nonlinear feedback design for fixed time stabilization of linear control systems two types of nonlinear control algorithms are presented for uncertain linear plants controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions the control design procedure uses block control principles and finite time attractivity properties of polynomial feedbacks controllers of the second type are modifications of the second order sliding mode control algorithms they provide global finite time stability of the closed loop system and allow to adjust a guaranteed settling time independently on initial conditions control algorithms are presented for both single input and multi input systems theoretical results are supported by numerical simulations

minimizing total tardiness on one machine is np hard the problem of minimizing the total tardiness for a set of independent jobs on one machine is considered lawler has given a pseudo polynomial time algorithm to solve this problem in spite of extensive research efforts for more than a decade the question of whether it can be solved in polynomial time or it is np hard in the ordinary sense remained open in this paper the problem is shown to be np hard in the ordinary sense

hybrid dead beat observers for a class of nonlinear systems this paper studies both the full order and the reduced order dead beat observer problem for a class of nonlinear systems linear in the unmeasured states a novel hybrid observer design strategy is proposed with the help of the notion of strong observability in finite time the proposed methodology is applied for the estimation of the frequency of a sinusoidal signal the results show that accurate estimation can be provided even if the signal is corrupted by high frequency noise a brief discussion of the robustness properties of the proposed observer with respect to measurement errors is also provided

robust exact differentiation via sliding mode technique abstract the main problem in differentiator design is to combine differentiation exactness with robustness in respect to possible measurement errors and input noises the proposed differentiator provides for proportionality of the maximal differentiation error to the square root of the maximal deviation of the measured input signal from the base signal such an order of the differentiation error is shown to be the best possible one when the only information known on the base signal is an upper bound for lipschitz s constant of the derivative

interval estimation for lpv systems applying high order sliding mode techniques in this paper the problem of design of interval observers for linear parameter varying lpv systems containing non detectable or non strongly observable parts is addressed firstly a high order sliding mode hosm method is applied to the strongly observable subsystem obtained by an appropriate change of coordinates to estimate the state and its derivative secondly this information is used to decrease the level of uncertainty in the rest of the system which leads to improvement of accuracy of the set membership estimates generated by an interval observer moreover it is shown that hosm techniques allows us to relax the applicability conditions of standard interval observer design methods the efficiency of the proposed approach is demonstrated through simulation examples

a globally exponentially stable speed observer for a class of mechanical systems experimental and simulation comparison with high gain and sliding mode designs abstractit is shown in the paper that the problem of speed observation for mechanical systems that are partially linearisable via coordinate changes admits a very simple and robust exponentially s

reduced order observers for the sliding mode control of mechanical systems with elastic joints in this article the control of mechanical systems with elastic joints is addressed this kind of system is characterised by a high relative degree the mechanical control input must be designed to be continuous different reduced order observers are introduced and conditions are found to guarantee the exponential convergence of the observation errors the error stability is ensured provided a certain matrix inequality has a solution the proposed second order sliding mode point to point controller based on the observed state is proven to stabilise the mechanical system with elastic joints about the desired reference position

brief paper lyapunov function design for finite time convergence analysis twisting controller for second order sliding mode realization a generalization of the zubov method of a lyapunov function design is presented it is based on the characteristic method application and is related to resolving the first order partial differential equation of a special type a successful resolution of this equation guaranties a finite time convergence for the corresponding dynamics given by an ordinary differential equation with a discontinuous right hand side the suggested method is illustrated by its application to the so called twisting controller stability analysis the constructed lyapunov function as well as its level line sections is graphically illustrated

stability preserving maps for finite time convergence super twisting sliding mode algorithm the super twisting algorithm sta has become the prototype of second order sliding mode algorithm it achieves finite time convergence by means of a continuous action without using information about derivatives of the sliding constraint thus chattering associated to traditional sliding mode observers and controllers is reduced the stability and finite time convergence analysis have been jointly addressed from different points of view most of them based on the use of scaling symmetries homogeneity or non smooth lyapunov functions departing from these approaches in this contribution we decouple the stability analysis problem from that of finite time convergence a nonlinear change of coordinates and a time scaling are used in the new coordinates and time space the transformed system is stabilized using any appropriate standard design method conditions under which the combination of the nonlinear coordinates transformation and the time scaling is a stability preserving map are given provided convergence in the transformed space is faster than o 1 t where t is the transformed time convergence of the original system takes place in finite time the method is illustrated by designing a generalized super twisting observer able to cope with a broad class of perturbations

finite time and fixed time observer design implicit lyapunov function approach abstract this work deals with the problem of finite time and fixed time observation of linear multiple input multiple output mimo control systems the proposed nonlinear dynamic observers guarantee convergence of the observer states to the original system state in a finite and in a fixed defined a priori time algorithms for the observers parameters tuning are also provided and a robustness analysis against input disturbances and measurement noises is carried out the theoretical results are illustrated by numerical examples that consider both noisy and noise free measurements and a comparison with a high gain observer is included

observer based finite time coordinated tracking for general linear multi agent systems in this paper four observer based distributed controllers are proposed for general linear multi agent systems to achieve finite time coordinated tracking under different situations specifically for the cases of undirected communication graphs and directed communication graphs among the followers both the situations of relative state measurement and relative output measurement among neighboring agents are considered under both kinds of communication topologies when relative state information of the neighbors is available distributed observer based controllers are designed which achieve exact coordinated tracking in finite time when only relative output information is available another finite time observer is introduced for each follower to estimate the relative state information together with the distributed controllers designed for the state feedback case finite time exact coordinated tracking can still be achieved in this situation numerical simulations are provided to illustrate the effectiveness of the proposed controllers

fixed rate transmission over fading interference channels using point to point gaussian codes this paper investigates transmission schemes for fixed rate communications over a rayleigh block fading interference channel there are two source destination pairs where each source in the presence of a short term power constraint intends to communicate with its dedicated destination at a fixed data rate it encodes its messages using a point to point gaussian codebook the two users transmissions can be conducted orthogonally or non orthogonally in the latter case each destination performs either direct decoding by treating the interference as noise or successive interference cancellation sic to recover its desired message for each scheme we seek solutions of a power control problem to efficiently assign power to the sources such that the codewords can be successfully decoded at destinations however because of the random nature of fading the power control problem for some channel realizations may not have any feasible solution and the transmission will be in outage thus for each transmission scheme we first compute a lower bound and an upper bound on the outage probability next we use these results to find an outer bound and an inner bound on the epsilon outage achievable rate region i e the rate region in which the outage probability is below a certain value epsilon

a receiver centric approach to interference management fairness and outage optimization effective interference management in the multiuser interference channel necessitates that the users form their transmission and interference management decisions in coordination and adapt them to the state of the channel establishing such coordination often facilitated through information exchange is prohibitive in fast varying channels especially when the network size grows this paper focuses on the multiuser gaussian interference channel and offers a receiver centric approach to interference management in this approach the transmitters deploy rate splitting and superposition coding to generate their messages according to independent gaussian codebooks the receivers can freely decode any arbitrary set of interfering messages along with their designated messages in any desired joint or ordered fashion and treat the rest of the interferers as gaussian noise the proposed receiver centric interference management approach is applied to two class of problems outage optimization and fairness constrained rate allocation and constructive proofs are provided to establish the following properties for the proposed approach 1 the optimal set of codebooks to be decoded by each receiver is a local decision made by each receiver based on its local channel state information csi 2 the globally optimal transmission rates are related to locally optimal rates computed by the receivers based on their local information which implies that the transmitters do not require explicit knowledge of the csi and can determine their rates via limited feedback from the receivers and 3 obtaining the optimal interference management strategy at each receiver has controlled complexity

brief paper global sliding mode observer with adjusted gains for locally lipschitz systems a state observer design procedure is proposed for nonlinear locally lipschitz systems with high relative degree from the available for measurements output to the nonlinearity the possible presence of disturbances is taken into account the solution is based on logic based control and the high order super twisting observer the approach is applicable to nonlinear systems with bounded solutions

finite time observers application to secure communication in this paper control theory is used to formalize finite time chaos synchronization as a nonlinear finite time observer design issue this paper introduces a finite time observer for nonlinear systems that can be put into a linear canonical form up to an output injection the finite time convergence relies on the homogeneity properties of nonlinear systems the observer is then applied to the problem of secure data transmission based on the finite time chaos synchronization and the two channel transmission method

new precedence theorems for one machine weighted tardiness in an earlier paper by emmons emmons h 1969 one machine sequencing to minimize certain functions of job tardiness oper res 17 701 715 the problem of sequencing jobs on a single machine in order to minimize total tardiness was analyzed emmons provided three theorems for specifying precedence relations for pairs of jobs his theorems apply when the tardiness penalty for each job grows at the same rate rinnooy kan et al rinnooy kan a h g b j lageweg j k lenstra 1975 minimizing total costs in one machine scheduling oper res 23 908 927 later extended emmons s theorems to the case when job tardiness penalties can grow at different rates for different jobs provided here is a set of theorems stronger than those of rinnooy kan et al that more fully exploits the special properties of the weighted tardiness function allowing for greater reduction of the solution space

a continuous time observer which converges in finite time it is shown that a continuous time observer which comprises two standard nth order observers and a delay d can observe the state of an nth order linear system in finite time d exactly in particular almost any convergence time d can be assigned independent of the observer eigenvalues

minimum time output regulation for general linear heterodirectional hyperbolic systems this paper considers the minimum time output regulation problem for general linear heterodirectional hyperbolic systems with spatially varying coefficients for this a state feedback regulator ach

design of sliding observers for lipschitz nonlinear system using a new time averaged lyapunov function abstractthis paper provides a procedure for designing a sliding mode observer for a nonlinear system in the presence of gaussian input disturbances and sensor noises the paper first proposes a nov

stochastic output noise effects in sliding mode state estimation this paper is devoted to the analysis of effects of stochastic output noises acting on a stochastic continuous time system which states are estimated using mixed linear and sliding mode type observers such observers provide the stable with probability one estimates the averaged norm of estimation error converges to a zone where size is proportional to the acting noise power the main technique of the proof is based on the averaging concept applied within the frame of stochastic lyapunov like analysis the stochastic calculus it formula as well as some basic principles for stochastic processes are used to obtain the convergence results the size of the obtained zone is analysed as a function of the sliding mode gain parameter it is shown that the sliding mode term helps a high gain linear observer to make this zone smaller the illustrative example dealing with the circuit of a full bridge boost type pfp power factor precompensator concludes this study

spectral efficiency scaling laws in dense random wireless networks with multiple receive antennas this paper considers large random wireless networks where transmit and receive node pairs communicate within a certain range while sharing a common spectrum by modeling the spatial locations of nodes as a poisson point process analytical expressions for the ergodic spectral efficiency of a typical node pair are derived as a function of the channel state information available at a receiver csir in terms of relevant system parameters the density of communication links the number of receive antennas the path loss exponent and the operating signal to noise ratio one key finding is that when the receiver only exploits csir for the direct link the sum spectral efficiency increases linearly with the density provided the number of receive antennas increases as a certain superlinear function of the density when each receiver exploits csir for a set of dominant interfering links in addition to that of the direct link the sum spectral efficiency increases linearly with both the density and the path loss exponent if the number of antennas is a linear function of the density this observation demonstrates that having csir for dominant interfering links provides an order gain in the scaling law it is also shown that this linear scaling holds for direct csir when incorporating the effect of the receive antenna correlation provided that the rank of the spatial correlation matrix scales superlinearly with the density these scaling laws are derived from integral representations of the distribution of the signal to interference and noise ratio which are of independent interest and which in turn derived from stochastic geometry and more precisely from the theory of shot noise fields simulation results back the scaling laws and the integral representations

robustness bound for receding horizon finite memory control lyapunov krasovskii approach this article presents a robustness bound rb of receding horizon finite memory control rhfmc kwon w h and han s 2004 receding horizon finite memory controls of output feedback controls for state space systems ieee transactions on automatic control 49 1905 1915 for continuous time state space systems with norm bounded uncertainties the proposed rb is easily obtained by solving a convex problem in terms of a linear matrix inequality we show through a numerical example that the rhfmc can guarantee the robust stabilisation for a larger class of uncertain systems than linear quadratic gaussian controls when some poles of closed loop systems are close to an imaginary axis in the complex plane

a branch and bound algorithm for the total weighted tardiness problem this paper presents a new branch and bound algorithm for the single machine total weighted tardiness problem it obtains lower bounds using a lagrangian relaxation approach with subproblems that are total weighted completion time problems the well known subgradient optimization technique is replaced by a multiplier adjustment method that leads to an extremely fast bound calculation the method incorporates various devices for checking dynamic programming dominance in the search tree extensive computational results for problems with up to 50 jobs show the superiority of the algorithm over existing methods

finite time observer design for nonlinear impulsive systems with impact perturbation this paper investigates the observer design problem of nonlinear impulsive systems with impact perturbation by using the concept of normal form this paper proposes a full order finite time observer which guarantees the finite time convergence independent of the impact perturbation reduced order observer is additionally developed for the proposed normal form an illustrative example is given in order to illustrate the capability of the proposed method

sliding order and sliding accuracy in sliding mode control the synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered usually what is called sliding mode is employed in such synthesis this sliding mode is characterized in practice by a high frequency switching of the control it turns out that the deviation of the system from its prescribed constraints sliding accuracy is proportional to the switching time delay a new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced these algorithms feature a bounded control continuously depending on time with discontinuities only in the control derivative it is also shown that the sliding accuracy is proportional to the square of the switching time delay

a unified asymptotic analysis of area spectral efficiency in ultradense cellular networks this paper studies the asymptotic properties of average area spectral efficiency ase of a downlink cellular network in the limit of very dense base station bs and user densities this asymptotic analysis relies on three assumptions 1 interference is treated as noise 2 the bs locations are drawn from a poisson point process and 3 the path loss function is bounded above satisfying mild regularity conditions we consider three possible definitions of the average ase all of which give units of bits per second per unit bandwidth per unit area when there is no constraint on the minimum operational signal to interference plus noise ratio sinr and instantaneous full channel state information csi is available at the transmitter the average ase is proven to saturate to a constant which we derive in a closed form for the other two ase definitions wherein either a minimum sinr is enforced or csi is not available the average ase is instead shown to collapse to zero at high bs density we provide several familiar case studies for the class of considered path loss models and demonstrate that our results cover most previous models and results on ultradense networks as special cases

a note on distributed finite time observers the robust distributed estimation for a class of time invariant plants is achieved via a finite time observer its error reaching zero after a finite time in the absence of perturbation two types of robustness are also shown first input to state stability with respect to measurement noises and additive perturbations is proven second we demonstrate that the estimation error stays bounded in the presence of known transmission delays

robust deadbeat continuous time observer design based on modulation integrals abstract in this paper the state estimation problem of linear continuous time systems is dealt with by a non asymptotic state observer which allows the state estimation error to decay within an arbitrarily small finite time without resorting to high gain injection by processing the measured input and output signals through modulation integrals a number of auxiliary signals not affected by the initial conditions are obtained from which the system state can be computed by simple algebra the problem of internal instability of modulation integrals is addressed by resorting to a periodic rescaling mechanism that prevents error accumulation and singularities we show that the combination of modulation integrals with periodic rescaling can be implemented as a jump linear system the robustness of the devised method with respect to additive measurement perturbations on the system s input output is characterized by input to state stability arguments

stability proof for a well established super twisting parameter setting abstract several sufficient stability conditions exist for the super twisting algorithm for its tuning in practical applications however a popular parameter set is regularly used which is provided in literature without any stability proof this short note provides a novel simple sufficient stability condition which includes this very popular parameter setting

fixed time mathcal h _ infty control for port controlled hamiltonian systems in this paper the locally fixed time and globally fixed time mathcal h infty control problems for the port controlled hamiltonian pch systems are investigated via the interconnection and damping assignment passivity based control ida pbc technique compared with finite time stabilization where the convergence time of the closed loop system s states relies on the initial values the settling time of fixed time stabilization can be adjusted to achieve desired equilibrium point regardless of initial conditions the concepts of fixed time mathcal h infty control fixed time stability region or region of attraction and fixed time stability boundary are presented in this paper and the criterions of globally fixed time attractivity of a prespecified locally fixed time stability region are obtained combining the locally fixed time stability of an equilibrium point and the globally fixed time attractivity of a prespecified fixed time stability region the globally fixed time mathcal h infty control problem of pch system is effectively solved two novel control laws are designed to deal with the globally fixed time mathcal h infty control problem and the conservativeness in estimating the settling time is also briefly discussed an illustrative example shows that the theoretical results obtained in this paper work very well in the fixed time mathcal h infty control design for pch systems

optimal state estimation without the requirement of a priori statistics information of the initial state the result given by the kalman filter is the best linear unbiased estimate blue provided that the mean and variance of the initial state are known the same state estimation problem is reconsidered for multi input multi output mimo stochastic time varying discrete systems when the statistics knowledge about the initial state is not known the algorithm presented in this paper gives the blue of system states without the requirement of any a priori knowledge about the initial state the concept of complete reconstructibility of stochastic systems is established and the necessary and sufficient condition for complete reconstructibility is given when applied to a completely reconstructible deterministic system the proposed algorithms give the deadbeat state estimates even if the system is not observable

receding horizon unbiased fir filters for continuous time state space models without a priori initial state information a receding horizon unbiased finite impulse response filter rhuff is proposed for continuous time state space models linearity unbiasedness finite impulse response fir structure and independence of the initial state information will be required in advance in addition to a performance index of minimum variance the proposed rhuff is obtained by directly minimizing the performance index with the unbiasedness constraint the proposed rhuff is represented first in a standard fir form and then in an iterative form it is shown that the rhuff is equivalent to the existing receding horizon rh kalman fir filter the former is more systematic and logical while the latter is heuristic due to the handling of infinite covariance of the initial state information

global finite time observers for lipschitz nonlinear systems this technical note presents a global finite time observer design for a class of systems with lipschitz nonlinearity by applying a finite time stability theorem and a careful selection of the homogeneity powers and weights the problem of global and finite time stable observers is studied an observer design procedure is given and a numerical example is provided to illustrate the design method

nonuniform in time state estimation of dynamic systems in this paper it is shown that if a time varying uncertain system is robustly completely detectable then there exists an estimator for this system i e the state vector of the system can be estimated asymptotically if the time varying uncertain system is robustly completely observable it is shown that there exists an estimator for this system with assignable rate of convergence of the error moreover specialized constructions are developed for the special class of triangular systems

technical communique terminal sliding mode observers for a class of nonlinear systems this paper proposes a terminal sliding mode observer for a class of nonlinear systems to achieve finite time convergence for all error states compared to standard sliding mode observers which only enable finite time convergence of the output error the observer in this paper makes use of fractional powers to reduce other non output errors to zero in finite time a 2 degree of freedom robotic manipulator is used to demonstrate the effectiveness of the proposed observer

brief paper minimax fir smoothers for deterministic continuous time state space models in order to design a smoother for a deterministic continuous time state space model a new performance criterion is proposed which is given by a ratio of the current estimation error to the weighted energy of the deterministic disturbance applied during the recent finite horizon among smoothers with the deadbeat property and finite impulse response fir structure a minimax fir smoother mfs is obtained to optimize the proposed performance criterion to begin with the functional optimization problem is formulated with respect to kernel functions of the mfs and then its solution is explicitly presented the mfs depends only on inputs and outputs on the finite recent horizon and is independent of any a priori state information the mfs is first represented in an integral form for simple representation and then a differential form is introduced for efficient numerical computation as in h iir smoothing and h 2 iir filtering it is shown that the proposed mfs for a deterministic system can be interpreted as the minimum variance unbiased fir smoother for a stochastic system

a global high gain finite time observer a global finite time observer is designed for nonlinear systems which are uniformly observable and globally lipschitz this result is based on a high gain approach combined with recent advances on finite time stability using lyapunov function and homogeneity concepts

recursive solutions to deadbeat observers for time varying multivariable systems this paper describes a new construction of the deadbeat observer for the state estimation of linear time varying multivariable systems the proposed design methods are computationally attractive because of their simplicity and recursive nature and are recommendable even for time invariant multivariable systems

the approximate capacity of the many to one and one to many gaussian interference channels recently etkin tse and wang found the capacity region of the two user gaussian interference channel to within 1 bit s hz a natural goal is to apply this approach to the gaussian interference channel with an arbitrary number of users we make progress towards this goal by finding the capacity region of the many to one and one to many gaussian interference channels to within a constant number of bits the result makes use of a deterministic model to provide insight into the gaussian channel the deterministic model makes explicit the dimension of signal level a central theme emerges the use of lattice codes for alignment of interfering signals on the signal level

global and exact hosm differentiator with dynamic gains for output feedback sliding mode control in this paper we introduce a global differentiator based on higher order sliding modes hosm and dynamic gains to solve the problem of trajectory tracking via output feedback for a class of uncertain nonlinear plants with arbitrary relative degree and disturbances norm observers for the unmeasured state are employed to dominate the disturbances as well as to adapt the gains of the proposed differentiator since the nonlinearities may be state dependent and time varying uniform global stability and robust exact tracking are guaranteed employing the proposed hosm based exact differentiator the obtained results are not restricted to first order sliding mode control feedback but applies for second order sliding mode algorithms twisting super twisting and variable gain super twisting as well as quasi continuous hosm finite time controllers simulations with an aircraft pitch control application illustrate the claimed properties even in the presence of measurement noise

design of rls fir filter using covariance information in linear continuous time stochastic systems this paper addresses a new design method of recursive least squares rls and finite impulse response fir filter using covariance information in linear continuous time stochastic systems the signal process is observed with additive white noise it is assumed that the white observation noise is independent of the signal process the auto covariance function of the signal is expressed in the semi degenerate kernel form the rls fir filter uses the following information 1 the auto covariance function of the signal expressed in the semi degenerate kernel form 2 the variance of the white observation noise process 3 the observed values

weak convergence of nonlinear high gain tracking differentiator in this technical note the weak convergence of a nonlinear high gain tracking differentiator based on finite time stable system is presented under some easy checkable conditions an example is constructed by using homogeneity numerical simulation shows that this tracking differentiator takes advantages over the existing ones this result relaxes the strict conditions required in existing literature that the lyapunov function satisfies the global lipschitz condition and the setting time function is continuous at zero both of them seem very restrictive in applications

a fixed time output feedback control scheme for double integrator systems abstract a continuous output feedback control scheme rendering the closed loop double integrator system globally stable in finite time is presented in particular the convergence time is independent of initial conditions the bi limit homogeneous technique is used for controller and observer designs with fixed time convergence then a continuous output feedback control law is proposed for nominal double integrator system and its perturbed version the homogeneity and lyapunov techniques are used to ensure the fixed time stability of the closed loop system under output feedback control framework finally the efficiency of the proposed algorithms is illustrated by numerical simulations

sliding motion on discontinuity surfaces of high co dimension a construction for selecting a filippov vector field in this paper we consider the issue of sliding motion in filippov systems on the intersection of two or more surfaces to this end we propose an extension of the filippov sliding vector field on manifolds of co dimension p with p 2 our model passes through the use of a multivalued sign function reformulation to justify our proposal we will restrict to cases where the sliding manifold is attractive for the case of co dimension p 2 we will distinguish between two types of attractive sliding manifold node like and spiral like the case of node like attractive manifold will be further extended to the case of p 3 finally we compare our model to other existing methodologies on some examples

prescribed time output feedback for linear systems in controllable canonical form abstract for linear systems in the controllable canonical form we introduce a prescribed time output feedback controller which provides for easy prescription of estimation and stabilization convergence times irrespective of initial conditions and with minimal tuning of the observer and controller parameters we show that the closed loop output feedback system is fixed time globally uniformly asymptotically stable as well as convergent to zero in the prescribed time further we show that a separation principle holds between the prescribed time controller and the prescribed time observer provided the scaling power of the time varying observer gains exceeds the scaling power of the controller gains by twice the order of the system i e provided the observer is fast enough relative to the controller irrespective of the constant gains of both

receding horizon recursive state estimation describes a receding horizon discrete time state observer using the deterministic least squares framework the state estimation horizon which determines the number of past measurement samples used to reconstruct the state vector is introduced as a tuning parameter for the proposed state observer a stability result concerning the choice of the state estimation horizon is established it is also shown that the fixed memory receding horizon state observer can be related to the standard dynamic observer by using an appropriate end point state weighting on the estimator cost function

a new varying gain exponent based differentiator observer an efficient balance between linear and sliding mode algorithms it is well known that the supertwisting algorithm is robust to matched perturbation but is sensitive to measurement noise contrary to this the classical linear algorithm is less sensitive to measurement noise but less robust to perturbation to combine both the good accuracy of the supertwisting algorithm with respect to perturbation and the good performance of the linear algorithm with respect to measurement noise this article proposes a new differentiator observer with a varying exponent gain alpha whose variation depends on the magnitude of measurement noise high frequency signal when the magnitude of measurement noise increases respectively decreases alpha tends to 1 respectively tends to 0 5 and the proposed differentiator observer behaves as a linear algorithm respectively as a supertwisting algorithm thus by one parameter alpha the differentiator observer can take care of high frequency noise and matched perturbations a complete stability analysis of the proposed differentiator observer is provided to highlight the applicability of the proposed methodology the dedicated differentiator observer is respectively validated on the electropneumatic actuator and electric machine test benches these experimental results are compared to those of linear and supertwisting algorithms

quasi deadbeat minimax filters for deterministic state space models in this note a quasi deadbeat property is introduced and a quasi deadbeat minimax filter dmf is proposed as a new class of filters for deterministic discrete time state space models constraints such as linearity quasi deadbeat property and independence of the initial state information will be required in advance in addition to a new performance index of the worst case gain between the disturbance and the current estimation error the proposed dmf is obtained by directly minimizing the new performance index with above constraints finite impulse response fir and infinite impulse response iir structures are suggested with emphasis on the fir structure the proposed dmf is represented first in a standard batch form and then in an iterative form it is shown that the dmf with fir and iir structures for deterministic systems are similar in form to the existing receding horizon unbiased fir filter rhuff and the kalman filter respectively for stochastic systems

brief a receding horizon unbiased fir filter for discrete time state space models this paper concerns with a new linear finite impulse response fir filter called the receding horizon unbiased fir rhuf filter for the state estimation in discrete time state space models to obtain the rhuf filter linearity unbiasedness and fir structure will be required beforehand in addition to a performance criteria of minimum variance the rhuf filter is obtained by directly solving an optimization problem with the unbiasedness constraint the rhuf filter has time invariance and deadbeat properties the rhuf filter is represented in both a batch form and an iterative form it is shown that the rhuf filter is equivalent to the existing receding horizon kalman fir rhkf filter whose optimality is not clear to understand the former is more systematic and logical while the latter is heuristic due to handling of infinite covariance of the initial state information

a simple nonlinear observer for a class of uncertain mechanical systems a simple nonlinear observer is proposed for a class of uncertain nonlinear multiple input multiple output mimo mechanical systems whose dynamics are first order differentiable the global asymptotic observation of the proposed observer is proved thus the observer can be designed independently of the controller furthermore the proposed observer is formulated without any detailed model knowledge of the system these advantages make it easy to implement numerical simulations are included to illustrate the effectiveness of the proposed observer

linear function dead beat observers with disturbance localization for linear periodic discrete time systems abstract in this paper the classical notion of a conditioned invariant subspace is extended to the case of linear periodic discrete time systems properly characterized and suitably specialized to the notion of an outer reconstructible subspace these ideas are used in order to find necessary and sufficient conditions for the existence of a linear function dead beat observer for such systems under unknown and unmeasurable disturbances and a synthesis procedure for such an observer

least squares finite impulse response fixed lag smoother and filter in linear discrete time stochastic systems abstract this paper proposes the least squares ls finite impulse response fir fixed lag smoother and filter in linear discrete time wide sense stationary stochastic systems the fir fixed lag smoothing estimate is given as a linear convolution sum of the impulse response function and the observed values it is assumed that the signal is observed with additional white noise which is uncorrelated with the signal process by solving the simultaneous linear equations transformed from the wiener hopf equation the optimal impulse response function is obtained the necessary information of the ls fir fixed lag smoothing algorithm is the auto covariance function of the signal process and the variance of the observation noise process in particular this paper proposes the levinson durbin algorithm which needs less amount of arithmetic operations than the gauss jordan elimination method in the inverse of the toeplitz matrix for the optimal impulse response function from the numerical simulation example the proposed ls fir fixed lag smoother and filter are superior in estimation accuracy to the rls wiener fir estimators

a continuous time recursive fixed lag smoother converging in finite time in this technical note we propose a new fixed lag smoother that estimates the fixed delayed state for a stochastic continuous time system the estimation error variance of the proposed smoother is minimized under the constraint that the estimated state converges to the real state exactly in finite time after noises or uncertainties disappear for numerical computing the proposed smoother is represented in a recursive form unlike other approaches any additional processes such as batch processing and sampling data through discrete time techniques are not required to achieve the finite time convergence a numerical example is presented to illustrate the finite time convergence of the proposed smoother in comparison with the asymptotic convergence of an optimal smoother

directional sensitivity of continuous least squares state estimators abstract least squares state estimators present an alternative to luenberger observers and yield an exact deadbeat estimate of the state vector of a dynamic system as the optimal solution to a least squares problem in some vector or functional space for instance the conventional l 2 optimal finite memory observer is shown to be a special case of the continuous least squares state estimator sensitivity of these estimators to structured uncertainty in the system matrix of the plant is studied using the frechet derivative it is shown that the state estimation error caused by the plant model s mismatch is proportional to the frechet derivative of the symbol of the parameterization operator used for the estimator implementation evaluated for the nominal value of the system matrix for the special case of state estimation in a single tone continuous oscillator the crucial impact of the parameterization operator choice on the state estimator sensitivity to the plant model s uncertainty is investigated in detail

one machine sequencing to minimize total tardiness a fourth theorem for emmons in 1969 h emmons provided three theorems emmons 1 3 for determining precedence relations between pairs of jobs for the single machine tardiness problem we show here a fourth straightforward theorem that uses the information when the jobs in the pair are both known to precede a third job in an optimum sequence the new theorem augments the three emmons theorems and is shown to be a generalization of a theorem by elmaghraby

finite time global stabilization by means of time varying distributed delay feedback the paper contains certain results concerning the finite time global stabilization for triangular control systems described by retarded functional differential equations by means of time varying distributed delay feedback these results enable us to present solutions to feedback stabilization problems for systems with delayed input the results are obtained by using the backstepping technique

neural network based distributed attitude coordination control for spacecraft formation flying with input saturation this brief considers the attitude coordination control problem for spacecraft formation flying when only a subset of the group members has access to the common reference attitude a quaternion based distributed attitude coordination control scheme is proposed with consideration of the input saturation and with the aid of the sliding mode observer separation principle theorem chebyshev neural networks smooth projection algorithm and robust control technique using graph theory and a lyapunov based approach it is shown that the distributed controller can guarantee the attitude of all spacecraft to converge to a common time varying reference attitude when the reference attitude is available only to a portion of the group of spacecraft numerical simulations are presented to demonstrate the performance of the proposed distributed controller

estimation of solutions of observable nonlinear systems with disturbances a family of continuous time observable nonlinear systems with input and output is considered a new technique of estimation of the state variables is proposed it relies on the use of past values of the output as done to construct some observers which converge in finite time and on a recent technical result pertaining to the theory of the monotone systems it applies to systems with additive disturbances and disturbances in the output the nonlinear terms are not supposed to be globally lipschitz but it is requested that they depend only on the input and output variables

a receding horizon kalman fir filter for discrete time invariant systems a receding horizon kalman fir filter is presented that combines the kalman filter and the receding horizon strategy when the horizon initial state is assumed to be unknown the suggested filter is a fir filter form which has many good inherent properties it can always be defined irrespective of singularity problems caused by unknown information about the horizon initial state the suggested filter can be represented in either an iterative form or a standard fir form it is also shown that the suggested filter possesses the unbiasedness property and the remarkable deadbeat property irrespective of any horizon initial condition the validity of the suggested filter is illustrated by numerical examples

fixed time observer with simple gains for uncertain systems abstract in this article we consider the problem of fixed time observer for nonlinear systems that is a finite time observer whose settling time can be bounded independently of the initial condition we consider a large class of nonlinear systems which includes two main classes linearizable systems up to input output injection and uniformly observable systems furthermore the effect of noise and uncertainty is analyzed

a discontinuous output feedback controller and velocity observer for nonlinear mechanical systems in this paper we develop a new discontinuous output feedback tracking controller for a class of uncertain nonlinear multi input multi output mechanical systems whose dynamics are first order differentiable a novel filter design and lyapunov type stability analysis are used to prove semi global asymptotic tracking as a by product of the proposed framework we also present the design of a new simple discontinuous velocity observer that ensures global asymptotic velocity observation

soft decoding based strategies for relay and interference channels analysis and achievable rates using ldpc codes we provide a rigorous mathematical analysis of two communication strategies soft decode and forward soft df for relay channels and soft partial interference cancelation soft ic for interference channels both strategies involve soft estimation which assists the decoding process we consider ldpc codes not because of their practical benefits but because of their analytic tractability which enables an asymptotic analysis similar to random coding methods of information theory unlike some works on the closely related demodulate and forward we assume non memoryless code structure aware estimation with soft df we develop simultaneous density evolution to bound the decoding error probability at the destination this result applies to erasure relay channels in one variant of soft df the relay applies wyner ziv coding to enhance its communication with the destination borrowing from compress and forward to analyze soft ic we adapt existing techniques for iterative multiuser detection and focus on binary input additive white gaussian noise interference channels we prove that optimal point to point codes are unsuitable for soft ic as well as for all strategies that apply partial decoding to improve upon single user detection and multiuser detection including han kobayashi

a receding horizon kalman fir filter for linear continuous time systems a receding horizon kalman finite impulse response fir filter is suggested for continuous time systems combining the kalman filter with the receding horizon strategy in the suggested filter the horizon initial state is assumed to be unknown it can always be obtained irrespective of unknown information on the horizon initial state the filter may be the first stochastic fir form for continuous time systems that may have many good inherent properties the suggested filter can be represented in an iterative form and also in a standard fir form the suggested filter turns out to be a remarkable deadbeat observer the validity of the suggested filter is illustrated by numerical examples

l_2 e fir filters for deterministic continuous time state space signal models in this paper a new l2 e performance criterion is introduced which is represented as a gain between the disturbance during the recent time interval and the current estimation error based on the l2 e performance criterion the l2 e finite impulse response fir filter leff is proposed for deterministic continuous time state space signal models without requiring the stochastic information such as variances and means the leff is designed to minimize the maximum value of the l2 e performance criterion together with prior constraints such as linearity unbiased property in the deterministic sense and fir structure simultaneously via simulation the leff is compared with other deterministic infinite impulse response iir filters such as the hinfin and l2 linfin filters

second order sliding mode observer for mechanical systems the super twisting second order sliding mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems the finite time convergence of the observer is proved thus the observer can be designed independently of the controller a discrete version of the observer is considered and the corresponding accuracy is estimated

finite time output regulation for linear 2 2 hyperbolic systems using backstepping this contribution presents the backstepping design of output feedback regulators for boundary controlled linear 2 2 hyperbolic systems that achieve regulation in finite time it is assumed that the disturbances can act in domain at both boundaries and at the output to be controlled the latter need not be available for measurement and consists of in domain pointwise distributed or boundary outputs firstly a solution of the finite time state feedback regulator problem is given on the basis of the regulator equations they are formulated in backstepping coordinates so that a solution is attainable in closed form this leads to a very straightforward regulator design for 2 2 hyperbolic systems with a general class of outputs then a finite dimensional reference observer that converges in finite time is introduced which consists of two observers and a delay this result is extended to the backstepping design of finite time disturbance observers for 2 2 hyperbolic systems with a collocated measurement in particular two backstepping disturbance observers are determined so that after introducing a delay the disturbance model and plant states can be estimated in finite time hence by combining the state feedback regulator with these observers a finite time output feedback regulator is obtained for the state feedback regulator and the disturbance observer existence conditions are derived in terms of the plant transfer behaviour a simple example with an in domain pointwise and distributed output illustrates the theoretical results

a finite time convergent observer with robustness to piecewise constant measurement noise motivated by the design of observers with good performance and robustness to measurement noise the problem of estimating the state of a linear time invariant system in finite time and robustly with respect to measurement noise is considered using a hybrid systems framework a hybrid observer producing an estimate that converges to the plant state in finite time even under unknown piecewise constant noise is presented the stability and robustness properties of the observer are shown analytically and validated numerically

prescribed time observers for linear systems in observer canonical form for linear systems in the observer canonical form we introduce a state observer with time varying gains that tend to infinity as time approaches a prescribed convergence time the observer is shown to exhibit fixed time stability with an arbitrary convergence time which is prescribed by the user irrespective of initial conditions the output estimation error injection terms are also shown to remain uniformly bounded and converge to zero at the prescribed time

generalised observer design for dissipative lipschitz nonlinear systems in the presence of measurement noise this paper presents two novel observer concepts first it develops a globally exponentially stable nonlinear observer for noise free dissipative nonlinear systems second for a dissipative nonlinear system with measurement noise the paper develops an observer to guarantee a desired performance namely an upper limit on the ratio of the square of the weighted l2 norm of the error to the square of the weighted l2 norm of the measurement noise the necessary and sufficient conditions for both observers are reformulated as algebraic riccati equations ares so that standard solvers can be utilised in addition the paper presents necessary and sufficient conditions to be satisfied by the nonlinear system in order to ensure that the are and hence the observer design problem has a solution the use of the methodology developed in this paper is demonstrated through illustrative examples in literature there is no previous observer for dissipative system that provides both necessary and sufficient condition

performance of multi cell massive mimo systems with interference decoding we consider a multi cell massive mimo system where a time division duplex protocol is used to estimate the channel state information via uplink pilots when maximum ratio combining mrc is used at the bss the re use of pilots across cells causes the pilot contamination effect which yields interference components that do not vanish as the number of base station bs antennas m rightarrow infty when treating interference as noise tin this phenomenon limits the performance of multi cell massive mimo systems in this paper we analyze more advanced schemes based on simultaneous unique decoding sd as well as simultaneous non unique decoding snd of the interference that can provide unbounded rate as m rightarrow infty we also establish a worst case uncorrelated noise technique for multiple access channels to derive achievable rate expressions for finite m furthermore we study a much simpler subset of snd called s snd which provides a lower bound to snd and achieves unbounded rate as m rightarrow infty and also outperforms sd for finite m for the special cases of two cell and three cell systems using a maximum symmetric rate allocation policy we compare the performance of different interference decoding schemes with that of tin finally we numerically illustrate the improved performance of the proposed schemes

interference networks with point to point codes the paper establishes the capacity region of the gaussian interference channel with many transmitter receiver pairs constrained to use point to point codes the capacity region is shown to be strictly larger in general than the achievable rate regions when treating interference as noise using successive interference cancellation decoding and using joint decoding the gains in coverage and achievable rate using the optimal decoder are analyzed in terms of ensemble averages using stochastic geometry in a spatial network where the nodes are distributed according to a poisson point process and the channel path loss exponent is 2 it is shown that the density of users that can be supported by treating interference as noise can scale no faster than b2 as the bandwidth b grows while the density of users can scale linearly with b under optimal decoding

state and parameter estimation for nonlinear delay systems using sliding mode techniques in this technical note a class of time varying delay nonlinear systems is considered where both parametric uncertainty and structural uncertainty are involved the uncertain parameters are embedded in the system nonlinearly the bound on the structural uncertainty takes nonlinear form and is time delayed a sliding mode observer is proposed to estimate the system state and an adaptive law is proposed to estimate the unknown parameters simultaneously using the lyapunov razuminkhin approach sufficient conditions are developed such that the error system is uniformly ultimately bounded a simulation on a bioreactor system shows the effectiveness of the approach

the dispersion of nearest neighbor decoding for additive non gaussian channels we study the second order asymptotics of information transmission using random gaussian codebooks and nearest neighbor decoding over a power limited stationary memoryless additive non gaussian noise channel we show that the dispersion term depends on the non gaussian noise only through its second and fourth moments thus complementing the capacity result lapidoth 1996 which depends only on the second moment furthermore we characterize the second order asymptotics of point to point codes over k sender interference networks with non gaussian additive noise specifically we assume that each user s codebook is gaussian and that nn decoding is employed i e that interference from the k 1 unintended users gaussian interfering signals is treated as noise at each decoder we show that while the first order term in the asymptotic expansion of the maximum number of messages depends on the power of the interfering codewords only through their sum this does not hold for the second order term

separation results for the stabilization of nonlinear systems using different high gain observer designs high gain observers have been used in the design of output feedback controllers due to their ability to robustly estimate the unmeasured states while asymptotically attenuating disturbances the available techniques for the design of high gain observers can be classified into three groups pole placement algorithms riccati equation based algorithms and lyapunov equation based algorithms in 1 we presented separation results for globally bounded stabilizing state feedback controllers when the high gain observer is designed using pole placement so as to create a closed loop system with two time scale structure in this paper we show that the separation results of 1 hold for the other observer designs