An optimal regularization method for space-fractional backward diffusion problem

In this paper, a space-fractional backward diffusion problem (SFBDP) in a strip is considered. By the Fourier transform, we proposed an optimal modified method to solve this problem in the presence of noisy data. The convergence estimates for the approximate solutions with the regularization parameter selected by an a priori and an a posteriori strategy are provided, respectively. Numerical experiments show that the proposed methods are effective and stable.     

Regularized kernel-based BRDF model inversion method for ill-posed land surface parameter retrieval

In this paper, we consider the direct solution of the kernel-based bidirectional reflectance distribution function (BRDF) models for the retrieval of land surface albedos. This is an ill-posed problem due to nonuniqueness of the solution and the instability induced by error/noise and small singular values of the linearized system or the linear BRDF model. A robust inversion algorithm is critical for the BRDF/albedo retrieval from the limited number of satellite observations. We propose a promising algorithm for resolving this kind of ill-posed problem encountered in BRDF model inversion using remote sensing data.New techniques for robust estimation of BRDF model parameters are needed to cope with the scarcity of the number of observations. We are reminded by Cornelius Lanczos' dictum: “Lack of information cannot be remedied by mathematical trickery.” Thus identifying a priori information or appropriate constraints, and the embedding of the information or constraints into the regularization algorithm, are pivotal elements of a retrieval algorithm. We develop a regularization method, which is called the numerically truncated singular value decomposition (NTSVD). The method is based on the spectrum of the linear driven kernel, and the a priori information/constraint is based on the minimization of the l₂ norm of the parameters vector. The regularization algorithm is tested using field data as well as satellite data. Numerical experiments with a subset of measurements for each site demonstrate the robustness of the algorithm.     

Output synchronization for heterogeneous networks of non-introspective agents

In this paper we consider the output synchronization problem for heterogeneous networks of linear agents. The network’s communication infrastructure provides each agent with a linear combination of its own output relative to that of neighboring agents, and it allows the agents to exchange information about their own internal observer estimates. We design decentralized controllers based on setting the control input of a single root agent to zero and letting the remaining agents synchronize to the root agent. A distinguishing feature of our work is that the agents are assumed to be non-introspective, meaning that they possess no knowledge about their own state or output separate from what is received via the network. We also consider the problem of regulating the agreement trajectory according to an a priori specified reference model. In this case we assume that some of the agents have access to their own output relative to the reference trajectory.     

Estimation of Edge Parameters and Image Blur Using Polynomial Transforms

A method is presented for detecting blurred edges in images and for estimating the following edge parameters: position, orientation, amplitude, mean value, and edge slope. The method is based on a local image decomposition technique called a polynomial transform. The information that is made explicit by the polynomial transform is well suited to detect image features, such as edges, and to estimate feature parameters. By using the relationship between the polynomial coefficients of a blurred feature and those of the a priori assumed (unblurred) feature in the scene, the parameters of the blurred feature can be estimated. The performance of the proposed edge parameter estimation method in the presence of image noise has been analyzed. An algorithm is presented for estimating the spread of a position-invariant Gaussian blurring kernel, using estimates at different edge locations over the image. First a single-scale algorithm is developed in which one polynomial transform is used. A critical parameter of the single-scale algorithm is the window size, which has to be chosen a priori. Since the reliability of the estimate for the spread of the blurring kernel depends on the ratio of this spread to the window size, it is difficult to choose a window of appropriate size a priori. The problem is overcome by a multiscale blur estimation algorithm where several polynomial transforms at different scales are applied, and the appropriate scale for analysis is chosen a posteriori. By applying the blur estimation algorithm to natural and synthetic images with different amounts of blur and noise, it is shown that the algorithm gives reliable estimates for the spread of the blurring kernel even at low signal-to-noise ratios.     

On robustness to noise of least squares based adaptive control

Current engineering practice for adaptive control schemes is to base the design on globally convergent schemes for simple plant models. An important class of such schemes uses least squares estimation of assumed simple input-output models and constructs the controller using the parameter estimates. This paper studies the robustness of such schemes to the presence of unmodelled plant coloured noise. Such noise is sometimes an adequate model for unmodelled plant dynamics.The theory of the paper makes a connection between the least squares parameter error equations and those associated with extended least squares using a posteriori noise estimates for which there are known global convergence results. For the case of adaptive minimum variance control of minimum phase plants, this connection permits stronger convergence results than those hitherto derived from the theory of extended least squares based on a priori noise estimates.     

A nonparametric approach to design robust controllers for uncertain systems: Application to an air flow heating system

This paper presents an approach to design robust fixed structure controllers for uncertain systems using a finite set of measurements in the frequency domain. In traditional control system design, usually, based on measurements, a model of the plant, which is only an approximation of the physical system, is first built, and then control approaches are used to design a controller based on the identified model. Errors associated with the identification process as well as the inevitable uncertainties associated with plant parameter variations, external disturbances, measurement noise, etc. are expected to all contribute to the degradation of the performance of such a scheme. In this paper, we propose a nonparametric method that uses frequency-domain data to directly design a robust controller, for a class of uncertainties, without the need for model identification. The proposed technique, which is based on interval analysis, allows us to take into account the plant uncertainties during the controller synthesis itself. The technique relies on computing the controller parameters for which the set of all possible frequency responses of the closed-loop system are included in the envelope of a desired frequency response. Such an inclusion problem can be solved using interval techniques. The main advantages of the proposed approach are: (1) the control design does not require any mathematical model, (2) the controller is robust with respect to plant uncertainties, and (3) the controller structure can be chosen a priori, which allows us to select low-order controllers. To illustrate the proposed method and demonstrate its efficacy, an application to an air flow heating system is presented.     

Unknown input modeling and robust fault diagnosis using black box observers

A key issue that needs to be addressed while performing fault diagnosis using black box models is that of robustness against abrupt changes in unknown inputs. A fundamental difficulty with the robust FDI design approaches available in the literature is that they require some a priori knowledge of the model for unmeasured disturbances or modeling uncertainty. In this work, we propose a novel approach for modeling abrupt changes in unmeasured disturbances when innovation form of state space model (i.e. black box observer) is used for fault diagnosis. A disturbance coupling matrix is developed using singular value decomposition of the extended observability matrix and further used to formulate a robust fault diagnosis scheme based on generalized likelihood ratio test. The proposed modeling approach does not require any a priori knowledge of how these faults affect the system dynamics. To isolate sensor and actuator biases from step jumps in unmeasured disturbances, a statistically rigorous method is developed for distinguishing between faults modeled using different number of parameters. Simulation studies on a heavy oil fractionator example show that the proposed FDI methodology based on identified models can be used to effectively distinguish between sensor biases, actuator biases and other soft faults caused by changes in unmeasured disturbance variables. The fault tolerant control scheme, which makes use of the proposed robust FDI methodology, gives significantly better control performance than conventional controllers when soft faults occur. The experimental evaluation of the proposed FDI methodology on a laboratory scale stirred tank temperature control set-up corroborates these conclusions.     

Robust estimation of free-radical homopolymer reactors

In this work is presented a practical (i.e. nonlocal) robust estimation design to infer the main safety, production, and quality variables of batch, semibatch, or continuous free-radical homopolymer reactors with on-line measurements of free monomer, temperature, and volume. The solvability of the problem is established a priori, and the design features a robust nonlocal uniform convergence criterion coupled with a systematic construction-tuning procedure. The nonlocal stability framework exhibits the performance-robustness tradeoff, as well as the relationship between the sizes of the estimate error, initial state, exogenous input, and model parameter errors. The tuning of gains of the estimator can be executed with conventional filtering techniques for linear single-output filters. The polymerization of methyl methacrylate with AIBN initiator is considered as an application example, and the robust nonlocal functioning of the estimator is corroborated with numerical simulations.     

An improved method for independent component analysis with reference

Through incorporating a priori information available in some applications for independent component analysis (ICA) as the reference into the negentropy contrast function for FastICA, ICA with reference (ICA-R) or constrained ICA (cICA) is obtained as a constrained optimization problem. ICA-R achieves some advantages over earlier methods, whereas its computation load is somewhat high and its performance is strongly dependent on the threshold parameter. By alternately optimizing the negentropy contrast function for FastICA and the closeness measure for ICA-R, an improved method for ICA-R is proposed in this paper which can avoid the inherent drawbacks of ICA-R. The validity of the proposed method is demonstrated by simulation experiments.     

A one-shot domain-independent robust multimedia clustering methodology based on hybrid multimodal fusion

The existence of multiple modalities poses a challenge to the design of multimedia data clustering systems, as the unsupervised nature of the problem makes it very difficult to determine a priori whether a single modality should dominate the clustering process, or if modalities should be combined somehow. In order to fight against these indeterminacies—which come on top of those referring to the selection of the optimal clustering algorithm and data representation for the problem at hand–, this work introduces robust multimedia clustering, a one-shot methodology for domain independent multimedia data clustering based on hybrid multimodal fusion. By means of experimentation, we firstly justify the motivation of the proposed methodology by proving the relevance of multimedia clustering indeterminacies. Subsequently, a specific multimedia clustering system based on the requirements of the methodology is implemented and evaluated on three multimedia clustering applications—music genres, photographic topics and audio-visual objects classification—as a proof of concept, analyzing the quality of the obtained partitions and the time complexity of the proposal. The experimental results reveal that the implemented system, which includes a self-refining consensus clustering procedure for attaining high levels of robustness, allows to obtain, in a fully unsupervised manner, better quality partitions than 93 % of the clusterers available in our experiments, being even able to improve the quality of the best ones and outperforming state-of-the-art alternatives.     

A robust adaptive fuzzy variable structure tracking control for the wheeled mobile robot: Simulation and experimental results

In this paper an adaptive fuzzy variable structure control (kinematic control) integrated with a proportional plus derivative control (dynamic control) is proposed as a robust solution to the trajectory tracking control problem for a differential wheeled mobile robot. The variable structure controller, based on the sliding mode theory, is a well known, proven control method, fit to deal with uncertainties and disturbances (e.g., structural and parameter uncertainties, external disturbances and operating limitations). To minimize the problems found in practical implementations of the classical variable structure controllers, an adaptive fuzzy logic controller replaces the discontinuous portion of the control signals (avoiding the chattering), causing the loss of invariance, but still ensuring the robustness to uncertainties and disturbances without having any a priori knowledge of their boundaries. Moreover, the adaptive fuzzy logic controller is a feasible tool to approximate any real continuous nonlinear system to arbitrary accuracy, and has a simple structure by using triangular membership functions, a low number of rules that must be evaluated, resulting in a lower computational load for execution, making it feasible for real time implementation. Stability analysis and the convergence of tracking errors as well as the adaptation laws are guaranteed with basis on the Lyapunov theory. Simulation and experimental results are explored to show the verification and validation of the proposed control strategy.     

Decentralized adaptive stabilization for interconnected systems with dynamic input-output and nonlinear interactions

This paper considers the problem of robust decentralized adaptive output feedback stabilization for a class of interconnected systems with dynamic input and output interactions and nonlinear interactions by using MT-filters and the backstepping design method. It is shown that the closed-loop decentralized system based on MT-filters is globally uniformly bounded, all the signals except for the parameter estimates can be regulated to zero asymptotically, and the L₂ and L_∞ norms of the system outputs are also be bounded by functions of design parameters. The scheme is demonstrated by a simulation example.     

LMI APPROACH TO ROBUST FILTERING FOR DISCRETE TIME‐DELAY SYSTEMS WITH NONLINEAR DISTURBANCES

This paper investigates the problem of robust filtering for a class of uncertain nonlinear discrete‐time systems with multiple state delays. It is assumed that the parameter uncertainties appearing in all the system matrices reside in a polytope, and that the nonlinearities entering into both the state and measurement equations satisfy global Lipschitz conditions. Attention is focused on the design of robust full‐order and reduced‐order filters guaranteeing a prescribed noise attenuation level in an H∞ or l₂‐l∞ sense with respect to all energy‐bounded noise disturbances for all admissible uncertainties and time delays. Both delay‐dependent and independent approaches are developed by using linear matrix inequality (LMI) techniques, which are applicable to systems either with or without a priori information on the size of delays.     

A constrained SLAM approach to robust and accurate localisation of autonomous ground vehicles

For driving assistance systems, intelligent vehicles and autonomous robots to be viable in complex environments, it is necessary to have a reliable and robust localisation function. Due to the large variability and uncertainty of such complex environments, which include theme parks, university campuses, suburbs, industrial estates and the like, it is difficult to rely on a specific method or set of sensor data to correctly and robustly estimate the robot path/pose. The key to solving the localisation problem is to optimally use and fuse all useful sources of information available to the mobile platform. For the envisaged environment, it is not unusual to have approximate digital maps of the road network. In this paper, in addition to the typical sensory information provided by extereoceptive and proprioceptive sensors, it is shown how a priori approximate knowledge available in the form of a road map can be systematically fused within a Simultaneous Localisation and Map Building (SLAM) framework to obtain more accurate and robust localisation results. This reformulation of SLAM through the introduction of constraints in the form of a priori map information not only makes the problem theoretically more correct in the sense of observability but also makes the system viable and effective, yielding more accurate results. The results obtained in an actual environment are presented to validate the claims.     

Intelligent Control of Discrete Linear Systems Based on a Supervised Adaptive Multiestimation Scheme

A pole-placement based adaptive controller synthesised from a multiestimation scheme is designed for linear plants. A higher level switching structure between the various estimation schemes is used to supervise the reparameterisation of the adaptive controller in real time. The basic usefulness of the proposed scheme is to improve the transient response so that the closed-loop stability is guaranteed. The switching process is subject to a minimum dwelling or residence time within which the supervisor is not allowed to switch between the multiple estimation schemes. The high level supervision is based on the multiestimation identification scheme. The residence time condition guarantees the closed-loop stability. The above higher level switching structure is on-line supervised by a closed-loop tracking error based algorithm. This second supervision on-line tunes the free design parameters which appear as time varying weights in the loss function of the above switching structure. Thus, the closed-loop behaviour, compared to the constant parameter case one, is improved when the design parameter is not tightly initialised. Both supervisors are hierarchically organised in the sense that they act on the system at different rates. Furthermore, a projection algorithm has been considered in the estimation scheme in order to include a possible a priori knowledge of the estimates parameter vector value in the estimation algorithm.     

Fault estimator design for a class of switched systems with time-varying delay

This article studies the problem of fault estimator design for switched time-delay systems with impulsive control. The delay signal is assumed to be uniformly bounded, differentiable and has a bounded derivative. The problem is first formulated in the framework of H _∞ filtering by incorporating a priori knowledge of the fault into the design procedure. A hybrid controller, composed of a fault estimator and an impulsive controller, is constructed. Some delay-dependent sufficient conditions are derived on the existence of the hybrid controller by using the multiple Lyapunov functional approach. In addition, based on the cone complementarity algorithm, the solutions to the parameter matrices are obtained by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.     

Pole assignment for distributed systems by finite-dimensional control

The question of pole assignment for a class of distributed systems by means of finite dimensional control is considered. A finite dimensional compensator is usually designed based on a reduced order model, and it is not a priori known what effect this will have on the original infinite dimensional system. Explicit formulas are derived which enable one to calculate the eigenvalues of the resulting closed loop system. For a certain compensator design, estimates are derived which can be used to guarantee stability a priori. Numerical results are also presented.     

Some nonstandard error analysis of discontinuous Galerkin methods for elliptic problems

An a priori error analysis of discontinuous Galerkin methods for a general elliptic problem is derived under a mild elliptic regularity assumption on the solution. This is accomplished by using some techniques from a posteriori error analysis. The model problem is assumed to satisfy a Gårding type inequality. Optimal order L ₂ norm a priori error estimates are derived for an adjoint consistent interior penalty method.     

Makespan minimization on single batch-processing machine via ant colony optimization

This paper investigates the problem of minimizing makespan on a single batch-processing machine, and the machine can process multiple jobs simultaneously. Each job is characterized by release time, processing time, and job size. We established a mixed integer programming model and proposed a valid lower bound for this problem. By introducing a definition of waste and idle space (WIS), this problem is proven to be equivalent to minimizing the WIS for the schedule. Since the problem is NP-hard, we proposed a heuristic and an ant colony optimization (ACO) algorithm based on the theorems presented. A candidate list strategy and a new method to construct heuristic information were introduced for the ACO approach to achieve a satisfactory solution in a reasonable computational time. Through extensive computational experiments, appropriate ACO parameter values were chosen and the effectiveness of the proposed algorithms was evaluated by solution quality and run time. The results showed that the ACO algorithm combined with the candidate list was more robust and consistently outperformed genetic algorithm (GA), CPLEX, and the other two heuristics, especially for large job instances.     

Adaptive visual tracking using the prioritized Q-learning algorithm: MDP-based parameter learning approach

This paper introduces an adaptive visual tracking method that combines the adaptive appearance model and the optimization capability of the Markov decision process. Most tracking algorithms are limited due to variations in object appearance from changes in illumination, viewing angle, object scale, and object shape. This paper is motivated by the fact that tracking performance degradation is caused not only by changes in object appearance but also by the inflexible controls of tracker parameters. To the best of our knowledge, optimization of tracker parameters has not been thoroughly investigated, even though it critically influences tracking performance. The challenge is to equip an adaptive tracking algorithm with an optimization capability for a more flexible and robust appearance model. In this paper, the Markov decision process, which has been applied successfully in many dynamic systems, is employed to optimize an adaptive appearance model-based tracking algorithm. The adaptive visual tracking is formulated as a Markov decision process based dynamic parameter optimization problem with uncertain and incomplete information. The high computation requirements of the Markov decision process formulation are solved by the proposed prioritized Q-learning approach. We carried out extensive experiments using realistic video sets, and achieved very encouraging and competitive results.