We propose a semantic-aware neural reconstruction method to generate 3D high-fidelity models from sparse images. To tackle the challenge of severe radiance ambiguity caused by mismatched features in sparse input, we enrich neural implicit representations by adding patch-based semantic logits that are optimized together with the signed distance field and the radiance field. A novel regularization based on the geometric primitive masks is introduced to mitigate shape ambiguity. The performance of our approach has been verified in experimental evaluation. The average chamfer distances of our reconstruction on the DTU dataset can be reduced by 44% for SparseNeuS and 20% for VolRecon. When working as a plugin for those dense reconstruction baselines such as NeuS and Neuralangelo, the average error on the DTU dataset can be reduced by 69% and 68% respectively.

This paper introduces a novel curve-based slicing method for generating planar layers with dynamically varying orientations in digital light processing (DLP) 3D printing. Our approach effectively addresses key challenges in DLP printing, such as regions with large overhangs and staircase artifacts, while preserving its intrinsic advantages of high resolution and fast printing speeds. We formulate the slicing problem as an optimization task, in which parametric curves are computed to define both the slicing layers and the model partitioning through their tangent planes. These curves inherently define motion trajectories for the build platform and can be optimized to meet critical manufacturing objectives, including collision-free motion and floating-free deposition. We validate our method through physical experiments on a robotic multi-axis DLP printing setup, demonstrating that the optimized curves can robustly guide smooth, high-quality fabrication of complex geometries.

We introduce a general, scalable computational framework for multi-axis 3D printing based on implicit neural fields (INFs) that unifies all stages of tool-path generation and global collision-free motion planning. In our pipeline, input models are represented as signed distance fields, with fabrication objectives—such as support-free printing, surface finish quality, and extrusion control—directly encoded in the optimization of an implicit guidance field. This unified approach enables toolpath optimization across both surface and interior domains, allowing shell and infill paths to be generated via implicit field interpolation. The printing sequence and multi-axis motion are then jointly optimized over a continuous quaternion field. Our continuous formulation constructs the evolving printing object as a time-varying SDF, supporting differentiable global collision handling throughout INF-based motion planning. Compared to explicit-representation-based methods, INF-3DP achieves up to two orders of magnitude speedup and significantly reduces waypoint-to-surface error. We validate our framework on diverse, complex models and demonstrate its efficiency with physical fabrication experiments using a robot-assisted multi-axis system.

This paper presents the design of a sliding mode controller for networked control systems subject to successive Markovian packet dropouts. This paper adopts the Gilbert-Elliott channel model to describe the temporal correlation among packet losses, and proposes an update scheme to select the assumed available states for use in a sliding mode control law. A technique used in the theory of discrete-time Markov jump linear systems is applied to tackle the effect of the packet losses. This involves introducing a couple of Lyapunov functions dependent on the indicator functions of the instantaneous packet loss, and proving that the sliding mode controller is able to drive the system state trajectories into the neighborhood of the designed integral sliding surface in mean-square sense given that the corresponding Lyapunov inequalities are satisfied. The system is guaranteed thereafter to remain inside the neighborhood of the sliding surface. Simulated case studies are presented to illustrate the effectiveness of the control law.

The aim of this paper is to propose a method that generates the minimum number of linear time-invariant systems (LTIs) used in an affine set to determine any parameter-dependent nonlinear system. The implication is to reduce the order of LTIs containing core tensor, as it can be quite large in the case of a big number of parameters, as previously every parameter was added to the parameter-space in a new dimension. Therefore, this work introduces a joint higher order singular value decomposition (HOSVD) and canonical polyadic decomposition (CPD) to derive LTIs and a joint minimum volume simplex analysis (MVSA) CPD decomposition to obtain the convex polytopic model. The results are demonstrated in the example of three degrees of freedom aeroelastic wing section.

The paper discusses how the Tensor Product structure is useful to simplify kinetic models of biological networks and provides basic mathematical tools one can start the kinetic model with. The applied method known as joint HOSVD-CPD decomposition is helpful to identify latent parameters, this work is utilizing it to determine the role of different parameters in a biochemical reaction. A case study is presented demonstrating the results on peroxiredoxin I / thioredoxin / thioredoxin reductase system, as peroxiredoxins might have an important role in cancer modulation. After the transformation, it is clearly shown, which equation is taking part in the reaction, and what are the parameters the network depends on.

Recommender system has been widely used in e-commerce systems nowadays. Current methodologies focus on predicting users' preferences from their previous ratings. Although the prediction is largely helpful, it gives limited insight to managers of e-commerce systems on how to utilize the interactions between users and items for designing new business and marketing strategies. Besides, big data collected by e-commerce systems raise another challenge in recommendation - how to incorporate large amount of additional information such as the contexts where the rating or buying event takes place. In this paper, we propose a novel method to simultaneously tackle the two challenges above based on the concept of embedding, by deriving a general distance-dependent rating model that characterizes the relationship between user and item with respective to the embedding space. The generalized model allows us to incorporate contextual information into the recommender system for rating prediction and item recommendation. We show that our embedding model is comparable to state-of-the-art context-aware recommendation algorithms in terms of accuracy, while allowing visualization as an analytics tool which gives intuitive insights to the recommendation in an understandable way. In addition, our algorithm also allows efficient recommendation by leveraging the neighborhood structure of the embedding space. We demonstrate the advantages of our method with experiments and results show that context-aware embedding is a promising approach for context-aware recommender systems.

Kronecker product (KP) approximation has recently been applied as a modeling and analysis tool on systems with hierarchical networked structure. In this paper, we propose a tensor product-based approach to the KP approximation problem with arbitrary number of factor matrices. The formulation involves a novel matrix-to-tensor transformation to convert the KP approximation problem to a best rank-(R1, …, RN) tensor product approximation problem. In addition, we develop an algorithm based on higher-order orthogonal iteration to solve the tensor approximation problem. We prove that the proposed approach is equivalent to conventional singular value decomposition-based approach for two matrix factor case proposed by Van Loan. Hence, our work is a generalization of Van Loan's approach to more than two factor matrices. We demonstrate our approach by several experiments and case studies. The results indicate that the tensor product formulation is effective for KP approximation.

Endoscopic submucosal dissection (ESD) is an effective and less invasive treatment for early gastric and colorectal cancers. Nevertheless, performing ESD through a flexible endoscope is technically challenging due to the limited controllability of the endoscopic instruments. Therefore, a surgical robotic system with high dexterity and better ergonomics is much needed. A master-slave dual-arm robot with customizing workspace for ESD is proposed for this study. The design is such that the procedure is completed without the need for changing the instrument. Our robot is mainly driven by tendon-sheath (TS) mechanism. Modeling and use of a controller for elongation compensation of tendon due to friction to increase position control accuracy are presented. Experiment shows that the controller greatly enhances the controllability of the robot. We have demonstrated that the design of the robot arm allows it to lift up to 48 g, which is sufficient for ESD. Six subjects, including three endoscopists and upper gastrointestinal surgeons, were invited to evaluate the system in an ex vivo experiment. Experienced surgeons were able to complete a dissection within 30 min. We have demonstrated a prototype robot that can facilitate the ESD procedure with bimanual tissue dissection. The system is competent to remove a lesion area precisely. Further studies are needed to evaluate the system in vivo.

The main purpose of this paper to demonstrate how to apply basic convex optimization on robot controller design specifically on the example of the inverted Furuta pendulum. The work shows how convex optimization can be implemented and that the Tensor Product-based approach could be easily applied for robot stabilization. The design stages are shown from the quasi Linear Parameter Varying form of the Lagrange-Euler equations through giving a deeper insight into Tensor Product model transformation until the optimal control problem formulation via Linear Matrix Inequalities. The design method is well supported by TPtool and CVX Mat Lab toolboxes that are both convenient to use. Numerical simulations have also been performed to show the power of the computational solution of robot stabilization.

The paper considers a general approach for linear parameter varying (LPV) control. The approach is based on polytopic representation of the LPV system. First, a grid point based control design is applied for a set of linearized models of the LPV system. The design is based on linear time invariant (LTI) techniques. Such control design allows a larger flexibility in the controller structure than the conventional parallel distributed compensation (PDC) based polytopic control. The LPV controller is obtained by linear interpolation between the LTI controllers. The paper proposes linear matrix inequality (LMI) based convex optimization for robustness analysis of the resulting controller. The approach requires the plant and the controller to be defined by a common polytopic structure. It is proposed to obtain this common structure via unified TP model transformation. A simple numerical example shows the efficiency of the proposed control design approach.

Recently, an emerging numerical controller design based on Tensor-Product model transformation has proven to work on a number of nonlinear systems by both simulations and practical implementations. In this paper, aiming at fully utilizing the power of approximation of TP model transformation, a new control stability analysis is proposed in a probabilistic framework. We utilize the matrix 2-norm to characterize the maximum deviation of the approximated system from the actual one. However, the theoretical boundary of the maximum deviation is hard to determine. Therefore, probabilistic error bound estimation is introduced with the aid of Chebyshev inequality to define a practical bound of deviation for the approximated system. This new analysis technique allows practical controller design for approximated TP system model by solving a set of Linear Matrix Inequalities (LMI). Examples using the benchmark Translational Oscillator with Rotational Actuator (TORA) system are presented to illustrate our formulation, showing that the designed controller can guarantee asymptotic stability with sufficiently high probability.

In this paper, we propose a framework for practical large-scale face alignment, based on the recent development of Robust Alignment by Sparse and Low-rank Decomposition for linearly correlated images (RASL). Unfortunately, the original implementation is not applicable in large image dataset. We extend this technique to deal with the situation with millions of images, with the aid of l1-regularized least squares. Our proposal is applied onto the photo-real talking head, a challenging application which requires highly precise alignments of faces from video sequences. We verify the efficacy of our algorithm with experiments using real talking head data. Our method attains comparable quality to RASL in the experiments.

Smooth hinging hyperplane (SHH) has been proposed as an improvement over the well-known hinging hyperplane (HH) by the fact that it retains the useful features of HH while overcoming HH's drawback of nondifferentiability. This paper introduces a formal characterization of smooth hinge function (SHF), which can be used to generate SHH as a neural network. A method for the general construction of SHF is also given. Furthermore, the work proves that SHH is better than HH in functional approximation, i.e., the optimal error of SHH approximating a general function is always smaller or equal to that of HH. Particularly, in the case that the SHF is generated via the integration of a class of sigmoidal functions, it is further proven that the corresponding SHH of the 2m SHFs would outperform a neural network with m of the sigmoidal function from which the SHF is derived. Any upper bound established on the approximation error of a neural network of m sigmoidal activation functions can hence be translated to the SHH of m SHFs by replacing m with [m/2]. The work also includes an algorithm for the identification of SHH making use of its differentiability property. Simulation experiments are presented to validate the theoretical conclusions to possible extent.

In this paper, a novel scheme for electrocardiogram (ECG)denoising is presented based on ECG dynamic model and empirical mode decomposition (EMD). Firstly,we pre-filter the noisy ECG by making the model fit it in the MMSE sense, in order to preserve the important morphological features, especially the QRS complex. After that, the model is subtracted from the noisy ECG, and the residual signal is then decomposed using EMD and denoised by discarding the noise components from the decomposition results. Finally, the resultant ECG is obtained by combining the model and the denoised residue. Experiments conducted on both real and synthetic ECG data have demonstrated that the proposed method is a superior tool for ECG denoising.

This paper describes a method to generate stroke trajectories executed by a 5-DOF robotic art system. A brush footprint model is proposed to represent the footprint outline, which is sensitive to the applied stress. After extracting real brush footprints from experiments, the model parameters are obtained using linear regression. Trajectories are searched along the segmented strokes of Chinese characters by varying the shape of brush footprint. The generated trajectory is 5-DOF, which is compatible to the robot art system. Simulations and experiments were conducted using calligraphy of Bada Shanren, a famous Chinese ancient artist, as an example.

This paper presents a novel brush stroke generation scheme based on Genetic Algorithms (GA) and pre-defined brush template models. The work is part of an endeavor to attempt imitating master works of famous past calligraphers. The concept is to parametrize, in some computational sense, the writing styles and techniques of certain calligraphers and then executes the results in a robot drawing platform developed in our laboratory. The present work describes the algorithmic development, simulation studies and experimentation of the GA-based stroke generation scheme upon given certain calligraphic characters. To further study the effectiveness of calligraphic writing with the robot platform, the Cross-Entropy method of the Traveling Salesman problem is incorporated to determine the sequence of stroke execution.

A robot drawing platform supporting four degrees of freedom (x, y, z and z-rotation) of a brush-pen motion for studying Chinese painting and calligraphy has been operational in our laboratory. This paper describes the real-time capturing and data analysis of the brush footprint using the new hardware and software capabilities in the platform. They include a transparent drawing plate and an underneath camera system, together with projective rectification and video segmentation algorithms. Preliminary result of the footprint analysis and nonparametric modeling, and their applications to well-known Chinese calligraphy are demonstrated

This paper generalizes a previous Cartesian approach for interpolating fuzzy rules comprised of membership functions with finite number of characteristic points. Instead of representing membership functions as points in Cartesian spaces, they now become elements in the space of square, integrable function. Interpolation is thus conducted between the antecedent and consequent function spaces. The generalized representation allows an extended class of membership functions satisfying two monotonicity conditions to be accommodated in the interpolation process. They include the popular bell-shaped membership functions, which were not possible before with the Cartesian representation. The work also extends the similarity triangle-based interpolation technique from the previous Cartesian representation to the new representation. Ensuing issues on computational complexity and nonunique conclusion are discussed. Other concepts such as spanning set and extensibility functions are also presented under the generalized framework. Examples to illustrate the extended approach and to compare with the Cartesian approach are given.

Our work targets a network architecture and accompanying algorithms for countering distributed denial-of-service (DDoS) attacks directed at an Internet server. The basic mechanism is for a server under stress to install a router throttle at selected upstream routers. The throttle can be the leaky-bucket rate at which a router can forward packets destined for the server. Hence, before aggressive packets can converge to overwhelm the server, participating routers proactively regulate the contributing packet rates to more moderate levels, thus forestalling an impending attack. In allocating the server capacity among the routers, we propose a notion of level-k max-min fairness. We first present a control-theoretic model to evaluate algorithm convergence under a variety of system parameters. In addition, we present packet network simulation results using a realistic global network topology, and various models of good user and attacker distributions and behavior. Using a generator model of web requests parameterized by empirical data, we also evaluate the impact of throttling in protecting user access to a web server. First, for aggressive attackers, the throttle mechanism is highly effective in preferentially dropping attacker traffic over good user traffic. In particular, level-k max-min fairness gives better good-user protection than recursive pushback of max-min fair rate limits proposed in the literature. Second, throttling can regulate the experienced server load to below its design limit - in the presence of user dynamics - so that the server can remain operational during a DDoS attack. Lastly, we present implementation results of our prototype on a Pentium III/866 MHz machine. The results show that router throttling has low deployment overhead in time and memory.

An approach of grid point sampling and SVD consolidation has been proposed recently for nonlinear plant modeling and control system design. The approach calls for generating the plant's linear approximations over a set of grid points in the domains of the state variables, and then conduct SVD consolidation to obtain a TS fuzzy model representation for the plant. Going a step further, grid point controllers may also be generated and then joined with the plant parameters for SVD reduction, thereby possibly resulting in new fuzzy structure over that of the original plant. Numerous works have been conducted for both cases. The present work aims to explore two outstanding issues regarding the approach. The first concerns its ability to extract inherent fuzzy structure of the plant, and the second studies the condition under which grid point controller design would maintain the fuzzy structure of the plant. We use a simple numerical example to illustrate the key ideas.

This paper presents a multi-biometric verification system that combines speaker verification, fingerprint verification with face identification. Their respective equal error rates (EER) are 4.3%, 5.1 % and the range of (5.1 % to 11.5%) for matched conditions in facial image capture. Fusion of the three by majority voting gave a relative improvement of 48 % over speaker verification (i.e. the best-performing biometric). Fusion by weighted average scores produced a further relative improvement of 52%. We propose the use of fuzzy logic decision fusion, in order to account for external conditions that affect verification performance. Examples include recording conditions of utterances for speaker verification, lighting and facial expressions in face identification and finger placement and pressure for fingerprint verification. The fuzzy logic framework incorporates some external factors relating to face and fingerprint verification and achieved an additional improvement of 19%. 1.

One of the usual important criteria to be considered in real time control applications is the computational complexity of the controllers, observers and models applied. In the paper a higher order singular value decomposition (HOSVD) based complexity reduction technique is proposed for Takagi Sugeno (TS) fuzzy models, which is capable of defining the contribution of each local linear model included in the TS fuzzy model. This helps us with discarding the weakly contributing ones according to a given threshold. Reducing the number of models leads directly to the computational complexity reduction.

The ability to manipulate and control biological cells with reflective-force information is a key technology necessary for many new applications in Bio-MEMS, but is currently lacking in all cellular manipulators. We report in this paper our preliminary experimental work in using an ionic conducting polymer film (ICPF) to develop a biological cellular robotic gripper with force sensing capability. ICPF actuators are able to give large deflection with small input voltage (/spl sim/5V) in aqueous environments, and also able to give relatively large output voltage due to deflection by mechanical forces. Thus, ICPF actuators are investigated as possible cellular force-reflection controlled manipulators in our work. However, an universally accepted or accurate dynamic model for ICPF actuators does not exit yet due to the complex interdependent physical mechanisms which govern their actuation behavior electrical, chemical, and mechanical. This makes grasping control and manipulation hard ID achieve, especially if the ICPF actuators are to be used in manipulating moving biological targets. In this paper we propose a neural-fuzzy based scheme to control the movement of ICPF micro actuators.

This paper reports a preliminary effort in designing and constructing an artificial face to mimic human facial expressions. The face was built over the surface of a plastic human-size skull, with shape memory alloy (SMA) wires providing the needed actuation in place of human muscles. Due to the special properties that they have, the modeling and control aspects of the SMA wires constitute a great challenge to the success of our objective. In this work, a special configuration of neural networks is adopted for the purpose. Various selected points on the artificial face, including the opening and closing of the mouth, are controlled as such to emulate human expressions. A software face model is also implemented for interfacing. Overall acceptable performance is demonstrated experimentally.

This paper is motivated by the fact that though fuzzy and B-spline techniques are popular engineering tools, their utilisation is being restricted by their exponential complexity property. As a result SVD based reduction techniques have emerged. These methods apply singular value decomposition to the characteristic matrix of the rule base. The maximum size of the rule base taken into consideration is limited by size of operation memory available for singular value decomposition. The method proposed in this paper is capable of applying singular value decomposition step by step to the partitions of the rule base. Therefore, using the proposed extension, there is no limit, theoretically, for the size of the rule bases.

During the past few years, efficient singular value-based complexity reduction tools have been developed for fuzzy logic techniques. The paper introduces a singular value-based reduction method to the generalised type neural network. The method conducts singular value decomposition of the weighting functions defined on the connections among the neurons and generates certain linear combinations of the original weighting functions to form a new connection-net for the complexity reduced neural network.

Sparse rule base and interpolation have been proposed as possible solution to alleviate the geometric complexity problem of large fuzzy set. However, no formal method to extract sparse rule base is yet available. This paper combines the recently introduced Cartesian representation of membership functions and a mountain method-based clustering technique for the extraction. A case study is included to demonstrate the effectiveness of the approach.

One of the reasons why fuzzy methodology is successful is that fuzzy systems are universal approximators, i.e., we can approximate an arbitrary continuous function within any given accuracy by a fuzzy system. In some practical applications (e.g., in control), it is desirable to approximate not only the original function, but also its derivatives (so that, e.g., a fuzzy control approximating a smooth control will also be smooth). In our paper, we show that for any given accuracy, we can approximate an arbitrary smooth function by a fuzzy system so that not only the function is approximated within this accuracy, but its derivatives are approximated as well. In other words, we prove that fuzzy systems are universal approximators for smooth functions and their derivatives. ©2000 John Wiley & Sons, Inc.

Function approximation is a very important practical problem: in many practical applications, we know the exact form of the functional dependence y=f(x1,…,xn) between physical quantities, but this exact dependence is complicated, so we need a lot of computer space to store it, and a lot of time to process it, i.e., to predict y from the given xi. It is therefore necessary to find a simpler approximate expression g(x1,…,xn)≈f(x1,…,xn) for this same dependence. This problem has been analyzed in numerical mathematics for several centuries, and it is, therefore, one of the most thoroughly analyzed problems of applied mathematics. There are many results related to approximation by polynomials, trigonometric polynomials, splines of different type, etc. Since this problem has been analyzed for so long, no wonder that for many reasonable formulations of the optimality criteria, the corresponding problems of finding the optimal approximations have already been solved. Lately, however, new clustering-related techniques have been applied to solve this problem (by Yager, Filev, Chu, and others). At first glance, since for most traditional optimality criteria, optimal approximations are already known, the clustering approach can only lead to non-optimal approximations, i.e., approximations of inferior quality. We show, however, that there exist new reasonable criteria with respect to which clustering-based function approximation is indeed the optimal method of function approximation. © 2000 John Wiley & Sons, Inc.

This paper introduces a new approach for fuzzy interpolation and extrapolation of sparse rule base comprising of membership functions with finite number of characteristic points. The approach calls for representing membership functions as points in high-dimensional Cartesian spaces using the locations of their characteristic points as coordinates. Hence, a fuzzy rule base can be viewed as a set of mappings between the antecedent and consequent spaces and the interpolation and extrapolation problem becomes searching for an image in the consequent space upon given an antecedent observation. The present approach divides observations into two groups: 1) observations within the antecedent spanning set contain the same geometric properties as the given antecedents; and 2) observations lying outside the antecedent spanning set contain new geometric properties beyond those of the given rules. Heuristic reasoning must therefore be applied. In this case, a two-step approach with certain flexibility to accommodate additional criteria and design objectives is formulated.

We address the problem of transferring human control strategies (HCS) from an expert model to an apprentice model. The proposed algorithm allows us to develop useful apprentice models that incorporate some of the robust aspects of the expert HCS models. We first describe our experimental platform, a real-time graphic driving simulator, for collecting and modeling human control strategies. Then, we discuss an adaptive neural network learning architecture for abstracting HCS models. Next, we define a hidden Markov model (HMM) based similarity measure which allows us to compare different human control strategies. This similarity measure is combined subsequently with simultaneously perturbed stochastic approximation to develop our proposed transfer learning algorithm. In this algorithm, an expert HCS model influences both the structure and the parametric representation of the eventual apprentice HCS model. Finally, we describe some experimental results of the proposed algorithm.

Introduces a singular value-based method for reducing a given fuzzy rule set. The method conducts singular value decomposition of the rule consequents and generates certain linear combinations of the original membership functions to form new ones for the reduced set. The present work characterizes membership functions by the conditions of sum normalization (SN), nonnegativeness (NN), and normality (NO). Algorithms to preserve the SN and NN conditions in the new membership functions are presented. Preservation of the NO condition relates to a high-dimensional convex hull problem and is not always feasible in which case a closed-to-NO solution may be sought. The proposed method is applicable regardless of the adopted inference paradigms. With product-sum-gravity inference and singleton support fuzzy rule base, output errors between the full and reduced fuzzy set are bounded by the sum of the discarded singular values. The work discusses three specific applications of fuzzy reduction: fuzzy rule base with singleton support, fuzzy rule base with nonsingleton support (which includes the case of missing rules), and the Takagi-Sugeno-Kang (TSK) model. Numerical examples are presented to illustrate the reduction process.

In the last few years, modeling dynamic human control strategy (HCS) is becoming an increasingly popular paradigm in a number of different research areas, such as the intelligent vehicle highway system, virtual reality and robotics. Usually, these models are derived empirically, rather than analytically, from real human input-output control data. As such, there is a great need to develop adequate performance criteria for these models, as few guarantees exist about their theoretical performance. It is our goal in this paper to develop several such criteria. In this paper, we first collect driving data from different individuals through a real-time graphic driving simulator. We then model each individual's control strategy through the flexible cascade neural network learning architecture. Next, we develop two performance measures for evaluating the resulting HCS models, one dealing with obstacle avoidance, the other with tight-turning behavior. Finally, we evaluate the relative skill of different HCS models through the proposed performance criteria.

Modeling the dynamic human control strategy (HCS) is becoming an increasingly popular paradigm in a number of different research areas, ranging from robotics to intelligent vehicle highway systems. Usually, HCS models are derived empirically, rather than analytically, from real human input-output data. While these empirical models offer an effective means of transferring intelligent behaviors from humans to robots and other machines, the models are not explicitly optimized with respect to potentially important performance criteria. We therefore propose an iterative algorithm for optimizing an initially stable HCS model with respect to an independent, user-specified performance criterion. We first collect driving data from different individuals through a real-time graphic driving simulator. Next, we describe how we model each individual's control strategy through flexible cascade neural networks. Once we have initially stable HCS models, we propose simultaneously perturbed stochastic approximation (SPSA) to optimize these models with respect to a chosen performance criterion. Finally, we describe and discuss some experimental results with the proposed algorithm.

Fuzzy rule base reduction has emerged recently as an important topic of research in fuzzy theories. Main difficulty of any generated rule bases is that the number of rules increases exponentially with the number of variables and fuzzy terms. Singular value decomposition (SVD) based method has been first published for Sugeno algorithm. It was then extended to the Takagi-Sugeno controller, to rule bases with nonsingleton consequents and to fuzzy rule interpolation algorithms. However, the application of these methods are restricted to some special inference engines and rule bases. In this paper we introduce a general SVD-based rule base reduction method for arbitrary rule base, namely arbitrary shaped antecedents, inference algorithm, and consequent sets described by arbitrary (but finite) number of parameters. We demonstrate the use of the proposed method on a control system of automatically guided vehicle.

A new representation which expresses a product-sum-gravity (PSG) inference in terms of additive and multiplicative subsystem inferences of single variable is proposed. The representation yields additional insight into the structure of a fuzzy system and produces an approximate functional characterization of its inferred output. The form of the approximating function is dictated by the choice or polynomial, sinusoidal, or other designs of subsystem inferences. With polynomial inferences, the inferred output approximates a polynomial function the order of which is dependent on the numbers of input membership functions. Explicit expressions for the function and corresponding error of approximation are readily obtained for analysis. Subsystem inferences emulating sinusoidal functions are also discussed. With proper scaling, they produce a set of orthonormal subsystem inferences. The orthonormal set points to a possible "modal" analysis of fuzzy inference and yields solution to an additive decomposable approximation problem. This work also shows that, as the numbers of input membership functions become large, a fuzzy system with PSG inference would converge toward polynomial or Fourier series expansions. The result suggests a new framework to consider fuzzy systems as universal approximators.

This paper introduces a new approach for fuzzy approximation of continuous function on a compact domain. The approach calls for sampling the function over a set of rectangular grid points and applying singular value decomposition to the sample matrix. The resulting quantities are then tailored to become rule consequences and membership functions via the conditions of sum normalization and non-negativeness. The inference paradigm of product-sum-gravity is apparent from the structure of the decomposition equation. All information are extracted directly from the function samples. The present approach yields a class of equivalent fuzzy approximator to a given function. A tight bounding technique to facilitate normal or close-to-normal membership functions is also formulated. The fuzzy output approximates the given function to within an error which is dependent on the sampling intervals and the singular values discarded from the approximation process. Trade-off between the number of membership functions and the desired approximation accuracy is also discussed.