Showing papers on "Adaptive algorithm published in 2009"
TL;DR: This paper proposes a self- Adaptive DE (SaDE) algorithm, in which both trial vector generation strategies and their associated control parameter values are gradually self-adapted by learning from their previous experiences in generating promising solutions.
Abstract: Differential evolution (DE) is an efficient and powerful population-based stochastic search technique for solving optimization problems over continuous space, which has been widely applied in many scientific and engineering fields. However, the success of DE in solving a specific problem crucially depends on appropriately choosing trial vector generation strategies and their associated control parameter values. Employing a trial-and-error scheme to search for the most suitable strategy and its associated parameter settings requires high computational costs. Moreover, at different stages of evolution, different strategies coupled with different parameter settings may be required in order to achieve the best performance. In this paper, we propose a self-adaptive DE (SaDE) algorithm, in which both trial vector generation strategies and their associated control parameter values are gradually self-adapted by learning from their previous experiences in generating promising solutions. Consequently, a more suitable generation strategy along with its parameter settings can be determined adaptively to match different phases of the search process/evolution. The performance of the SaDE algorithm is extensively evaluated (using codes available from P. N. Suganthan) on a suite of 26 bound-constrained numerical optimization problems and compares favorably with the conventional DE and several state-of-the-art parameter adaptive DE variants.
3,085 citations
TL;DR: Simulation results show that JADE is better than, or at least comparable to, other classic or adaptive DE algorithms, the canonical particle swarm optimization, and other evolutionary algorithms from the literature in terms of convergence performance for a set of 20 benchmark problems.
Abstract: A new differential evolution (DE) algorithm, JADE, is proposed to improve optimization performance by implementing a new mutation strategy ldquoDE/current-to-p bestrdquo with optional external archive and updating control parameters in an adaptive manner. The DE/current-to-pbest is a generalization of the classic ldquoDE/current-to-best,rdquo while the optional archive operation utilizes historical data to provide information of progress direction. Both operations diversify the population and improve the convergence performance. The parameter adaptation automatically updates the control parameters to appropriate values and avoids a user's prior knowledge of the relationship between the parameter settings and the characteristics of optimization problems. It is thus helpful to improve the robustness of the algorithm. Simulation results show that JADE is better than, or at least comparable to, other classic or adaptive DE algorithms, the canonical particle swarm optimization, and other evolutionary algorithms from the literature in terms of convergence performance for a set of 20 benchmark problems. JADE with an external archive shows promising results for relatively high dimensional problems. In addition, it clearly shows that there is no fixed control parameter setting suitable for various problems or even at different optimization stages of a single problem.
2,778 citations
14 Jun 2009
TL;DR: This paper presents an online adaptive algorithm implemented as an actor/critic structure which involves simultaneous continuous-time adaptation of both actor and critic neural networks, and calls this ‘synchronous’ policy iteration.
Abstract: In this paper we discuss an online algorithm based on policy iteration for learning the continuous-time (CT) optimal control solution with infinite horizon cost for nonlinear systems with known dynamics. We present an online adaptive algorithm implemented as an actor/critic structure which involves simultaneous continuous-time adaptation of both actor and critic neural networks. We call this ‘synchronous’ policy iteration. A persistence of excitation condition is shown to guarantee convergence of the critic to the actual optimal value function. Novel tuning algorithms are given for both critic and actor networks, with extra terms in the actor tuning law being required to guarantee closed-loop dynamical stability. The convergence to the optimal controller is proven, and stability of the system is also guaranteed. Simulation examples show the effectiveness of the new algorithm.
648 citations
TL;DR: The near-optimal control problem for a class of nonlinear discrete-time systems with control constraints is solved by iterative adaptive dynamic programming algorithm.
Abstract: In this paper, the near-optimal control problem for a class of nonlinear discrete-time systems with control constraints is solved by iterative adaptive dynamic programming algorithm. First, a novel nonquadratic performance functional is introduced to overcome the control constraints, and then an iterative adaptive dynamic programming algorithm is developed to solve the optimal feedback control problem of the original constrained system with convergence analysis. In the present control scheme, there are three neural networks used as parametric structures for facilitating the implementation of the iterative algorithm. Two examples are given to demonstrate the convergence and feasibility of the proposed optimal control scheme.
574 citations
TL;DR: A generic on‐line version of the expectation–maximization (EM) algorithm applicable to latent variable models of independent observations that is suitable for conditional models, as illustrated in the case of the mixture of linear regressions model.
Abstract: In this contribution, we propose a generic online (also sometimes called adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm applicable to latent variable models of independent observations. Compared to the algorithm of Titterington (1984), this approach is more directly connected to the usual EM algorithm and does not rely on integration with respect to the complete data distribution. The resulting algorithm is usually simpler and is shown to achieve convergence to the stationary points of the Kullback-Leibler divergence between the marginal distribution of the observation and the model distribution at the optimal rate, i.e., that of the maximum likelihood estimator. In addition, the proposed approach is also suitable for conditional (or regression) models, as illustrated in the case of the mixture of linear regressions model.
495 citations
TL;DR: The proposed adaptive stochastic gradient descent method is compared to a standard, non-adaptive Robbins-Monro (RM) algorithm and indicates that ASGD is robust to variations in the registration framework and is less sensitive to the settings of the user-defined parameters than RM.
Abstract: We present a stochastic gradient descent optimisation method for image registration with adaptive step size prediction. The method is based on the theoretical work by Plakhov and Cruz (J. Math. Sci. 120(1):964---973, 2004). Our main methodological contribution is the derivation of an image-driven mechanism to select proper values for the most important free parameters of the method. The selection mechanism employs general characteristics of the cost functions that commonly occur in intensity-based image registration. Also, the theoretical convergence conditions of the optimisation method are taken into account. The proposed adaptive stochastic gradient descent (ASGD) method is compared to a standard, non-adaptive Robbins-Monro (RM) algorithm. Both ASGD and RM employ a stochastic subsampling technique to accelerate the optimisation process. Registration experiments were performed on 3D CT and MR data of the head, lungs, and prostate, using various similarity measures and transformation models. The results indicate that ASGD is robust to these variations in the registration framework and is less sensitive to the settings of the user-defined parameters than RM. The main disadvantage of RM is the need for a predetermined step size function. The ASGD method provides a solution for that issue.
432 citations
TL;DR: A fully distributed least mean-square algorithm is developed in this paper, offering simplicity and flexibility while solely requiring single-hop communications among sensors, and stability of the novel D-LMS algorithm is established to guarantee that local sensor estimation error norms remain bounded most of the time.
Abstract: Adaptive algorithms based on in-network processing of distributed observations are well-motivated for online parameter estimation and tracking of (non)stationary signals using ad hoc wireless sensor networks (WSNs). To this end, a fully distributed least mean-square (D-LMS) algorithm is developed in this paper, offering simplicity and flexibility while solely requiring single-hop communications among sensors. The resultant estimator minimizes a pertinent squared-error cost by resorting to i) the alternating-direction method of multipliers so as to gain the desired degree of parallelization and ii) a stochastic approximation iteration to cope with the time-varying statistics of the process under consideration. Information is efficiently percolated across the WSN using a subset of ldquobridgerdquo sensors, which further tradeoff communication cost for robustness to sensor failures. For a linear data model and under mild assumptions aligned with those considered in the centralized LMS, stability of the novel D-LMS algorithm is established to guarantee that local sensor estimation error norms remain bounded most of the time. Interestingly, this weak stochastic stability result extends to the pragmatic setup where intersensor communications are corrupted by additive noise. In the absence of observation and communication noise, consensus is achieved almost surely as local estimates are shown exponentially convergent to the parameter of interest with probability one. Mean-square error performance of D-LMS is also assessed. Numerical simulations: i) illustrate that D-LMS outperforms existing alternatives that rely either on information diffusion among neighboring sensors, or, local sensor filtering; ii) highlight its tracking capabilities; and iii) corroborate the stability and performance analysis results.
365 citations
TL;DR: An iterative least squares (LS) procedure to jointly optimize the interpolation, decimation and filtering tasks for reduced-rank adaptive filtering for interference suppression in code-division multiple-access (CDMA) systems is described.
Abstract: We present an adaptive reduced-rank signal processing technique for performing dimensionality reduction in general adaptive filtering problems. The proposed method is based on the concept of joint and iterative interpolation, decimation and filtering. We describe an iterative least squares (LS) procedure to jointly optimize the interpolation, decimation and filtering tasks for reduced-rank adaptive filtering. In order to design the decimation unit, we present the optimal decimation scheme and also propose low-complexity decimation structures. We then develop low-complexity least-mean squares (LMS) and recursive least squares (RLS) algorithms for the proposed scheme along with automatic rank and branch adaptation techniques. An analysis of the convergence properties and issues of the proposed algorithms is carried out and the key features of the optimization problem such as the existence of multiple solutions are discussed. We consider the application of the proposed algorithms to interference suppression in code-division multiple-access (CDMA) systems. Simulations results show that the proposed algorithms outperform the best known reduced-rank schemes with lower complexity.
348 citations
TL;DR: A new matrix learning scheme to extend relevance learning vector quantization (RLVQ), an efficient prototype-based classification algorithm, toward a general adaptive metric by introducing a full matrix of relevance factors in the distance measure.
Abstract: We propose a new matrix learning scheme to extend relevance learning vector quantization (RLVQ), an efficient prototype-based classification algorithm, toward a general adaptive metric By introducing a full matrix of relevance factors in the distance measure, correlations between different features and their importance for the classification scheme can be taken into account and automated, and general metric adaptation takes place during training In comparison to the weighted Euclidean metric used in RLVQ and its variations, a full matrix is more powerful to represent the internal structure of the data appropriately Large margin generalization bounds can be transferred to this case, leading to bounds that are independent of the input dimensionality This also holds for local metrics attached to each prototype, which corresponds to piecewise quadratic decision boundaries The algorithm is tested in comparison to alternative learning vector quantization schemes using an artificial data set, a benchmark multiclass problem from the VCI repository, and a problem from bioinformatics, the recognition of splice sites for C elegans
344 citations
TL;DR: In this article, a general approximation approach on l 0 norm, a typical metric of system sparsity, is proposed and integrated into the cost function of the LMS algorithm, which is equivalent to add a zero attractor in the iterations, by which the convergence rate of small coefficients, that dominate the sparse system, can be effectively improved.
Abstract: In order to improve the performance of least mean square (LMS) based system identification of sparse systems, a new adaptive algorithm is proposed which utilizes the sparsity property of such systems. A general approximating approach on l 0 norm-a typical metric of system sparsity, is proposed and integrated into the cost function of the LMS algorithm. This integration is equivalent to add a zero attractor in the iterations, by which the convergence rate of small coefficients, that dominate the sparse system, can be effectively improved. Moreover, using partial updating method, the computational complexity is reduced. The simulations demonstrate that the proposed algorithm can effectively improve the performance of LMS-based identification algorithms on sparse system.
343 citations
TL;DR: In this article, the authors highlight the practical viability of a new and novel hybrid control technique applied to a vehicle active suspension system of a quarter car model using skyhook and adaptive neuro active force control (SANAFC).
TL;DR: In this paper, the problem of fast active fault-tolerant control using adaptive fault diagnosis observer (AFDO) is studied using a fast adaptive fault estimation (FAFE) algorithm.
Abstract: The problem of fast active fault-tolerant control is studied using adaptive fault diagnosis observer (AFDO). Existence conditions for linear time-invariant system are first introduced to verify whether or not the adaptive observer for fault diagnosis exists. Then a novel fast adaptive fault estimation (FAFE) algorithm is proposed to enhance the performance of fault estimation. Using the on-line obtained fault information, the observer-based fault tolerant controller based on the separation property is designed to compensate for the loss of actuator effectiveness by stabilising the closed-loop system. Furthermore, an extension to a class of nonlinear systems is extensively investigated. Finally, simulation results are presented to illustrate the efficiency of the proposed techniques.
TL;DR: An adaptive regret based learning procedure is applied which tracks the set of correlated equilibria of the game, treated as a distributed stochastic approximation, which is shown to perform very well compared with other similar adaptive algorithms.
Abstract: We consider dynamic spectrum access among cognitive radios from an adaptive, game theoretic learning perspective. Spectrum-agile cognitive radios compete for channels temporarily vacated by licensed primary users in order to satisfy their own demands while minimizing interference. For both slowly varying primary user activity and slowly varying statistics of "fast" primary user activity, we apply an adaptive regret based learning procedure which tracks the set of correlated equilibria of the game, treated as a distributed stochastic approximation. This procedure is shown to perform very well compared with other similar adaptive algorithms. We also estimate channel contention for a simple CSMA channel sharing scheme.
TL;DR: Two adaptive algorithms to update the decomposition of a PARAFAC decomposition at instant t+1 are proposed, the new tensor being obtained from the old one after appending a new slice in the 'time' dimension.
Abstract: The PARAFAC decomposition of a higher-order tensor is a powerful multilinear algebra tool that becomes more and more popular in a number of disciplines. Existing PARAFAC algorithms are computationally demanding and operate in batch mode - both serious drawbacks for on-line applications. When the data are serially acquired, or the underlying model changes with time, adaptive PARAFAC algorithms that can track the sought decomposition at low complexity would be highly desirable. This is a challenging task that has not been addressed in the literature, and the topic of this paper. Given an estimate of the PARAFAC decomposition of a tensor at instant t, we propose two adaptive algorithms to update the decomposition at instant t+1, the new tensor being obtained from the old one after appending a new slice in the 'time' dimension. The proposed algorithms can yield estimation performance that is very close to that obtained via repeated application of state-of-art batch algorithms, at orders of magnitude lower complexity. The effectiveness of the proposed algorithms is illustrated using a MIMO radar application (tracking of directions of arrival and directions of departure) as an example.
TL;DR: This paper proposes an adaptive mode switching algorithm combined with rate selection to maintain a user's target throughput while achieving energy efficiency and shows that there exists a crossover point on the transmission rate below which SIMO consumes less power than MIMO when circuit power is included.
Abstract: In this paper, we propose a mechanism to switch between multiple-input multiple-output (MIMO) with two transmit antennas and single-input multiple-output (SIMO) to conserve mobile terminals' energy. We focus on saving uplink RF transmission energy of mobile terminals in cellular systems supporting best effort traffic. The key idea is to judiciously slow down transmission rates when a base station is underutilized. We show that there exists a crossover point on the transmission rate below which SIMO consumes less power than MIMO when circuit power is included. The crossover point is an increasing function of the circuit power, the number of receive antennas and channel correlation, all of which increase the potential energy savings resulting from mode switching. We propose an adaptive mode switching algorithm combined with rate selection to maintain a user's target throughput while achieving energy efficiency. Extensive flow-level simulations under dynamic loads confirm that the proposed technique can reduce the transmission energy by more than 50% and enables an effective tradeoff between file transfer delay and energy conservation.
TL;DR: This paper draws attention to the deficient performance of standard adaptation when the target distribution is multimodal and proposes a parallel chain adaptation strategy that incorporates multiple Markov chains which are run in parallel.
Abstract: Starting with the seminal paper of Haario, Saksman and Tamminen (Haario et al. (2001)), a substantial amount of work has been done to validate adaptive Markov chain Monte Carlo algorithms. In this paper we focus on two practical aspects of adaptive Metropolis samplers. First, we draw attention to the deficient performance of standard adaptation when the target distribution is multi-modal. We propose a parallel chain adaptation strategy that incorporates multiple Markov chains which are run in parallel. Second, we note that
TL;DR: Numerical results for the inviscid compressible flow over an idealized four-element airfoil geometry demonstrate that both pure h-refinement and pure p-enrichment algorithms achieve equivalent error reductions at each adaptation cycle compared to a uniform refinement approach, but requiring fewer degrees of freedom.
18 Dec 2009
TL;DR: An adaptive algorithm is proposed, based on the recently developed theory of adaptive compressive sensing, to collect information from WSNs in an energy efficient manner and to perform “projections” iteratively to maximise the amount of information gain per energy expenditure.
Abstract: We consider the problem of using Wireless Sensor Networks (WSNs) to measure the temporal-spatial field of some scalar physical quantities. Our goal is to obtain a sufficiently accurate approximation of the temporal-spatial field with as little energy as possible. We propose an adaptive algorithm, based on the recently developed theory of adaptive compressive sensing, to collect information from WSNs in an energy efficient manner. The key idea of the algorithm is to perform “projections” iteratively to maximise the amount of information gain per energy expenditure. We prove that this maximisation problem is NP-hard and propose a number of heuristics to solve this problem. We evaluate the performance of our proposed algorithms using data from both simulation and an outdoor WSN testbed. The results show that our proposed algorithms are able to give a more accurate approximation of the temporal-spatial field for a given energy expenditure.
TL;DR: A new adaptive neurocontrol algorithm for a single-input-single-output (SISO) strict-feedback nonlinear system is proposed, which demonstrates that the state- Feedback control of the strict- feedback system can be viewed as the output-feed back control problem of the system in the normal form.
Abstract: In this brief, a new adaptive neurocontrol algorithm for a single-input-single-output (SISO) strict-feedback nonlinear system is proposed. Most of the previous adaptive neural control algorithms for strict-feedback nonlinear systems were based on the backstepping scheme, which makes the control law and stability analysis very complicated. The main contribution of the proposed method is that it demonstrates that the state-feedback control of the strict-feedback system can be viewed as the output-feedback control problem of the system in the normal form. As a result, the proposed control algorithm is considerably simpler than the previous ones based on backstepping. Depending heavily on the universal approximation property of the neural network (NN), only one NN is employed to approximate the lumped uncertain system nonlinearity. The Lyapunov stability of the NN weights and filtered tracking error is guaranteed in the semiglobal sense.
TL;DR: This paper considers the impact of having a slowly time-varying domain over which the minimization takes place, and provides a general set of sufficient conditions for the convergence and correctness of the adaptive algorithm.
Abstract: The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application in many areas such as signal processing, information theory, control, and finance. A general set of sufficient conditions for the convergence and correctness of the algorithm are known when the underlying problem parameters are fixed. In many practical situations, however, the underlying problem parameters are changing over time, and the use of an adaptive algorithm is more appropriate. In this paper, we study such an adaptive version of the alternating minimization algorithm. More precisely, we consider the impact of having a slowly time-varying domain over which the minimization takes place. As a main result of this paper, we provide a general set of sufficient conditions for the convergence and correctness of the adaptive algorithm. Perhaps somewhat surprisingly, these conditions seem to be the minimal ones one would expect in such an adaptive setting. We present applications of our results to adaptive decomposition of mixtures, adaptive log-optimal portfolio selection, and adaptive filter design.
TL;DR: In this article, a modified version of the SM normalized least mean square (SM-NLMS), the affine projection (SMAP), and the bounding ellipsoidal adaptive constrained (BEACON) recursive least-square technique are proposed.
Abstract: This paper presents set-membership (SM) adaptive algorithms based on time-varying error bounds for code-division multiple-access (CDMA) interference suppression. We introduce a modified family of SM adaptive algorithms for parameter estimation with time-varying error bounds. The considered algorithms include modified versions of the SM normalized least mean square (SM-NLMS), the affine projection (SM-AP), and the bounding ellipsoidal adaptive constrained (BEACON) recursive least-square technique. The important issue of error-bound specification is addressed in a new framework that takes into account parameter estimation dependency, multiaccess, and intersymbol interference (ISI) for direct-sequence CDMA (DS-CDMA) communications. An algorithm for tracking and estimating the interference power is proposed and analyzed. This algorithm is then incorporated into the proposed time-varying error bound mechanisms. Computer simulations show that the proposed algorithms are capable of outperforming previously reported techniques with a significantly lower number of parameter updates and a reduced risk of overbounding or underbounding.
17 Nov 2009
TL;DR: The results show that affect recognition from EEG signals might be possible and an adaptive algorithm improves the performance of the classification task.
Abstract: Research on affective computing is growing rapidly and new applications are being developed more frequently. They use information about the affective/mental states of users to adapt their interfaces or add new functionalities. Face activity, voice, text physiology and other information about the user are used as input to affect recognition modules, which are built as classification algorithms. Brain EEG signals have rarely been used to build such classifiers due to the lack of a clear theoretical framework. We present here an evaluation of three different classification techniques and their adaptive variations of a 10-class emotion recognition experiment. Our results show that affect recognition from EEG signals might be possible and an adaptive algorithm improves the performance of the classification task.
TL;DR: An algorithm that takes advantage of the information from the ongoing wireless communication links to calculate the estimated position of sensor nodes to incorporate the practical multiple transmit-power information into the process of particle filtering.
Abstract: Power scheduling and localization play important roles in network topology management. Distributed power scheduling is an efficient way to construct a reliable and energy-efficient network topology. Localization provides geographical information for topology management. However, during the course of transmission power control, localization based on the received signal strength (RSS) is a challenging problem because of the inconsistent RSS indication (RSSI) measurements in wireless sensor networks. This paper presents an algorithm that takes advantage of the information from the ongoing wireless communication links to calculate the estimated position of sensor nodes. Considering the existing transmit-power-aware medium access control (MAC) protocols, we propose a localization algorithm based on particle filtering for sensor networks assisted by multiple transmit-power information. Therefore, the primary contribution of this paper is the elegant strategy on how to incorporate the practical multiple transmit-power information into the process of particle filtering. Furthermore, a general message-passing framework of the transmit-power-aware MAC is seamlessly integrated with the tracking service. The proposed particle-filtering-based localization algorithm uses the RSS information from the beacons or the neighboring nodes to infer the position of the concerned node without the requirement of any additional hardware instruments. Theoretical analysis and simulation results are presented to demonstrate the performance of the proposed localization method. The simulation results show that the proposed algorithm outperforms the existing algorithms that do not utilize multiple power information.
TL;DR: In this article, the notion of a posteriori estimation and control of modeling error is extended to large-scale problems in molecular statics, where a molecular model is used to simulate the deformation of polymeric materials used in the fabrication of semiconductor devices.
TL;DR: A new learning/adaptive algorithm that can provide with convergent, an efficient and safe fine-tuning of general LNCS is introduced and it significantly outperforms the algorithms proposed by Kosmatopoulos as well as other existing adaptive optimization algorithms.
Abstract: Despite the continuous advances in the fields of intelligent control and computing, the design and deployment of efficient large scale nonlinear control systems (LNCSs) requires a tedious fine-tuning of the LNCS parameters before and during the actual system operation. In the majority of LNCSs the fine-tuning process is performed by experienced personnel based on field observations via experimentation with different combinations of controller parameters, without the use of a systematic approach. The existing adaptive/neural/fuzzy control methodologies cannot be used towards the development of a systematic, automated fine-tuning procedure for general LNCS due to the strict assumptions they impose on the controlled system dynamics; on the other hand, adaptive optimization methodologies fail to guarantee an efficient and safe performance during the fine-tuning process, mainly due to the fact that these methodologies involve the use of random perturbations. In this paper, we introduce and analyze, both by means of mathematical arguments and simulation experiments, a new learning/adaptive algorithm that can provide with convergent, an efficient and safe fine-tuning of general LNCS. The proposed algorithm consists of a combination of two different algorithms proposed by Kosmatopoulos (2007 and 2008) and the incremental-extreme learning machine neural networks (I-ELM-NNs). Among the nice properties of the proposed algorithm is that it significantly outperforms the algorithms proposed by Kosmatopoulos as well as other existing adaptive optimization algorithms. Moreover, contrary to the algorithms proposed by Kosmatopoulos , the proposed algorithm can operate efficiently in the case where the exogenous system inputs (e.g., disturbances, commands, demand, etc.) are unbounded signals.
TL;DR: An innovative multi-resolution approach for the real-time DOA estimation of multiple signals impinging on a planar array based on a support vector classifier and it exploits a multi-scaling procedure to enhance the angular resolution of the detection process in the regions of incidence of the incoming waves.
Abstract: The knowledge of the directions of arrival (DOAs) of the signals impinging on an antenna receiver enables the use of adaptive control algorithm suitable for limiting the effects of interferences and increasing the gain towards the desired signals in order to improve the performances of wireless communication systems. In this paper, an innovative multi-resolution approach for the real-time DOA estimation of multiple signals impinging on a planar array is presented. The method is based on a support vector classifier and it exploits a multi-scaling procedure to enhance the angular resolution of the detection process in the regions of incidence of the incoming waves. The data acquired from the array sensors are iteratively processed with a support vector machine (SVM) customized to the problem at hand. The final result is the definition of a map of the probability that a signal impinges on the antenna from a fixed angular direction. Selected numerical results, concerned with both single and multiple signals, are provided to assess potentialities and current limitations of the proposed approach.
TL;DR: In this paper optimal control problems governed by elliptic semilinear equations and subject to pointwise state constraints are considered and a posteriori error estimates are derived assessing the error with respect to the cost functional.
Abstract: In this paper optimal control problems governed by elliptic semilinear equations and subject to pointwise state constraints are considered. These problems are discretized using finite element methods and a posteriori error estimates are derived assessing the error with respect to the cost functional. These estimates are used to obtain quantitative information on the discretization error as well as for guiding an adaptive algorithm for local mesh refinement. Numerical examples illustrate the behavior of the method.
TL;DR: Application to a HDD system shows that the proposed adaptive disturbance rejection scheme exhibits good capability of disturbance rejection, and comparing with the traditional disturbance observer method, the new method incurs much less drop in phase margin.
Abstract: In this paper, a new adaptive disturbance rejection scheme is introduced. In the proposed scheme, adaptive frequency estimation technique is incorporated into the traditional disturbance observer method. The frequency of the dominant disturbance is estimated online by a fast stable adaptive algorithm, and the estimated frequency is used to adaptively tune the bandwidth of the disturbance observer. Application to a HDD system shows that the proposed method exhibits good capability of disturbance rejection. Comparing with the traditional disturbance observer method, the new method incurs much less drop in phase margin.
TL;DR: A sequential implicit multiscale finite-volume framework for coupled flow and transport with general prolongation and restriction operations for both pressure and saturation, in which three adaptive prolongation operators for the saturation are used.
TL;DR: This paper presents a general adaptive SA algorithm that is based on a simple method for estimating the Jacobian matrix while concurrently estimating the primary parameters of interest, and introduces two enhancements that generally improve the quality of the estimates for underlying Jacobian (Hessian) matrices.
Abstract: It is known that a stochastic approximation (SA) analogue of the deterministic Newton-Raphson algorithm provides an asymptotically optimal or near-optimal form of stochastic search. However, directly determining the required Jacobian matrix (or Hessian matrix for optimization) has often been difficult or impossible in practice. This paper presents a general adaptive SA algorithm that is based on a simple method for estimating the Jacobian matrix while concurrently estimating the primary parameters of interest. Relative to prior methods for adaptively estimating the Jacobian matrix, the paper introduces two enhancements that generally improve the quality of the estimates for underlying Jacobian (Hessian) matrices, thereby improving the quality of the estimates for the primary parameters of interest. The first enhancement rests on a feedback process that uses previous Jacobian estimates to reduce the error in the current estimate. The second enhancement is based on an optimal weighting of per-iteration Jacobian estimates. From the use of simultaneous perturbations, the algorithm requires only a small number of loss function or gradient measurements per iteration - independent of the problem dimension - to adaptively estimate the Jacobian matrix and parameters of primary interest.