls in this paper we consider a linear time varying system with state and control delay terms both lumped and distributed subject to unknown square integrable disturbances using a differential games approach we provide a necessary and sufficient condition for the existence of an optimal control law minimizing the h norm of the operator mapping the disturbance to the weighted control and terminal state

stabilization of second order evolution equations with unbounded feedback with time dependent delay we consider abstract second order evolution equations with unbounded feedback with time varying delay existence results are obtained under some realistic assumptions we prove the exponential decay under some conditions by introducing an abstract lyapunov functional our abstract framework is applied to the wave to the beam and to the plate equations with boundary delays

asymptotically optimal anomaly detection via sequential testing sequential detection of independent anomalous processes among k processes is considered at each time only m 1 leq m leq k processes can be observed and the observations from each chosen process follow two different distributions depending on whether the process is normal or abnormal each anomalous process incurs a cost per unit time until its anomaly is identified and fixed switching across processes and state declarations are allowed at all times while decisions are based on all past observations and actions the objective is a sequential search strategy that minimizes the total expected cost incurred by all the processes during the detection process under reliability constraints we develop index type algorithms for the case with both known observation distributions and the case when the observation distributions have unknown parameters we show that the proposed algorithms are asymptotically optimal in terms of minimizing the total expected cost as the error constraints approach zero simulation results demonstrate strong performance in the finite regime

prediction based stabilization of linear systems subject to input dependent input delay of integral type in this paper it is proved that a predictor based feedback controller can effectively yield asymptotic convergence for a class of linear systems subject to input dependent input delay this class is characterized by the delay being implicitly related to past values of the input via an integral model this situation is representative of systems where transport phenomena take place as is frequent in the process industry the sufficient conditions obtained for asymptotic stabilization bring a local result and require the magnitude of the feedback gain to be consistent with the initial conditions scale arguments of proof for this novel result include general halanay inequalities for delay differential equations and build on recent advances of backstepping techniques for uncertain or varying delay systems

exponential input to state stabilization of a class of diagonal boundary control systems with delay boundary control abstract this paper deals with the exponential input to state stabilization with respect to boundary disturbances of a class of diagonal infinite dimensional systems via delay boundary control the considered input delays are uncertain and time varying the proposed control strategy consists of a constant delay predictor feedback controller designed on a truncated finite dimensional model capturing the unstable modes of the original infinite dimensional system we show that the resulting closed loop system is exponentially input to state stable with fading memory of both additive boundary input perturbations and disturbances in the computation of the predictor feedback

new formulation of predictors for finite dimensional linear control systems with input delay we consider a one dimensional controlled reaction diffusion equation where the control acts on the boundary and is subject to a constant delay such a model is a paradigm for more general parabolic systems coupled with a transport equation we prove that this is possible to stabilize in h 1 norm this process by means of an explicit predictor based feedback control that is designed from a finite dimensional subsystem the implementation is very simple and efficient and is based on standard tools of pole shifting our feedback acts on the system as a finite dimensional predictor we compare our approach with the backstepping method

nonlinear discrete time systems with delayed control a reduction in this work the notion of reduction is introduced for discrete time nonlinear input delayed systems the retarded dynamics is reduced to a new system which is free of delays and equivalent in terms of stabilizability to the original one different stabilizing strategies are proposed over the reduced model connections with existing predictor based methods are discussed the methodology is also worked out over particular classes of time delay systems as sampled data dynamics affected by an entire input delay

stabilization of distributed control systems with delay abstract in this paper the asymptotic stabilization of linear distributed parameter control systems with delay is considered specifically we are concerned with the class of control systems described by the equation x t a x t l x t b u t where a is the infinitesimal generator of a strongly continuous semigroup on a banach space x assuming appropriate conditions we will show that the usual spectral controllability assumption implies the feedback stabilization of the system applications to systems described by partial differential equations with delay are given

boundary feedback stabilization of a reaction diffusion equation with robin boundary conditions and state delay abstract this paper discusses the boundary feedback stabilization of a reaction diffusion equation with robin boundary conditions and in the presence of a time varying state delay the proposed control design strategy is based on a finite dimensional truncated model obtained via a spectral decomposition by an adequate selection of the number of modes of the original infinite dimensional system we show that the design performed on the finite dimensional truncated model achieves the exponential stabilization of the original infinite dimensional system in the presence of distributed disturbances we show that the closed loop system is exponentially input to state stable with fading memory

a predictor control for multivariable systems with general delays in inputs and outputs subject to unmeasurable disturbances this paper is concerned with a linear predictor control for multivariable systems with general delays in inputs and outputs subject to unmeasurable disturbances the previous results given by watanabe and sato 1984 are extended to the general delay case involving distributed delays a predictor control scheme which can yield a zero steady state error with desired transient responses is proposed

stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks in this paper we consider in a bounded and smooth domain the wave equation with a delay term in the boundary condition we also consider the wave equation with a delayed velocity term and mixed dirichlet neumann boundary condition in both cases under suitable assumptions we prove exponential stability of the solution these results are obtained by introducing suitable energies and by using some observability inequalities if one of the above assumptions is not satisfied some instability results are also given by constructing some sequences of delays for which the energy of some solutions does not tend to zero

an lmi condition for the robustness of constant delay linear predictor feedback with respect to uncertain time varying input delays abstract this paper discusses the robustness of the constant delay predictor feedback in the case of an uncertain time varying input delay specifically we study the stability of the closed loop system when the predictor feedback is designed based on the knowledge of the nominal value of the time varying delay by resorting to an adequate lyapunov krasovskii functional we derive an lmi based sufficient condition ensuring the exponential stability of the closed loop system for small enough variations of the time varying delay around its nominal value these results are extended to the feedback stabilization of a class of diagonal infinite dimensional boundary control systems in the presence of a time varying delay in the boundary control input

conditions for robustness and nonrobustness of thestability of feedback systems with respect to small delays inthe feedback loop it has been observed that for many stable feedback control systems the introduction of arbitrarily small time delays into the loop causes instability in this paper we present a systematic frequency domain treatment of this phenomenon for distributed parameter systems we consider the class of all matrix valued transfer functions which are bounded on some right half plane and which have a limit at spinfty along the real axis such transfer functions are called regular under the assumption that a regular transfer function is stabilized by unity output feedback we give sufficient conditions for the robustness and for the nonrobustness of the stability with respect to small time delays in the loop these conditions are given in terms of the high frequency behavior of the open loop system moreover we discuss robustness of stability with respect to small delays for feedback systems with dynamic compensators in particular we show that if a plant with infinitely many poles in the closed right half plane is stabilized by a controller then the stability is not robust with respect to delays we show that the instability created by small delays is itself robust to small delays three examples are given to illustrate these results

receding horizon controls for input delayed systems this paper presents a receding horizon control rhc for an unconstrained input delayed system to begin with we derive a finite horizon optimal control for a quadratic cost function including two final weighting terms the rhc is easily obtained by changing the initial and final times of the finite horizon optimal control a linear matrix inequality lmi condition on two final weighting matrices is proposed to meet the cost monotonicity under which the optimal cost on the horizon is monotonically nonincreasing with time and hence the asymptotical stability is guaranteed only if an observability condition is met it is shown through simulation that the proposed rhc stabilizes the input delayed system effectively and its performance can be tuned by adjusting weighting matrices with respect to the state and the input

sequential testing for sparse recovery this paper studies sequential methods for recovery of sparse signals in high dimensions when compared with fixed sample size procedures in the sparse setting sequential methods can result in a large reduction in the number of samples needed for reliable signal support recovery starting with a lower bound we show any coordinate wise sequential sampling procedure fails in the high dimensional limit provided the average number of measurements per dimension is less then log s d p 0 p 1 where s is the level of sparsity and d p 0 p 1 is the kullback leibler divergence between the underlying distributions a series of sequential probability ratio tests which require complete knowledge of the underlying distributions is shown to achieve this bound motivated by real world experiments and recent work in adaptive sensing we introduce a simple procedure termed sequential thresholding which can be implemented when the underlying testing problem satisfies a monotone likelihood ratio assumption sequential thresholding guarantees exact support recovery provided the average number of measurements per dimension grows faster than log s d p 0 p 1 achieving the lower bound for comparison we show any nonsequential procedure fails provided the number of measurements grows at a rate less than log n d p 1 p 0 where n is the total dimension of the problem

adaptive control scheme for uncertain time delay systems the paper exposes some of the potential of a recently introduced backstepping transformation for linear uncertain time delay systems to address the classic problems of equilibrium regulation under partial measurements disturbance rejection parameter or delay adaptation for each of these problems an implementable control strategy is proposed it is analyzed through a convergence analysis of infinite dimensional dynamics based on a transport partial differential equation representation of the estimated input delay and the mentioned backstepping transformation the considered controllers contain this representation of the system under the form of a distributed parameter system and use it to determine relevant adaptation strategies an illustration example is proposed

feedback stabilization of a 1 d linear reaction diffusion equation with delay boundary control the goal of this paper is to design a stabilizing feedback boundary control for a reaction diffusion partial differential equation pde where the boundary control is subject to a constant delay while the equation may be unstable without any control for this system which is equivalent to a parabolic equation coupled with a transport equation a prediction based control is explicitly computed by splitting the infinite dimensional system into two parts a finite dimensional unstable part and a stable infinite dimensional part a finite dimensional delayed controller is computed for the unstable part and it is shown that this controller stabilizes the whole pde the proof is based on an explicit expression of the classical artstein transformation combined with an adequately designed lyapunov function a numerical simulation illustrates the constructive feedback design method

quickest search over multiple sequences the problem of sequentially finding an independent and identically distributed sequence that is drawn from a probability distribution q1 by searching over multiple sequences some of which are drawn from q1 and the others of which are drawn from a different distribution q0 is considered in the problem considered the number of sequences with distribution q1 is assumed to be a random variable whose value is unknown within a bayesian formulation a sequential decision rule is derived that optimizes a trade off between the probability of false alarm and the number of samples needed for the decision in the case in which one can observe one sequence at a time it is shown that the cumulative sum cusum test which is well known to be optimal for a non bayesian statistical change point detection formulation is optimal for the problem under study specifically the cusum test is run on the first sequence if a reset event occurs in the cusum test then the sequence under examination is abandoned and the rule switches to the next sequence if the cusum test stops then the rule declares that the sequence under examination when the test stops is generated by q1 the result is derived by assuming that there are infinitely many sequences so that a sequence that has been examined once is not retested if there are finitely many sequences the result is also valid under a memorylessness condition expressions for the performance of the optimal sequential decision rule are also developed the general case in which multiple sequences can be examined simultaneously is considered the optimal solution for this general scenario is derived

consensusability of multi agent systems with time varying communication delay abstract this paper studies the consensusability problem of continuous time multi agent systems with time varying communication delay in undirected network we design a consensus protocol based on the low gain solution of a parametric algebraic riccati equation are and not use the precise information of the amount of time varying delay by studying the joint effect of agent dynamic and network topology sufficient conditions are given for consensus when all poles of the system matrix are on the closed left half plane in case of non zero poles on the imaginary axis maximal admissible upper bound of the time varying delay is given in terms of both the agent dynamic and network topology otherwise consensus can be achieved for the time varying delay with arbitrarily large upper bound finally simulation results are presented to demonstrate the effectiveness of the theoretical results

new stability and exact observability conditions for semilinear wave equations the problem of estimating the initial state of 1 d wave equations with globally lipschitz nonlinearities from boundary measurements on a finite interval was solved recently by using the sequence of forward and backward observers and deriving the upper bound for exact observability time in terms of linear matrix inequalities lmis fridman 2013 in the present paper we generalize this result to n d wave equations on a hypercube this extension includes new lmi based exponential stability conditions for n d wave equations as well as an upper bound on the minimum exact observability time in terms of lmis for 1 d wave equations with locally lipschitz nonlinearities we find an estimate on the region of initial conditions that are guaranteed to be uniquely recovered from the measurements the efficiency of the results is illustrated by numerical examples

pi regulation of a reaction diffusion equation with delayed boundary control the general context of this work is the feedback control of an infinite dimensional system so that the closed loop system satisfies a fading memory property and achieves the setpoint tracking of a given reference signal more specifically this paper is concerned with the proportional integral pi regulation control of the left neumann trace of a one dimensional reaction diffusion equation with a delayed right dirichlet boundary control in this setting the studied reaction diffusion equation might be either open loop stable or unstable the proposed control strategy goes as follows first a finite dimensional truncated model that captures the unstable dynamics of the original infinite dimensional system is obtained via spectral decomposition the truncated model is then augmented by an integral component on the tracking error of the left neumann trace after resorting to the artstein transformation to handle the control input delay the pi controller is designed by pole shifting stability of the resulting closed loop infinite dimensional system consisting of the original reaction diffusion equation with the pi controller is then established thanks to an adequate lyapunov function in the case of a time varying reference input and a time varying distributed disturbance our stability result takes the form of an exponential input to state stability iss estimate with fading memory finally another exponential iss estimate with fading memory is established for the tracking performance of the reference signal by the system output in particular these results assess the setpoint regulation of the left neumann trace in the presence of distributed perturbations that converge to a steady state value and with a time derivative that converges to zero numerical simulations are carried out to illustrate the efficiency of our control strategy

not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks we present two examples of hyperbolic partial differential equations which are stabilized by boundary feedback controls and then destabilized by small delays in these controls we show that in a general case when the controls are distributed stabilized hyperbolic systems possess nontrivial periodic solutions if small time delays are introduced into their feedbacks we also indicate by means of an example that the general case of this phenomenon is harder to demonstrate for boundary control problems

searching for anomalies over composite hypotheses the problem of detecting anomalies in multiple processes is considered we consider a composite hypothesis case in which the measurements drawn when observing a process follow a common distribution with an unknown parameter vector whose value lies in normal or abnormal parameter spaces depending on its state the objective is a sequential search strategy that minimizes the expected detection time subject to an error probability constraint we develop a deterministic search algorithm with the following desired properties first when no additional side information on the process states is known the proposed algorithm is asymptotically optimal in terms of minimizing the detection delay as the error probability approaches zero second when the parameter value under the null hypothesis is known and equal for all normal processes the proposed algorithm is asymptotically optimal as well with better detection time determined by the true null state third when the parameter value under the null hypothesis is unknown but is known to be equal for all normal processes the proposed algorithm is consistent in terms of achieving error probability that decays to zero with the detection delay finally an explicit upper bound on the error probability under the proposed algorithm is established for the finite sample regime extensive experiments on synthetic dataset and darpa intrusion detection dataset are conducted demonstrating strong performance of the proposed algorithm over existing methods

a positivity based approach to delay dependent stability of systems with large time varying delays abstract in this paper we propose new explicit tests for positivity and exponential stability of systems with large time varying delays our approach is based on nonoscillation of solutions of the corresponding diagonal scalar delay differential equations numerical examples illustrate the efficiency of the results

rapid stabilisation of an euler bernoulli beam with the internal delay control in this paper we are concerned with rapid stabilisation of an euler bernoulli beam with internal delayed control herein we introduce a new approach of the feedback control design from the system

predictor based sampled data exponential stabilization through continuous discrete observers the problem of stabilizing a linear continuous time system with discrete time measurements and a sampled input with a pointwise constant delay is considered in a first part we design a continuous discrete observer which converges when the maximum time interval between two consecutive measurements is sufficiently small in a second part we construct a dynamic output feedback by using a technique which is strongly reminiscent of the reduction model approach it stabilizes the system when the maximal time between two consecutive sampling instants is sufficiently small no limitation on the size of the delay is imposed and an iss property with respect to additive disturbances is established

recursive predictor design for state and output feedback controllers for linear time delay systems this paper presents a recursive method to design state and output feedback controllers for mimo block feedforward linear systems with delays in the inputs outputs and interconnections between the blocks the resulting controller is of predictor type which means that it contains finite integrals over past state and input values the method is a generalization of the well known model reduction approach for systems with input delay a recursive procedure replaces delay terms with non delay ones step by step from the top of the cascade structure down controller gains are computed for the proxy system without delays while the construction guarantees the same closed loop poles for the delay system and the proxy one the observer is designed by applying the duality argument and the separation principle is also shown to apply

the infinite time quadratic control problem for linear systems with state and control delays an evolution equation approach we show how a linear differential delay equation with delays in the control can be reformulated as an evolution equation with bounded input operator as a simple application we solve an infinite time quadratic cost control problem for the delay differential equation we also point out how our results even when specialized to the case where delays in the control disappear extend results previously published in the literature

new predictive scheme for the control of lti systems with input delay and unknown disturbances a new predictive scheme is proposed for the control of linear time invariant lti systems with a constant and known delay in the input and unknown disturbances it has been achieved to include disturbances effect in the prediction even though there are completely unknown the artstein reduction is then revisited thanks to the computation of this new prediction an extensive comparison with the standard scheme is presented throughout the article it is proved that the new scheme leads to feedback controllers that are able to reject perfectly constant disturbances for time varying ones a better attenuation is achieved for a wide range of perturbations and for both linear and nonlinear controllers a criterion is given to characterize this class of perturbations finally some simulations illustrate the results

control of linear systems with fixed noncommensurate point delays the first solution is given to the fundamental open problem of stabilizability and detectability necessary sufficient conditions for internal stabilization by feedback of retarded and a large class of neutral delay differential systems with several fixed noncommensurate point delays using causal compensators observers and state feedback or dynamic output feedback which are also the same type of neutral or retarded delay differential systems with fixed point delays only our results are rank conditions on the system matrices zi f g and zif t h t evaluated at points in the complex plane and are the weakest possible generally applicable sufficient such rank conditions for stabilization of neutral systems in the light of what is known on the stability of such systems these conditions are necessary for most practical purposes the class of systems we consider includes all retarded delay differential systems with noncommensurate fixed point delays in the case of retarded systems these rank conditions are necessary and sufficient conditions for stabilization via compensators which are causal retarded delay differential systems with fixed point delays only these constitute the first full solution of these previously unsolved problems of stabilizability and detectability which together are necessary and sufficient conditions for internal stabilization by feedback for delay differential systems even in the retarded single fixed point delay case an application of our results to a problem of practical importance in control of linear systems with no delays provides a stabilization criterion interesting in itself

feedback stabilization of linear autonomous time lag systems a stabilization theory which employs well established finite dimensional control system tools is developed for the stabilization of linear autonomous time lag systems the main ideas include 1 a set whose elements are matrices each of which is a left zero of the system characteristic quasi polynomial matrix and 2 a linear transformation which reduces the delay system to a delay free system whose state matrix is a direct sum of n elements of the matrix set where n is some positive integer from the definition of this matrix set it is shown that each of its elements inherits its spectrum from that of the delay system so that by design the system unstable poles may be embedded in the spectrum of the delay free system under the assumption of spectral stabilizability it is then shown how to obtain a stabilizing feedback control law on the basis of the delay free system numerical examples are presented to confirm the theory

rapid exponential stabilisation of linear kdv equation with long input delay on the left boundary in this paper we consider the one dimensional linear kdv korteweg de vries equation posed in bounded interval with delay boundary control acting on the left boundary by dirichlet condition where

linear quadratic regulation and stabilization of discrete time systems with delay and multiplicative noise this paper is concerned with the long standing problems of linear quadratic regulation lqr control and stabilization for a class of discrete time stochastic systems involving multiplicative noises and input delay these fundamental problems have attracted resurgent interests due to development of networked control systems an explicit analytical expression is given for the optimal lqr controller more specifically the optimal lqr controller is shown to be a linear function of the conditional expectation of the state with the feedback gain based on a riccati zxl difference equation it is also shown that the system is stabilizable in the mean square sense if and only if an algebraic riccati zxl equation has a particular solution these results are based on a new technical tool which establishes a non homogeneous relationship between the state and the costate of this class of systems and the introduction of a new lyapunov function for the finite horizon optimal control design

output stabilization of time varying input delay systems using interval observation technique the output stabilization problem for a linear system with an unknown bounded time varying input delay is considered the interval observation technique is applied in order to obtain guaranteed interval estimate of the system state the procedure of the interval observer synthesis uses lower and upper estimates of the unknown delay and requires to solve a special silvester s equation the interval predictor is introduced in order to design a linear stabilizing feedback the control design procedure is based on linear matrix inequalities lmi the theoretical results are supported by numerical simulations and compared with a control design scheme based on a luenberger like observer

an internal state decomposition approach to a discrete time h2 control problem with irrational input non minimum phase property abstract an internal state decomposition approach to a class of discrete time h 2 control problems with irrational non minimum phase property at the control input is proposed this is a generalization of the state variable transformation to derive the discrete time smith predictor for a single input delay system the h 2 optimal controller is derived using the orthogonality principle in h 2 space as a direct consequence of the state decomposition the characterization of the optimal cost by the previous and alternative truncation operators is also discussed

method of lyapunov functionals construction in stability of delay evolution equations the investigation of stability for hereditary systems is often related to the construction of lyapunov functionals the general method of lyapunov functionals construction which was proposed by v kolmanovskii and l shaikhet and successfully used already for functional differential equations for difference equations with discrete time for difference equations with continuous time is used here to investigate the stability of delay evolution equations in particular partial differential equations

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

global steady state controllability of one dimensional semilinear heat equations we investigate the problem of exact boundary controllability of semilinear one dimensional heat equations we prove that it is possible to move from any steady state to any other by means of a boundary control provided that both are in the same connected component of the set of steady states the proof is based on an effective feedback stabilization procedure which is implemented

nonmonotonic reasoning preferential models and cumulative logics abstract many systems that exhibit nonmonotonic behavior have been described and studied already in the literature the general notion of nonmonotonic reasoning though has almost always been described only negatively by the property it does not enjoy i e monotonicity we study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties we concentrate on a number of families of nonmonotonic consequence relations defined in the style of gentzen 13 both proof theoretic and semantic points of view are developed in parallel the former point of view was pioneered by gabbay 10 while the latter has been advocated by shoham 38 five such families are defined and characterized by representation theorems relating the two points of view one of the families of interest that of preferential relations turns out to have been studied by adams 2 the preferential models proposed here are a much stronger tool than adams probabilistic semantics the basic language used in this paper is that of propositional logic the extension of our results to first order predicate calculi and the study of the computational complexity of the decision problems described in this paper will be treated in another paper

constructive method for finite dimensional observer based control of 1 d parabolic pdes abstract the objective of the present paper is finite dimensional observer based control of the 1 d linear heat equation with constructive and feasible design conditions we propose a method which is applicable to boundary or non local sensing together with non local actuation or to dirichlet actuation with non local sensing we use a modal decomposition approach the dimension of the controller n 0 is equal to the number of modes which decay slower than a given decay rate 0 the observer may have a larger dimension n n 0 the observer and controller gains are found separately by solving n 0 n 0 dimensional lyapunov inequalities we suggest a direct lyapunov approach to the full order closed loop system and provide linear matrix inequalities lmis for finding n and the exponential decay rate of the closed loop system we prove that the lmis are always feasible for large enough n the proposed method is different from existing qualitative methods that do not give easily verifiable and efficient bounds on the observer based controller dimension and the resulting closed loop performance numerical examples demonstrate that our lmi conditions lead to non conservative bounds on n and the resulting decay rate

input delay compensation of linear systems with both state and input delays by nested prediction abstract in this paper we consider the input delay compensation of linear systems with both state and input delays under the condition that the open loop time delay systems in the absence of input delay can be stabilized by delayed state feedback a nested predictor based approach is established to predict the future states so that the delays in the input are compensated it is shown that the compensated closed loop system in the presence of input delay possesses the same characteristic equation as the closed loop system in the absence of input delay the proposed approach can be generalized to general linear systems having multiple state delays and or multiple input delays to implement the nested predictor based controllers by applying numerical integration approaches an augmented nested predictor based approach by adding input filters is proposed two numerical examples are worked out to show the effectiveness of the proposed approach

output feedback adaptive control of a wave pde with boundary anti damping abstract we develop an adaptive output feedback controller for a wave pde in one dimension with actuation on one boundary and with an unknown anti damping term on the opposite boundary this model is representative of a torsional stick slip instability in drillstrings in deep oil drilling as well as of various acoustic instabilities the key feature of the proposed controller is that it requires only the measurements of boundary values and not of the entire distributed state of the system our approach is based on employing riemann variables to convert the wave pde into a cascade of two delay elements with the first of the two delay elements being fed by control and the same element in turn feeding into a scalar ode this enables us to employ a prediction based design for systems with input delays suitably converted to the adaptive output feedback setting the result s relevance is illustrated with simulation example

rapid boundary stabilization of the wave equation the boundary stabilization of the wave equation in bounded domains is studied it is shown that a particular choice of the feedback leads to fast energy decay explicit decay rate estimates are obt

adaptive sinusoidal disturbance cancellation for unknown lti systems despite input delay solutions exist for the problems of canceling sinusoidal disturbances and compensating input delays in this paper two problems are considered simultaneously and an adaptive controller is designed to cancel unknown sinusoidal disturbances forcing an unknown linear time invariant system in controllable canonical form despite input delay the design is based on three steps 1 parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters 2 representation of the delay as a transport pde 3 design of the adaptive controller by using the backstepping boundary control technique for pdes it is proven that the equilibrium of the closed loop system is stable and the state of the considered system converges to zero as t with perfect disturbance estimation the effectiveness of the controller is illustrated with a simulation example of a second order system

stability criteria of linear systems with multiple input delays under truncated predictor feedback abstract the model reduction technique as a feedback design approach for linear systems with input delays achieves finite spectrum assignment of the closed loop system in a delay free form the resulting predictor type feedback law contains a distributed term that involves the convolution between the past input and the state transition matrix and hence causes difficulty in its implementation for the purpose of easy implementation the truncated predictor feedback tpf simplifies the predictor feedback by discarding the distributed term and delay independent truncated predictor feedback further eliminates the delay dependent exponential factor in this paper we consider the stabilization of a general linear system with multiple time varying input delays by tpf or delay independent tpf stability criteria expressed in terms of input delays and the feedback parameter are derived through lyapunov krasovskii stability analysis and then numerically studied under both feedback laws

local stabilization of nonlinear systems through the reduction model approach we study a general class of nonlinear systems with input delays of arbitrary size we adapt the reduction model approach to prove local asymptotic stability of the closed loop input delayed systems using feedbacks that may be nonlinear our lyapunov krasovskii functionals make it possible to determine estimates of the basins of attraction for the closed loop systems

prediction based control for lti systems with uncertain time varying delays and partial state knowledge abstractthe stability of a prediction based controller for linear time invariant lti systems is studied in the presence of time varying input and output delays the uncertain delay case is treated as well as the partial state knowledge case the reduction method is used in order to prove the convergence of the closed loop system including the state observer the predictor and the plant explicit conditions that guarantee the closed loop stability are given thanks to a lyapunov razumikhin analysis simulations illustrate the theoretical results

quickest linear search over correlated sequences consider a set of random sequences each consisting of independent and identically distributed random variables drawn from one of the two known distributions f 0 and f 1 the underlying distributions of different sequences are correlated induced by an inherent physical coupling in the mechanisms generating these sequences the objective is to design the quickest data adaptive and sequential search procedure for identifying one sequence generated according to f 1 the optimal design involves striking a balance between the average delay in reaching a decision and the rate of false alarms as two opposing figures of merit optimal and asymptotically optimal decision rules are derived which can take radically different forms depending on the correlation structure performance and sampling complexity analyses are provided to delineate the tradeoff between decision delay and quality the generalization to parallel sampling in which multiple sequences are sampled at the same time is also investigated

uniform exponential energy decay of wave equations in a bounded region with l2 0 l2 γ feedback control in the dirichlet boundary conditions etant donne un ouvert borne r n n 2 on considere l equation d onde w tt w dans o avec des conditions initiales w o x w o x l 2 w 1 o x w 1 x h 1 et des conditions aux limites non homogenes de type dirichlet w t u t sur o etant la frontiere de

note on boundary stabilization of wave equations an energy decay rate is obtained for solutions of wave type equations in a bounded region in mathbb r n whose boundary consists partly of a nontrapping reflecting surface and partly of an energy absorbing surface unlike most previous results on this subject the results presented here are potentially valid for regions having connected boundaries

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

boundary control of partial differential equations using frequency domain optimization techniques abstract we present a frequency domain based h control strategy to solve boundary control problems for systems governed by parabolic or hyperbolic partial differential equation where controllers are constrained to be physically implementable and of simple structure suited for practical applications the efficiency of our technique is demonstrated by controlling a reaction diffusion equation with input delay and a wave equation with boundary anti damping

delay robustness of linear predictor feedback without restriction on delay rate robustness is established for the predictor feedback for linear time invariant systems with respect to possibly time varying perturbations of the input delay with a constant nominal delay the prior results have addressed qualitatively constant delay perturbations robustness of stability in l 2 norm of actuator state and delay perturbations with restricted rate of change robustness of stability in h 1 norm of actuator state the present work provides simple formulas that allow direct and accurate computation of the least upper bound of the magnitude of the delay perturbation for which the exponential stability in supremum norm on the actuator state is preserved while the prior work has employed lyapunov krasovskii functionals constructed via backstepping the present work employs a particular form of small gain analysis two cases are considered the case of measurable possibly discontinuous time varying perturbations and the case of constant perturbations

robustness with respect to delays for exponential stability of distributed parameter systems in this paper we address the question of whether the open loop exponential growth rate of a linear system can be improved by a feedback in such a way that this improvement is robust with respect to small delays in the feedback loop when the input operator is admissible and the class of possible feedbacks consists of compact operators we find that if a feedback can improve the exponential growth rate then it can do so robustly furthermore we find that if the control space is finite dimensional and a bounded feedback cannot be found to improve exponential stability then a large class of unbounded feedbacks cannot improve the exponential growth rate robustly even if such feedbacks can improve the exponential growth rate in the absence of delays

control of transport pde nonlinear ode cascades with state dependent propagation speed in this paper we deal with the control of a transport partial differential equation nonlinear ordinary differential equation pde nonlinear ode cascade system in which the transport coefficient depends on the ode state we develop a pde based predictor feedback boundary control law which compensates the transport dynamics of the actuator and guarantees global asymptotic stability of the closed loop system the stability proof is based on an infinite dimensional backstepping transformation and a lyapunov like argument the relation of the pde ode cascade with a state dependent propagation speed to an ode system with a state dependent input delay which is defined implicitly via an integral of past values of the ode state is also highlighted and the corresponding equivalent predictor feedback design is presented together with an alternative proof of global asymptotic stability of the closed loop system based on the construction of a lyapunov functional the practical relevance of our control framework is illustrated in an example that is concerned with the control of a metal rolling process

robustness of adaptive control under time delays for three dimensional curve tracking we analyze the robustness of a class of controllers that enable three dimensional curve tracking by a free moving particle the free particle tracks the closest point on the curve by building a strict lyapunov function and robustly forward invariant sets we show input to state stability under predictable tolerance and safety bounds that guarantee robustness under control uncertainty input delays and a class of polygonal state constraints including adaptive tracking and parameter identification under unknown control gains such an understanding may provide certified performance when the control laws are applied to real life systems

observer based output feedback control of linear systems with input and output delays abstract this paper is concerned with observer based output feedback control of linear systems with both multiple input and output delays our recently developed truncated predictor feedback tpf approach for state feedback stabilization of time delay systems is generalized to the design of observers by imposing some restrictions on the open loop system two classes of observer based output feedback controllers one being finite dimensional and the other infinite dimensional are constructed it is further shown that the infinite dimensional observer based output feedback controllers can be generalized to linear systems with both time varying input and output delays it is also shown that the separation principle holds for the infinite dimensional observer based output feedback controllers but does not hold for the finite dimensional ones numerical examples are worked out to illustrate the effectiveness of the proposed approaches

nonmonotonic inference based on expectations abstract we show how nonmonotonic inferences may elegantly be interpreted in terms of underlying expectations the fundamental idea is that when we reason we make use of not only the information that we firmly believe but also expectations that guide our beliefs without quite being part of them we propose two ways of modelling the expectations used in nonmonotonic reasoning by expectation sets equipped with selection functions and by expectation relations for each of these we prove representation theorems and establish relations with several other modellings in the area including poole systems and preferential models we also show that by using the notion of expectation one can unify the treatment of the theory of belief revision and that of nonmonotonic inference relations this is accomplished by viewing the relation of epistemic entrenchment used in gardenfors 18 and gardenfors and makinson 20 as a kind of expectation ordering thus we see belief revision and nonmonotonic reasoning as basically the same process albeit used for two different purposes

on compensating long actuator delays in nonlinear control we are interested in finite escape open loop unstable plants that are globally stabilizable in the absence of actuator delay but require controller redesign in the presence of delay the simplest such plant is z t z t 2 u t d where d is actuator delay of arbitrary length for this system we present a control law that compensates the delay and achieves feedback linearization of the entire ode delay infinite dimensional cascade however even though exponential stability is achieved the result is not global because the plant can have a finite escape with an initial condition z 0 ges 1 d before the feedback control reaches it at t d we prove a stability result whose region of attraction is essentially z 0 1 d and for which we derive an asymptotic stability bound in terms of the system norm z t 2 intt t d u thetas 2dthetas

defaults in domain theory abstract this paper uses ideas from artificial intelligence to show how default notions can be defined over scott domains we combine these ideas with ideas arising in domain theory to shed some light on the properties of nonmonotonicity in a general model theoretic setting we consider in particular a notion of default nonmonotonic entailment between prime open sets in the scott topology of a domain we investigate in what ways this notion obeys the so called laws of cautious monotony and cautious cut proposed by gabbay kraus lehmann and magidor our notion of nonmonotonic entailment does not necessarily satisfy cautious monotony but does satisfy cautious cut in fact we show that any reasonable notion of nonmonotonic entailment on prime opens over a scott domain satisfying in particular the law of cautious cut can be concretely represented using our notion of default entailment we also give a variety of sufficient conditions for defaults to induce cumulative entailments those satisfying cautious monotony in particular we show that defaults with unique extensions are a representation of cumulative nonmonotonic entailment furthermore a simple characterization is given for those default sets which determine unique extensions in coherent domains finally a characterization is given for scott domains in which default entailment must be cumulative this is the class of daisy domains it is shown to be cartesian closed a purely domain theoretic result

prediction based control for systems with state and several input delays in this contribution an extension of the prediction based design scheme proposed in tsubakino etal 2015 for compensation of input delays to the case of systems with input and state delays is presented to derive safely implementable control laws we propose to apply additional input filters and obtain a closed loop system in the form of a set of retarded type differential equations an example illustrating the design scheme is given

predictor based stabilization of neutral type systems with input delay in this contribution we present an extension of the prediction scheme proposed in manitius and olbrot 1979 for the compensation of the input delay to the case of linear neutral type systems with input delay for simplicity of the presentation we treat the case of systems with one state delay

asymptotic stability of a problem with balakrishnantaylor damping and a time delay in this paper we investigate the asymptotic stability of the viscoelastic kirchhoff equation with balakrishnantaylor damping and a delay term we establish general energy decay result by suitable lyapunov functionals

non monotonic logic i abstract non monotonic logical systems are logics in which the introduction of new axioms can invalidate old theorems such logics are very important in modeling the beliefs of active processes which acting in the presence of incomplete information must make and subsequently revise assumptions in light of new observations we present the motivation and history of such logics we develop model and proof theories a proof procedure and applications for one non monotonic logic in particular we prove the completeness of the non monotonic predicate calculus and the decidability of the non monotonic sentential calculus we also discuss characteristic properties of this logic and its relationship to stronger logics logics of incomplete information and truth maintenance systems

exponential stabilization of linear systems with time varying delayed state feedback via partial spectrum assignment abstract we consider the problem of controlling a linear system when the state is available with a known time varying delay delayed state feedback control or the actuator is affected by a delay the solution proposed in this paper consists in partially assigning the spectrum of the closed loop system to guarantee the exponential zero state stability with a prescribed decay rate by means of a finite dimensional control law a non conservative bound on the maximum allowed delay for the prescribed decay rate is presented which holds for both cases of constant and time varying delays an advantage over recent and similar approaches is that differentiability or continuity of the delay function is not required we compare the performance of our approach in terms of delay bound and input signal with another recent approach

control for ito stochastic systems with input delay this paper examines the long standing problem of linear quadratic regulation and stabilization for ito stochastic systems with input delay this problem remains a primary challenge because the separation principle does not hold for ito stochastic systems this paper presents a complete solution to the problem 1 the sufficient and necessary solvability condition of the optimal control and the analytical controller are given based on the modified riccati differential equation defined herein 2 the sufficient and necessary stabilization condition in mean square sense is explored we show that the ito stochastic system with input delay is stabilized if and only if the modified algebraic riccati equation developed in this paper has a unique positive definite solution the essential obstacle encountered in this paper concerns a delayed forward backward stochastic differential equation d fbsde which is mathematical challenging

exponential stability and inequalities of solutions of abstract functional differential equations abstract with the lyapunov second method we study the abstract functional differential equation d u d t f t u t we obtain inequalities of solutions and exponential stability with conditions like i w 1 u t x v t u t w 2 d t u t t h t l s w 1 u s x d s ii v 1 t u t t w 2 d t u t p t applications in ordinary and partial functional differential equations are given

delay adaptive control for nonlinear systems we present a systematic delay adaptive prediction based control design for nonlinear systems with unknown long actuator delay our approach is based on the representation of the constant actuator delay as a transport partial differential equation pde in which the convective speed is inversely proportional to the unknown delay we study two different frameworks assuming first that the actuator state is measured and relaxing afterward for the full state feedback case we prove global asymptotic convergence of the proposed adaptive controller while in the second case replacing the actuator state by its adaptive estimate we prove local regulation the relevance of the obtained results are illustrated by simulations of a biological activator repressor system

stabilization of discrete time linear systems with an unknown time varying delay by switched low gain feedback in this note we investigate the stabilization of discrete time linear systems with an unknown time varying delay existing literature on the stabilization of time delay systems require some knowledge such as an upper bound of the delay in this paper by proposing a switched low gain feedback control law we are able to achieve asymptotic stabilization of the system without any knowledge of the delay in addition the proposed switched low gain feedback law also significantly improves the closed loop system performance in terms of overshoot and convergence speed in comparison with the traditional fixed gain design simulation study illustrates the effectiveness of our theoretical results

an analysis of delay dependent stability for ordinary and partial differential equations with fixed and distributed delays this paper is concerned with the study of the stability of ordinary and partial differential equations with both fixed and distributed delays and with the study of the stability of discretizations of such differential equations we start with a delay dependent asymptotic stability analysis of scalar ordinary differential equations with real coefficients we study the exact stability region of the continuous problem as a function of the parameters of the model next it is proved that a time discretization based on the trapezium rule can preserve the asymptotic stability for the considered set of test problems in the second part of the paper we study delay partial differential equations the stability region of the fully continuous problem is analyzed first then a semidiscretization in space is applied it is shown that the spatial discretization leads to a reduction of the stability region when the standard second order central difference operator is employed to approximate the diffusion operator finally we consider the delay dependent stability of the fully discrete problem where the partial differential equation is discretized both in space and in time some numerical examples and further discussions are given

general decay of the solution for a viscoelastic wave equation with a time varying delay term in the internal feedback in this paper we consider a viscoelastic wave equation with a time varying delay term the coefficient of which is not necessarily positive by introducing suitable energy and lyapunov functionals under suitable assumptions we establish a general energy decay result from which the exponential and polynomial types of decay are only special cases