a high order internal model based iterative learning control scheme for nonlinear systems with time iteration varying parameters in this technical note we propose a new iterative learning control ilc scheme for nonlinear systems with parametric uncertainties that are temporally and iteratively varying the time varying characteristics of the parameters are described by a set of unknown basis functions that can be any continuous functions the iteratively varying characteristics of the parameters are described by a high order internal model hoim that is essentially an auto regression model in the iteration domain the new parametric learning law with hoim is designed to effectively handle the unknown basis functions the method of composite energy function is used to derive convergence properties of the hoim based ilc namely the pointwise convergence along the time axis and asymptotic convergence along the iteration axis comparing with existing ilc schemes the hoim based ilc can deal with nonlinear systems with more generic parametric uncertainties that may not be repeatable along the iteration axis the validity of the hoim based ilc under identical initialization condition i i c and the alignment condition is also explored

technical communique adaptive ilc for a class of discrete time systems with iteration varying trajectory and random initial condition in this work we present a discrete time adaptive iterative learning control ailc scheme to deal with systems with time varying parametric uncertainties using the analogy between the discrete time axis and the iterative learning axis the new adaptive ilc can incorporate a recursive least squares rls algorithm hence the learning gain can be tuned iteratively along the learning axis and pointwisely along the time axis when the initial states are random and the reference trajectory is iteration varying the new ailc can achieve the pointwise convergence over a finite time interval asymptotically along the iterative learning axis

technical communique iterative learning control of linear discrete time multivariable systems the authors present an iterative learning control rule for linear discrete time multivariable systems the control rule assures a zero output error for the whole desired trajectory after only one learning iteration the robustness of the control rule is studied and two numerical examples are used to validate the new control rule

correspondence comments on adaptive ilc for a class of discrete time systems with iteration varying trajectory and random initial condition this note points out some errors in the proof of the asymptotic learning convergence of the tracking error in chi hou and xu chi r h hou z s xu j x 2008 adaptive ilc for a class of discrete time systems with iteration varying trajectory and random initial condition automatica 44 8 2207 2213

basis functions and parameter optimisation in high order iterative learning control in this paper a new parameter optimal high order iterative learning control ilc algorithms is proposed to extend the work of owens and feng parameter optimisation in iterative learning control international journal of control 14 11 1059 1069 if the original plant is positive this new algorithm will result in convergent learning where the convergence is monotonic to zero tracking error if the original plant is not positive it can be shown that by adding a suitable set of basis functions into the algorithm the tracking error will again converge monotonically to zero this provides a considerable improvement to earlier work on parameter optimal ilc as it opens up the possibility of globally convergent algorithms for any linear plant g the number of parameters needed to ensure convergence could however become large the paper shows that the use of low order parameterisations is capable of achieving much of the benefit achieved in the ideal case

a synthetic approach for robust constrained iterative learning control of piecewise affine batch processes for industrial nonlinear batch processes that can be practically divided into a series of piecewise affine operating regions a two dimensional 2d closed loop iterative learning control ilc method is proposed for robust tracking of the set point profile against cycle to cycle process uncertainties and load disturbances both state feedback and output feedback are considered for the control design together with the process input and output constraints for implementation based on a 2d system description for the batch operation a few synthetic performance and robust control objectives are proposed for developing the 2d ilc schemes in combination with the 2d lyapunov krasovskii functions that can guarantee monotonic state energy or output error decrease in both the time during a cycle and batch from cycle to cycle directions both the polyhedral and norm bounded descriptions of process uncertainties are considered to derive the corresponding linear matrix inequality lmi conditions for the closed loop ilc system robust stability an important merit of these lmi conditions is that there are adjustable convergence indices prescribed for both the time and batch directions and an adjustable robust control performance level for the closed loop system by specifying optimizing these adjustable parameters to solve these lmi conditions the 2d ilc controller can be explicitly derived for implementation the application to a highly nonlinear continuous stirred tank reactor cstr is shown to illustrate the effectiveness and merits of the proposed ilc method

non linear iterative learning by an adaptive lyapunov technique we consider the iterative learning control problem from an adaptive control viewpoint it is shown that some standard lyapunov adaptive designs can be modified in a straightforward manner to give a solution to either the feedback or feedforward ilc problem some of the common assumptions of non linear iterative learning control are relaxed e g we relax the common linear growth asssumption on the non linearities and handle systems of arbitrary relative degree it is shown that generally a linear rate of convergence of the mse can be achieved and a simple robustness analysis is given for linear plants we show that a linear rate of mse convergence can be achieved for non minimum phase plants

discrete time adaptive iterative learning control for high order nonlinear systems with unknown control directions an adaptive iterative learning control method is proposed for a class of nonlinear strict feedback discrete time systems with random initial conditions and iteration varying desired trajectories an n step ahead predictor approach is employed to estimate the future states in the control design discrete nussbaum gain method is utilised to deal with the lack of a priori knowledge of control directions the proposed control algorithm guarantees the boundedness of all the signals in the controlled system the tracking error converges to zero asymptotically along the iterative learning axis except for beginning states affected by random initial conditions the effectiveness of the proposed control scheme is verified through numerical simulation

punctuality and idleness in just in time scheduling abstract in scheduling problems with irregular cost functions such as deviation functions in earliness tardiness scheduling problems optimal solutions usually contain some idleness periods during which no activity is processed then minimizing the penalties for not delivering on time and minimizing the idleness cost are two complementary criteria for a schedule a dynamic programming procedure in which the states are represented by continuous two dimensional piecewise linear functions is proposed to compute the cost of the pareto optimal schedules

iterative learning control synthesis based on 2 d system theory an algorithm is presented for iterative learning of the control input for a linear discrete time multivariable system necessary and sufficient conditions are stated for convergence of the proposed algorithm the algorithm synthesis and analysis are based on two dimensional 2 d system theory a numerical example is given

a survey on iterative learning control for nonlinear systems in this article we review the recent advances in iterative learning control ilc for nonlinear dynamic systems in the research field of ilc two categories of system nonlinearities are considered namely the global lipschitz continuous glc functions and local lipschitz continuous llc functions ilc for glc systems is widely studied and analysed using contraction mapping approach and the focus of recent exploration moves to application problems though a number of theoretical issues remain open ilc for llc systems is currently a hot area and the recent research focuses on ilc design and analysis by means of lyapunov approach the objectives of this article are to introduce recent development and advances in nonlinear ilc schemes highlight their effectiveness and limitations as well as discuss the directions for further exploration of nonlinear ilc

a recovering beam search algorithm for the single machine just in time scheduling problem abstract we consider the just in time scheduling problem where the just in time notion is captured by means of multiple conflicting criteria the calculation of any non dominated solution for these criteria is achieved by solving an extension of the single machine problem of minimising the mean weighted deviation from distinct due dates in the extended problem each job to schedule is also constrained by a release date and a deadline this problem is np hard in the strong sense and we propose heuristic algorithms to solve it computational experiments show that among those algorithms the most effective heuristic in terms of quality is a recovering beam search algorithm

adaptive iterative learning control for linear systems with binary valued observations this brief presents a novel adaptive iterative learning control ilc algorithm for a class of single parameter systems with binary valued observations using the certainty equivalence principle the adaptive ilc algorithm is designed by employing a projection identification algorithm along the iteration axis it is shown that even though the available system information is very limited and the desired trajectory is iteration varying the proposed adaptive ilc algorithm can guarantee the convergence of parameter estimation over a finite time interval along the iterative axis meanwhile the tracking error is pointwise convergence asymptotically two examples are given to validate the effectiveness of the algorithm

iterative learning control design for linear discrete time systems with multiple high order internal models this work is focused on the iterative learning control ilc design for linear discrete time systems with iteration varying factors including reference initial state and exogenous disturbances first multiple high order internal models hoims are given for various iteration varying factors the reference is generated by an hoim and the initial state and the exogenous disturbances ultimately satisfy hoims but do not strictly follow hoims in finite iteration interval then a new ilc scheme a special high order ilc ho ilc is constructed according to an augmented hoim that is the aggregation of all hoims for simplicity the case with only iteration varying reference is first considered where the asymptotic stability and monotone convergence based ilc design methods are both presented by using the 2 d analysis approach next more iteration varying factors are further considered in this situation the hoim based ilc is transformed into a controller design problem of a 2 d roesser model with non zero boundary states and disturbances where the 2 d h performance is studied in consequence an ilc design criterion is presented to achieve perfect tracking and 2 d h performance for comparison the monotone convergence based ilc design method is extended to the situation with more iteration varying factors utilizing information provided by the multiple hoims it is verified that ho ilc outperforms low order ilc lo ilc in presence of iteration varying factors meanwhile the 2 d h based ilc is shown to be superior to the monotone convergence based ilc finally a microscale robotic deposition system with iteration varying factors is given to illustrate the advantage of the proposed 2 d h based ilc

iterative learning of model reference adaptive controller for uncertain nonlinear systems with only output measurement in this paper a model reference adaptive control strategy is used to design an iterative learning controller for a class of repeatable nonlinear systems with uncertain parameters high relative degree initial output resetting error input disturbance and output noise the class of nonlinear systems should satisfy some differential geometric conditions such that the plant can be transformed via a state transformation into an output feedback canonical form a suitable error model is derived based on signals filtered from plant input and output the learning controller compensates for the unknown parameters uncertainties and nonlinearity via projection type adaptation laws which update control parameters along the iteration domain it is shown that the internal signals remain bounded for all iterations the output tracking error will converge to a profile which can be tuned by design parameters and the learning speed is improved if the learning gain is large

iterative learning control for discrete nonlinear systems with randomly iteration varying lengths abstract this note proposes ilc for discrete time affine nonlinear systems with randomly iteration varying lengths no prior information on the probability distribution of random iteration length is required prior for controller design the conventional p type update law is used with a modified tracking error because of randomly iteration varying lengths a novel technical lemma is proposed for the strict convergence analysis in pointwise sense an illustrative example verifies the theoretical results

an algebraic approach to iterative learning control in this paper discrete time iterative learning control ilc systems are analysed from an algebraic point of view the algebraic analysis shows that a linear time invariant single input single output model can always represented equivalently as a static multivariable plant due to the finiteness of the time axis furthermore in this framework the ilc synthesis problem becomes a tracking problem of a multi channel step function the internal model principle states that for asymptotic tracking i e convergent learning it is required that an ilc algorithm has to contain an integrator along the iteration axis but at the same time the resulting closed loop system should be stable the question of stability can then be answered by analysing the closed loop poles along the iteration axis using standard results from multivariable polynomial systems theory this convergence theory suggests that time varying ilc control laws should be typically used instead of time invariant control laws in order to guarantee go

iterative learning control for non linear systems described by a blended multiple model representation this paper deals with the design of gain scheduling based iterative learning controllers for continuous time non linear systems described by a blended multiple model representation sufficient conditions guaranteeing the convergence of the infinity norm as well as the u norm of the tracking error are derived the effectiveness of the proposed control scheme is illustrated on an example of a non affine in input system

on initial conditions in iterative learning control initial conditions or initial resetting conditions play a fundamental role in all kinds of iterative learning control methods in this note we study five different initial conditions disclose the inherent relationship between each initial condition and corresponding learning convergence or boundedness property the iterative learning control method under consideration is based on lyapunov theory which is suitable for plants with time varying parametric uncertainties and local lipschitz nonlinearities

constrained group balancing why does it work abstract we consider a problem where a set of objects possessing multiple attributes must be partitioned into a certain number of groups so that the groups are as balanced as possible with respect to the number of objects possessing each attribute this multi criteria decision problem arises in a variety of practical applications ranging from assigning students to study groups to designing level schedules for jit assembly lines a direct approach enforcing balance through hard constraints may lead to infeasibility but works well in practice we analyze this phenomenon from the worst case and empirical perspectives as well as through an in depth analysis of one representative practical application the design of student groups at the rotman school of management university of toronto the goals of the analysis are to understand what classes of balancing problems may contain infeasible instances and how prevalent such instances are within these classes as well as to synthesize practical managerial insights that a decision maker could follow in order to increase the chances that balanced groups can be found

data driven control for relative degree systems via iterative learning iterative learning control ilc is a kind of effective data driven method that is developed based on online and or offline input output data the main purpose of this paper is to supply a unified 2 d analysis approach for both continuous time and discrete time ilc systems with relative degree it is shown that the 2 d roesser system framework can be established for general ilc systems regardless of relative degree under which convergence conditions can be provided to guarantee both asymptotic stability and monotonic convergence of the ilc processes in particular conditions for the monotonic convergence of ilc can be given in terms of linear matrix inequalities and formulas for the updating law can be derived simultaneously simulation results are presented to illustrate the effectiveness of ilc determined through the 2 d design approach in dealing with the higher order relative degree problem of ilc systems as well as the robustness of such ilc against uncertainties

stability of learning control with disturbances and uncertain initial conditions the authors investigate the effects of state disturbances output noise and errors in initial conditions on a class of learning control algorithms they present a simple learning algorithm and exhibit via a concise proof bounds on the asymptotic trajectory errors for the learned input and the corresponding state and output trajectories furthermore these bounds are continuous functions of the bounds on the initial condition errors state disturbances and output noise and the bounds are zero in the absence of these disturbances

subspace algorithms for identifying separable in denominator 2d systems with deterministic stochastic inputs abstractin this paper we present an algorithm for identifying two dimensional 2d causal recursive and separable in denominator crsd state space models in the roesser form with deterministic stochastic inputs the algorithm implements the n4sid po moesp and cca methods which are well known in the literature on 1d system identification but here we do so for the 2d crsd roesser model the algorithm solves the 2d system identification problem by maintaining the constraint structure imposed by the problem i e toeplitz and hankel and computes the horizontal and vertical system orders system parameter matrices and covariance matrices of a 2d crsd roesser model from a computational point of view the algorithm has been presented in a unified framework where the user can select which of the three methods to use furthermore the identification task is divided into three main parts 1 computing the deterministic horizontal model parameters 2 computing the deterministic vertical model parameters

periodic solutions of a class of singular hamiltonian systems soit r n 0 n n n 3 et soit v c 1 rx r on etudie l existence des solutions periodiques t u t avec une periode prescrite du systeme suivant de n equations differentielles d ordre 2 u v t u

minimizing variation of production rates in just in time systems a survey abstract in the past several years there has been growing interest in scheduling problems where jobs are penalized both for being early and for being tardy this notable deviation from previous work in which finishing early is generally regarded as being at least as desirable as finishing on time is perceived to be the one that well captures the scheduling dimension of jit production systems a number of excellent surveys on these problems has appeared over the last four years there is however another important scheduling objective in jit production systems which is to minimize variation of rates at which processes supply their outputs these scheduling problems are for example of primary concern in the toyota jit system thus far most research efforts in this area have been focused on minimizing variation of the rate at which different products are being produced on the final multi model assembly line which itself is a supplying process we shall review the results of this research and relate them to the due date based scheduling problems extensions and open problems will also be reviewed schedules that minimize variation of the rate at which different products are being produced on the line do not necessarily minimize variation in the line demand for outputs of processes that supply it few heuristics for the problem of minimizing the variation are available and hardly anything is known on its complexity as wel as exact algorithms to tackle it we shall review a mathematical programming model of the problem and open questions that result from it

optimal level schedules in mixed model multi level jit assembly systems with pegging abstract solving the level or balanced schedule problem is the most important scheduling goal for just in time production assembly systems for most industrial applications determining the optimal balanced schedule in a multi level facility is a very difficult combinatorial problem however if outputs at production levels which feed the final assembly level are dedicated or pegged to the final product into which they will be assembled then it can be shown that an efficient scheduling algorithm can be implemented to determine the optimal level schedule it can also be shown that several symmetrical properties of the pegging model can be exploited to significantly reduce the computational requirements of the problem

a multi objective genetic algorithm for mixed model sequencing on jit assembly lines this paper presents a multi objective genetic algorithm moga approach to a just in time jit sequencing problem where variation of production rates and number of setups are to be optimized simultaneously these two objectives are typically inversely correlated with each other and therefore simultaneously optimization of both is challenging moreover this type of problem is np hard hence attainment of ip lp solutions or solutions via total enumeration te is computationally prohibitive the moga approach searches for locally pareto optimal or locally non dominated frontier where simultaneous minimization of the production rates variation and the number of setups is desired performance of the proposed moga was compared against a te scheme in small problems and also against three other search heuristics in small medium and large problems experimental results show that the moga performs very well when compared against te in a considerably shorter time it also outperforms the comparator algorithms in terms of quality of solutions at the same level of diversity in reasonable amount of cpu time

adaptive control of nonlinear systems using neural networks layered networks are used in a nonlinear adaptive control problem the plant is an unknown feedback linearizable discrete time system represented by an input output model a state space model of the plant is obtained to define the zero dynamics which are assumed to be stable a linearizing feedback control is derived in terms of some unknown nonlinear functions to identify these functions it is assumed that they can be modelled by layered neural networks the weights of the networks are updated and used to generate the control a local convergence result is given computer simulations verify the theoretical result

initial shift issues on discrete time iterative learning control with system relative degree this paper deals with the initial shift problem that arises from discrete time iterative learning control a unified learning scheme is considered for a class of nonlinear systems with well defined relative degree which adopts the error data with anticipation in time and provides wider freedom for the updating law formation the sufficient convergence condition is derived to enable the system to possess asymptotic tracking capability and the converged output trajectory can be assessed by the initial condition the tracking performance is improved further by the introduction of initial rectifying action and the complete tracking is achieved over a specified interval

adaptive iterative learning control for nonlinearly parameterised systems with unknown time varying delays and input saturations in this work an adaptive iterative learning control ailc scheme is proposed to address a class of nonlinearly parameterised systems with both unknown time varying delays and input saturations by incorporating a saturation function a novel iterative learning control mechanism is constructed with a feedback term in the time domain and a fully saturated adaptive learning term in the iteration domain which is used to estimate the unknown time varying system uncertainty a new time weighted lyapunov krasovskii like composite energy function lkl cef is designed for the convergence analysis where time weighted inputs states and estimates of system uncertainty are all considered despite the existence of time varying parametric uncertainties time varying delays input saturations and local lipschitz nonlinearities the learning convergence is guaranteed with rigorous mathematical analysis simulation results verify the correctness and effectiveness of the proposed method further

a note on level schedules for mixed model assembly lines in just in time production systems this note formulates an assignment problem for obtaining optimal level schedules for mixed model assembly lines in jit production systems the problem was formulated as a quadratic integer programming problem in a recent paper by miltenburg 1989 where however only enumerative algorithms and heuristics were proposed for its solution our assignment formulation can also be extended to more general objective functions than the one used by miltenburg

two dimensional model and algorithm analysis for a class of iterative learning control systems the iterative learning control system ilcs has attracted considerable research interest in recent years however the theoretical results on some fundamental properties of the ilcs have not yet been established one of the common drawbacks shared by current approaches is lack of a suitable mathematical model which can clearly describe both the dynamics of the control system itself and the behaviour of the learning process as well in this paper a class of iterative learning control systems is analysed from the point of view of two dimensional 2 d system theory the 2 d model for a class of ilcs is established in the form of roessor s model based on which a general type of learning controller is proposed analysis of the 2 d error equation shows that the 2 d asymptotic stability of the 2 d model guarantees the learning convergence of an ilcs design criteria for a learning controller is also suggested the learning gain matrices are obtained from a recursive 2 d identifier using the input and output

brief iterative learning control with initial rectifying action this paper addresses the initial shift problem in iterative learning control with system relative degree the tracking error caused by nonzero initial shift is detected when applying a conventional learning algorithm finite initial rectifying action is introduced in the learning algorithm and is shown effective in the improvement of tracking performance in particular robustness with respect to variable initial shifts the uniform convergence of the output trajectory to a desired one jointed smoothly with a specified transient trajectory from the starting position is ensured in the presence of fixed initial shift

brief paper analysis of two particular iterative learning control schemes in frequency and time domains this paper deals with iterative learning control design for multiple input multiple output mimo linear time invariant lti systems two particular ilc schemes are considered and analyzed in both frequency and time domains some remarks on the convergence implementation robustness with respect to disturbances and reinitialization errors as well as positive realness issues related to both schemes are provided

adaptive boundary iterative learning control for an euler bernoulli beam system with input constraint this paper addresses the vibration control and the input constraint for an euler bernoulli beam system under aperiodic distributed disturbance and aperiodic boundary disturbance hyperbolic tangent functions and saturation functions are adopted to tackle the input constraint a restrained adaptive boundary iterative learning control abilc law is proposed based on a time weighted lyapunov krasovskii like composite energy function in order to deal with the uncertainty of a system parameter and reject the external disturbances three adaptive laws are designed and learned in the iteration domain all the system states of the closed loop system are proved to be bounded in each iteration along the iteration axis the displacements asymptotically converge toward zero simulation results are provided to illustrate the effectiveness of the proposed abilc scheme

brief paper stability analysis of discrete time iterative learning control systems with interval uncertainty this paper presents a stability analysis of the iterative learning control ilc problem for discrete time systems when the plant markov parameters are subject to interval uncertainty using the so called super vector approach to ilc vertex impulse response matrices are employed to develop sufficient conditions for both asymptotic stability and monotonic convergence of the ilc process it is shown that the stability of such interval ilc systems can be determined by checking the stability of the system using only the vertex points of the interval markov parameters

a minimax method for a class of hamiltonian systems with singular potentials abstract this paper presents a minimax method which gives existence and multiplicity results for time periodic solutions of a class of hamiltonian systems when a singular potential is present the singularity satisfies the strong force condition of gordon when milder singularities are permitted a notion of generalized t periodic solution is introduced and we get existence and multiplicity results for such solutions

brief adaptive robust iterative learning control with dead zone scheme an adaptive robust iterative learning control method based on a new dead zone scheme is presented for the control of nonlinear uncertain systems the new dead zone scheme ceases both learning and adaptation whenever the previous iteration error enters a pre specified error bound in the sequel enhances the robustness of the control system and meanwhile achieves arbitrary tracking accuracy for guaranteed stability it is indicated that the system will converge to the error bound within finite iterations and stay inside it and that the boundedness of the system signals for any iteration is ensured no finite escape time iterative learning control ilc and adaptive robust control are synthesized to achieve a new control paradigm the iterative learning control strategy is applied directly to deal with structured system uncertainties unknown time functions which are invariant over iterations the adaptive robust control strategy is used to handle non periodic system uncertainties associated with partially known bounding functions where the unknown parameters in the upper bounding functions are estimated with adaptation by integrating learning adaptation robust control and the new dead zone scheme using lyapunov s direct method the proposed scheme is able to handle fairly broad classes of nonlinear uncertain systems

technical communique on the disturbance properties of high order iterative learning control algorithms the disturbance properties of high order iterative learning control ilc algorithms are considered an error equation is formulated and using statistical models of the load and measurement disturbances an equation for the covariance matrix of the control error vector is derived the results are exemplified by analytic derivation of the covariance matrix for a second order ilc algorithm

convergence of iterative learning control for siso nonrepetitive systems subject to iteration dependent uncertainties abstract this paper studies the robust convergence properties of iterative learning control ilc for single input single output siso nonrepetitive systems subject to iteration dependent uncertainties that arise in not only initial states and external disturbances but also plant models given an extended relative degree condition it is possible to propose necessary and sufficient nas conditions for robust ilc convergence the tracking error bound is shown to depend continuously on the bounds of the iteration dependent uncertainties when the iteration dependent uncertainties are bounded nas conditions exist to guarantee bounded system trajectories and output tracking error if the iteration dependent uncertainties converge then nas conditions ensure bounded system trajectories and zero output tracking error the results are also extended to a class of affine nonlinear systems satisfying a lipschitz condition simulation tests on a representative batch process demonstrate the validity of the obtained robust ilc convergence results

brief h control and robust stabilization of two dimensional systems in roesser models feedback control of two dimensional 2 d systems is a problem of considerable importance in both theory and practical applications in this paper we present a state space solution to the problem of h control of 2 d systems for a linear discrete time 2 d system described by a 2 d state space roesser model a 2 d dynamic output feedback controller is designed to achieve the closed loop system asymptotic stability and a specified h performance using a linear matrix inequality lmi approach we further give a solution for robust stabilization of 2 d systems subject to a class of norm bounded uncertainties the results are demonstrated by an application example of stabilization of processes expressed in a darboux equation

note on cyclic sequences in the product rate variation problem abstract sequencing units on a production or assembly line in order to attenuate the variations in the rates of resource consumption is a problem that has received growing attention in recent years in the present study a particular case the product rate variation prv problem with convex discrepancy function is analysed its equivalence to the determination of a minimal path on a graph is shown in addition a useful property when the number of units for each kind of product to be sequenced is divisible by k with k as an positive integer is established in this case an optimum sequence is obtained by repeating k times an optimum sequence in the reduced problem once the units of each product have been divided by k

robust discrete time iterative learning control for nonlinear systems with varying initial state shifts this note is concerned with the robust discrete time iterative learning control ilc design for nonlinear systems with varying initial state shifts a two gain ilc law is considered using a 2d analysis approach sufficient conditions are derived to guarantee both convergence of the learning process for fixed initial condition and boundedness of the tracking error for variable initial condition it is shown that the error data with anticipation in time can well handle the varying initial state shifts in discrete time ilc

analysis of iterative learning control for a class of nonlinear discrete time systems abstract an output feedback iterative learning control scheme is proposed for a class of nonlinear discrete time systems in the presence of direct transmission from system inputs to outputs the convergence condition of the iterative learning control scheme is analyzed the effectiveness of suggested discrete time iterative learning control algorithm is demonstrated with a single link robotic manipulator as the illustrative example 1997 elsevier science ltd

a discrete time learning control algorithm for a class of linear time invariant systems a discretized version of the d type learning control algorithm is presented for a mimo linear discrete time system a necessary and sufficient condition for uniform convergence of the proposed learning algorithm is presented then we prove that the same condition is sufficient for the global robustness of the proposed learning algorithm to state disturbances measurement noise at the output and reinitialization error are present at each iteration a numerical example is given to illustrate the results

closed orbits of fixed energy for singular hamiltonian systems this paper deals with the existence of periodic solutions of q v q 0 such that 1 2 q 2 v q h where q r n h is a given number v c 2 r n 0 r has a singularity at x 0 and v denotes the gradient of v

model based iterative learning control with a quadratic criterion for time varying linear systems in this paper iterative learning control ilc based on a quadratic performance criterion is revisited and generalized for time varying linear constrained systems with deterministic stochastic disturbances and noises the main intended area of application for this generalized method is chemical process control where excessive input movements are undesirable and many process variables are subject to hard constraints it is shown that within the framework of the quadratic criterion based ilc q ilc various practical issues such as constraints disturbances measurement noises and model errors can be considered in a rigorous and systematic manner algorithms for the deterministic case the stochastic case and the case with bounded parameter uncertainties are developed and relevant properties such as the asymptotic convergence are established under some mild assumptions numerical examples are provided to demonstrate the performance of the proposed algorithms

level schedules for mixed model just in time processes a mixed model manufacturing facility running under a just in time jit production system is controlled by setting the production sequence of the final assembly process this sequence is set to achieve the primary goal of an organization operating under a jit system which is to maintain a constant rate of part usage in this paper a graph theoretic approach is used to determine an optimal solution for this goal for a new nonconvex objective function furthermore it is shown that a schedule always exists such that at all times the deviation of actual production from the desired level of production for every product is never more than one unit

optimality of first order ilc among higher order ilc higher order iterative learning control ho ilc algorithms use past system control information from more than one past iterative cycle this class of ilc algorithms have been proposed aiming at improving the learning efficiency and performance this paper addresses the optimality of ho ilc in the sense of minimizing the trace of the control error covariance matrix in the presence of a class of uncorrelated random disturbances it is shown that the optimal weighting matrices corresponding to the control information associated with more than one cycle preceding the current cycle are zero that is an optimal ho ilc does not add to the optimality of standard first order ilc in the sense of minimizing the trace of the control error covariance matrix the system under consideration is a linear discrete time varying systems with different relative degree between the input and each output

a class of subspace model identification algorithms to identify periodically and arbitrarily time varying systems abstract subspace model identification algorithms that allow the identification of a linear time varying ltv state space model from an ensemble set of input output measurements are presented in this paper each pair of input and output sequences in this ensemble is recorded when the underlying system to be identified undergoes the same time varying behavior the algorithms operate directly on the available ensemble of input output data and are a generalization of the recently proposed multivariable output error state space moesp class of algorithms to this ensemble type of identification problems a special case is considered in this paper where the repetition of this time varying behavior is intrinsic namely in periodically time varying systems an example of identifying a multirate sampled data system from a recorded input and output sequence demonstrates some of the capabilities of the presented subspace model identification algorithms

a stochastic iterative learning control algorithm with application to an induction motor a recursive optimal algorithm based on minimizing the input error covariance matrix is derived to generate the learning gain matrix of a p type ilc for linear discrete time varying systems with arbitrary relative degree it is shown that in the case where the number of inputs is not greater than the number of outputs the input error covariance matrix converges to zero at a rate inversely proportional to the number of iterations in the presence of uncorrelated random state disturbance reinitialization errors and measurement noise the state error covariance matrix converges to zero at a rate inversely proportional to the number of iterations in the presence of measurement noise in the case where the number of inputs is greater than the number of outputs then the system output error converges to zero at a rate inversely proportional to the number of iterations in presence of measurement noise another suboptimal recursive algorithm is also proposed based on unknown system dynamics and unknown disturb

h control for a class of 2 d nonlinear systems with intermittent measurements in this paper the problem of h control for a class of 2 d nonlinear systems with intermittent measurements and sector nonlinearities is considered a stochastic variable satisfying the bernoulli random binary distribution is utilized to characterize the data dropouts our attention is focused on the design of a state feedback controller such that the closed loop 2 d stochastic nonlinear system is mean square asymptotic stability and has an h disturbance attenuation performance a sufficient condition is established by means of linear matrix inequalities lmi technique and formulas can be given for the control law design the result is also extended to more general cases where the system matrices contain uncertain parameters numerical example is also given to illustrate the effectiveness of proposed approach

a prescribed energy problem for a singular hamiltonian system with a weak force we consider the existence of periodic solutions of a hamiltonian system q v q 0 hs such that 12 q t 2 v q t h for all t where q rn n 3 h 0 we prove the existence of a generalized solution that may enter the singularity 0 moreover under the assumption v q 1 q w q where 0 2 and q w q q 1 w q q 2 2w q 0 as q 0 we estimate the number of collisions of generalized solutions in particular we get the existence of a classical non collision solution of hs for l 2 when n 4 and for 4 3 2 when n 3

stabilization of singular 2 d continuous discrete systems by state feedback controllers necessary and sufficient conditions are established for the existence of a solution to the stabilization problem for singular two dimensional 2 d continuous discrete linear systems a procedure is presented for designing a state feedback controller such that the closed loop system is asymptotically stable and its response is impulse free

a transformed two stage method for reducing the part usage variation and a comparison of the product level and part level solutions in sequencing mixed model assembly lines abstract the minimization of the two stage variation in the mixed model sequencing problem of reducing the part level variation is transformed to product level terms the development is based on an existing simplification of the one stage part level variation a simplification of the two stage part level variation and the usage of a relationship matrix that evaluates the relevance among the product structures of various models algorithms based on these simplification and transformation are presented the transformation can be shown to be equivalent to that of bautista et al 1996 but results in a smaller empirical computational burden in minimizing the two stage variation and uses a relationship matrix that is independent of product mix changes the computational results show that the transformed two stage algorithm significantly outperforms the direct enumeration method in computation time for large problems and generally outperforms the one stage method in mean squared deviation the transformed two stage method can be used as a heuristic procedure or as an intermediate tool for another solution approach a more general sufficient condition than the existing conditions for the equivalence of the problems of minimizing the product level variation and minimizing the part level variation is also presented the computational experimentation demonstrates that there is a potential of obtaining significantly better solutions in part usage variation by directly considering the part level variation when this sufficient condition is not met