benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

robust fault reconstruction in uncertain linear systems using multiple sliding mode observers in cascade in observer based fault reconstruction one of the necessary conditions is that the first markov parameter from the fault to the output must be full rank this paper seeks to relax that requirement by using multiple sliding mode observers in cascade signals from an observer are used as the output of a fictitious system whose input is the fault another observer is then designed and implemented for the fictitious system this process is repeated until the first markov parameter of the fictitious system with respect to the fault is full rank the result is that robust fault reconstruction can be carried out for a wider class of systems compared to other works that also seek to relax the requirement of a full rank first markov parameter in addition this paper has also investigated and presented the necessary and sufficient conditions as easily testable conditions and also the precise number of observers required a simulation example verifies the effectiveness of the scheme

proper discretization of homogeneous differentiators homogeneous sliding mode based differentiators hd are known to provide for the high accuracy robust estimation of derivatives in the presence of sampling noises and discrete measurements provided that the differentiator dynamics evolve in continuous time the popular one step euler discrete time implementation is proved to cause differentiation accuracy deterioration if the differentiation order exceeds 1 a novel discrete time realization of the hd is proposed which preserves the ultimate accuracy of the continuous time hd also with discrete measurements

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

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

a nonlinear conjugate gradient method with a strong global convergence property conjugate gradient methods are widely used for unconstrained optimization especially large scale problems the strong wolfe conditions are usually used in the analyses and implementations of conjugate gradient methods this paper presents a new version of the conjugate gradient method which converges globally provided the line search satisfies the standard wolfe conditions the conditions on the objective function are also weak being similar to those required by the zoutendijk condition

optimal differentiation based on stochastic signal models the problem of estimating the time derivative of a signal from sampled measurements is addressed the measurements may be corrupted by colored noise a key idea is to use stochastic models of the signal to be differentiated and of the measurement noise two approaches are suggested the first is based on a continuous time stochastic process as a model of the signal the second uses a discrete time arma model of the signal and a discrete time approximation of the derivative operator digital differentiators are presented in a shift operator polynomial form they minimize the mean square estimation error and are calculated from a linear polynomial equation and a polynomial spectral factorization the three obstacles to perfect differentiation namely a finite smoothing lag measurement noise and aliasing effects due to sampling are discussed

hosm observer for a class of non minimum phase causal nonlinear mimo systems a higher order sliding mode observer is proposed for asymptotic identification of the full state vector and the vector of unknown inputs for mimo nonlinear causal systems with unstable internal dynamics the problem is addressed via consistent application of exact higher order sliding mode differentiators in conjunction with the method of stable system center a numerical example illustrates the performance of the proposed algorithm

theoretical explanation of observed decreasing failure rate pooled data on the times of successive failures of the air conditioning system of a fleet of jet airplanes seemed to indicate that the life distribution had a decreasing failure rate more refined analysis showed that the failure distribution for each airplane separately was exponential but with a different failure rate using the theorem that a mixture of distributions each having a non increasing failure rate e g a mixture of exponential distributions itself has a non increasing failure rate the apparent decreasing failure rate of the pooled air conditioning life distribution was satisfactorily explained the present study has implications in other areas where an observed decreasing failure rate may well be the result of mixing exponential distributions having different parameters

unknown input and state estimation for unobservable systems the concept of strong detectability and its relation with the concept of invariant zeros is reviewed for strongly detectable systems which includes the strongly observable systems it is proposed a hierarchical design of a robust observer whose trajectories converge to those of the original state vector furthermore it is shown that neither left invertibility is a sufficient condition nor strong detectability is a necessary condition to estimate the unknown inputs it is shown that the necessary and sufficient condition for estimating the unknown inputs is that the set of the invariant zeros that do not belong to the set of unobservable modes be within the interior of the left half plane of the complex space this shows that the unknown inputs could be estimated even if it is impossible to estimate the entire state vector of the system two numerical examples illustrate the effectiveness of the proposed estimation schemes

the convergence properties of rmil conjugate gradient method under the strong wolfe line search abstract in dai 2016 based on the global convergence of rmil conjugate gradient method dai has modified it and called the modified version rmil which has good numerical results and globally convergent under the exact line search in this paper we established the sufficient descent property and the global convergence of rmil via strong wolfe line search method moreover numerical results based on well known optimization problems show that the modified method is competitive when compare with other conjugate gradient methods

discrete differentiators based on sliding modes abstract sliding mode based differentiation of the input f t yields exact estimations of the derivatives f f n provided an upper bound l t of f n 1 t is available in real time in practice it involves discrete sampling and numerical integration of the internal variables between the measurements accuracy asymptotics of different discretization schemes are calculated for discrete noisy sampling whereas sampling and integration steps are independently variable or constant proposed discrete differentiators restore the optimal accuracy asymptotics of their continuous time counterparts event triggered sampling is considered extensive numeric experiments are presented and analyzed

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 hybrid robust non homogeneous finite time differentiator a variant of super twisting differentiator is proposed lyapunov function is designed and an estimate on finite time of derivatives estimation is given the differentiator is equipped with hybrid adaptation algorithm that ensures global differentiation ability independently on amplitude of the differentiated signal and measurement noise

a new class of nonlinear conjugate gradient coefficients with global convergence properties abstract nonlinear conjugate gradient cg methods have played an important role in solving large scale unconstrained optimization their wide application in many fields is due to their low memory requirements and global convergence properties numerous studies and modifications have been conducted recently to improve this method in this paper a new class of conjugate gradient coefficients k that possess global convergence properties is presented the global convergence result is established using exact line searches numerical result shows that the proposed formula is superior and more efficient when compared to other cg coefficients

algebraic differentiators through orthogonal polynomials series expansions numerical differentiation is undoubtedly a fundamental problem in signal processing and control engineering due to its countless applications the goal of this paper is to address this question wi

interpolating sliding mode observer for a ball and beam system abstracta principle of interpolating sliding mode observer is introduced in this paper the observer incorporates multiple linear observers through interpolation of multiple estimates which is treated as a type of adaptation the principle is then applied to the ball and beam system for observation of the slope of the beam from the measurement of the ball position the linearised model of the ball and beam system using multiple linearisation points is developed the observer dynamics implemented in matlab simulink real time workshop environment experiments conducted on the ball and beam experimental setup demonstrate excellent performance of the designed novel interpolating adaptive observer

improvements on stability analysis and stabilisation of constant and variable gain second order sliding mode algorithms via exact convex representations a novel lyapunov based methodology for both stability analysis and stabilisation of second order sliding mode algorithms in the presence of exogenous disturbances is presented nowadays second ord

homogeneous time varying systems robustness analysis the problem of stability robustness with respect to time varying perturbations of a given frequency spectrum is studied applying homogeneity framework the notion of finite time stability over time intervals of finite length i e short finite time stability is introduced and used for that purpose the results are applied to analyze the super twisting algorithm sta behavior under time varying perturbations some simulation examples illustrate these robustness properties

global convergence properties of conjugate gradient methods for optimization this paper explores the convergence of nonlinear conjugate gradient methods without restarts and with practical line searches the analysis covers two classes of methods that are globally convergent on smooth nonconvex functions some properties of the fletcher reeves method play an important role in the first family whereas the second family shares an important property with the polak ribiere method numerical experiments are presented

comments on a new class of nonlinear conjugate gradient coefficients with global convergence properties in rivaie et al 2012 1 an efficient cg algorithm has been proposed for solving unconstrained optimization problems however due to a wrong inequality 3 3 used in rivaie et al the proof of theorem 2 and the global convergence theorem 3 are not correct we present the necessary corrections then the proposed method in rivaie et al still converges globally finally we report some numerical comparisons

how pooling failure data may reverse increasing failure rates abstract although mixtures of decreasing failure rate dfr distributions are always dfr some mixtures of increasing failure rate ifr distributions can also be ultimately dfr in this article various types of discrete and continuous mixtures of ifr distributions are considered and conditions are developed for such mixtures to be ultimately dfr these conditions lead to an interesting result that certain mixtures of ifr distributions even those with very rapidly increasing failure rates e g weibull truncated extreme ultimately become dfr distributions it is common practice to pool data from several different ifr distributions to enlarge sample size for instance the results of this article sound a warning that such pooling may actually reverse the ifr property of the individual samples to a dfr property

an improved second order sliding mode control scheme robust against the measurement noise in this note the second order sliding mode control problem is tackled by explicitly taking into account the presence of measurement error with unknown upper bound spl delta under sensible assumptions regarding the uncertain dynamics of a broad class of nonlinear plants a new switching controller is proposed guaranteeing a sliding accuracy of order o spl delta simulations highlight the robustness and good performance of the proposed approach and confirm the expected precision order

a solution to the generalized problem of nonlinear map inversion abstract this paper deals with the generalization of some problems related to map inversion solutions of such problems are proposed by means of observers for which a structure is proposed

nonlinear extremum seeking inspired on second order sliding modes we present a new extremum seeking algorithm that uses super twisting like nonlinear terms in order to improve its precision in addition the algorithm is combined with second order sliding mode observers to build an optimization framework for uncertain dynamic systems in which the variable to optimize is not measured and needs to be estimated the relevance of the proposed framework is illustrated in the problem of biomass optimization of a biological reactor with uncertain kinetics

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

concurrent learning for parameter estimation using dynamic state derivative estimators a concurrent learning cl based parameter estimator is developed to identify the unknown parameters in a nonlinear system unlike state of the art cl techniques that assume knowledge of the state derivative or rely on numerical smoothing cl is implemented using a dynamic state derivative estimator a novel purging algorithm is introduced to discard possibly erroneous data recorded during the transient phase for cl asymptotic convergence of the error states to the origin is established under a persistent excitation condition and the error states are shown to be uniformly ultimately bounded under a finite excitation condition

exact differentiation and sliding mode observers for switched lagrangian systems abstract the main topic of this paper is the problem of constructing observers for switched mechanical systems which includes as a specific case the design of observers based on the high order sliding mode technique the high order sliding mode is used to overcome the chattering phenomena occurring which induce some irrelevant and undesirable phenomena for mechanical systems the proposed approach based on the fliess canonical form also allows observers to give an estimate of the discrete location of the system which indicates the dynamic evolution the convergence of the observers is proved and a stick mass friction system is used to illustrate the efficiency of the proposed hybrid observers

reversal of increasing failure rates when pooling failure data because mixtures of exponential distributions with constant failure rate have the decreasing failure rate dfr property as shown by proschan in the sixties it is not unexpected that mixtures of distributions that have a mildly increasing failure rate ifr also have this property what is perhaps surprising is that mixtures of ifr distributions with rapidly increasing failure rate may also behave in this manner two striking examples of such mixtures are presented here and illustrated graphically this phenomenon could be the cause of concern in practice when it is suspected that a sample is based on pooled data

singularly perturbed analysis of chattering in relay control systems for sliding mode control systems with fast actuators sufficient conditions for the exponential decreasing of the amplitude of chattering and unlimited growth of frequency are found the connection between the stability of actuators and the stability of the plant on the one hand and the stability of the sliding mode system as the whole on the other hand is investigated the algorithm for correction of sliding mode equations is suggested for taking into account the presence of fast actuators

super twisting algorithm in presence of time and state dependent perturbations abstractin this paper generalized super twisting algorithm is applied to a class of systems whose perturbation and uncertain control coefficient are time and state dependent a non smooth strict lyapunov function is used to obtain the conditions for the global finite time stability and to estimate the time of convergence

reduced order observer in the sliding mode control of nonlinear nonaffine systems the note considers the variable structure control of nonlinear known nonaffine systems when the state vector is not completely available and the use of observers is required the strategy of introducing integrators in the input channel is exploited to enlarge the class of tractable control systems a new reduced order observer is proposed and conditions are found under which it is proven the convergence to the unique ideal solution of both system and observer the control problem is solved by forcing a sliding regime for the observer while satisfying an exponential stability criterion for the observation error state equation

finite time convergent differentiator based on singular perturbation technique a finite time convergent differentiator is presented that is based on singular perturbation technique the merits of this differentiator exist in three aspects rapidly finite time convergence compared with other typical differentiators no chattering phenomenon and besides the derivatives of the derivable signals the generalized derivatives of some classes of signals can be obtained for example the generalized derivative of a triangular wave is square wave etc the theoretical results are confirmed by computer simulations

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

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

universal single input single output siso sliding mode controllers with finite time convergence an universal controller is constructed formulated in input output terms only which causes the output of any uncertain smooth single input single output siso minimum phase dynamic system with known relative degree to vanish in finite time this allows exact tracking of arbitrary real time smooth signals only one parameter is to be adjusted since the approach is based on higher order finite time convergence sliding modes the control can be made arbitrarily smooth providing for the arbitrarily high tracking accuracy order with respect to the sampling step

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

continuous terminal sliding mode controller for uncertain systems with relative degree two a continuous homogeneous sliding mode control algorithm is proposed this algorithm ensures finite time convergence to the third order sliding set using only information about the output and its first derivative we prove the convergence of the proposed algorithm via a homogeneous continuously differentiable and strict lyapunov function

partial synchronization of chaotic systems with uncertainty we suggest an approach to partial synchronization of chaotic systems with uncertainty this method contains two steps i transforming the synchronization system into the canonical form by the well known feedback linearization theory and ii finding a control signal to ensure the asymptotic stability of the canonical system this partial synchronization approach requires very little system information by applying a finite time convergence technique to estimate uncertainties caused by unknown states parameters or structure we also argue in detail that this partial synchronization method can be extended to parameter identification sub structure estimation and even phase detection several examples are presented to illustrate the partial synchronization approach suggested

continuously implemented sliding mode adaptive unknown input observers under noisy measurements we propose an estimator for nonlinear systems with unmatched unknown inputs and under measurement noise the estimator design is based on the combination of observer design for descriptor systems sliding modes theory and adaptive control the estimation of the measurement noise is achieved thanks to the transformation of the original system into a singular form where the measurement noise makes part of the augmented state two adaptive parameters are updated online one to compensate for the unknown bounds on the states the unknown inputs and the measurement noise and a second one to compensate for the effect of the nonlinearities to join robust state estimation and unknown inputs reconstruction our approach borrows inspiration from sliding mode theory however all signals are continuously implemented we demonstrate that both state and unknown inputs estimation are achieved up to arbitrarily small tolerance the utility of our theoretical results is illustrated through simulation case studies

chattering analysis a formal mathematical definition of chattering is proposed chattering phenomena are classified into three types in particular the first type is harmless and cannot be avoided chattering properties of various control approaches are considered the dangerous second and third types of chattering phenomena are proved to be removable by proper use of high order sliding modes hosm fast stable actuators and sensors only generate the first type of chattering in hosm systems and practically never affect the sliding motion computer simulation confirms the theoretical results

an easy design for interval observers this paper deals with the problem of interval estimation the proposed approach is based on the use of successive derivatives in continuous time or forward measurements in discrete time in an alg

an improved wei yao liu nonlinear conjugate gradient method for optimization computation in this paper we take a little modification to the wei yao liu nonlinear conjugate gradient method proposed by wei et al z wei s yao l liu the convergence properties of some new conjugate gradient methods appl math comput 183 2006 1341 1350 such that the modified method possesses better convergence properties in fact we prove that the modified method satisfies sufficient descent condition with greater parameter email protected 0 12 in the strong wolfe line search and converges globally for nonconvex minimization we also extend these results to the hestenes stiefel method and prove that the modified hs method is globally convergent for nonconvex functions with the standard wolfe conditions numerical results are reported by using some test problems in the cute library

technical communique an observation algorithm for nonlinear systems with unknown inputs this paper deals with the design of unknown input observers for nonlinear systems an algorithm which determines if the state and the unknown input of the system can be recovered in finite time is introduced this algorithm leads to the transformation of the system into an extended block triangular observable form suitable for the design of finite time observers the proposed method is useful to relax some restrictive conditions of the existing nonlinear unknown input observer design procedures

sliding mode based differentiation and filtering the proposed k th order filter is based on sliding modes sms it exactly estimates k input derivatives in the absence of noises and is robust to noises of small magnitudes or having small average values estimation accuracy asymptotics are calculated the filter is applied to the real time accurate estimation of the equivalent control in sm control systems