Self-learning fuzzy logic controllers for pursuit-evasion differential games

This paper addresses the problem of tuning the input and the output parameters of a fuzzy logic controller. The system learns autonomously without supervision or a priori training data. Two novel techniques are proposed. The first technique combines Q(λ)-learning with function approximation (fuzzy inference system) to tune the parameters of a fuzzy logic controller operating in continuous state and action spaces. The second technique combines Q(λ)-learning with genetic algorithms to tune the parameters of a fuzzy logic controller in the discrete state and action spaces. The proposed techniques are applied to different pursuit-evasion differential games. The proposed techniques are compared with the classical control strategy, Q(λ)-learning only, reward-based genetic algorithms learning, and with the technique proposed by Dai et al. (2005) [19] in which a neural network is used as a function approximation for Q-learning. Computer simulations show the usefulness of the proposed techniques.     

Model-free Q-learning designs for linear discrete-time zero-sum games with application to H-infinity control

In this paper, the optimal strategies for discrete-time linear system quadratic zero-sum games related to the H-infinity optimal control problem are solved in forward time without knowing the system dynamical matrices. The idea is to solve for an action dependent value function Q(x,u,w) of the zero-sum game instead of solving for the state dependent value function V(x) which satisfies a corresponding game algebraic Riccati equation (GARE). Since the state and actions spaces are continuous, two action networks and one critic network are used that are adaptively tuned in forward time using adaptive critic methods. The result is a Q-learning approximate dynamic programming (ADP) model-free approach that solves the zero-sum game forward in time. It is shown that the critic converges to the game value function and the action networks converge to the Nash equilibrium of the game. Proofs of convergence of the algorithm are shown. It is proven that the algorithm ends up to be a model-free iterative algorithm to solve the GARE of the linear quadratic discrete-time zero-sum game. The effectiveness of this method is shown by performing an H-infinity control autopilot design for an F-16 aircraft.     

Guaranteed robustness bounds for matched-disturbance nonlinear systems

This paper considers input affine nonlinear systems with matched disturbances and shows how to compute an a priori upper bound of the H_∞ attenuation level achieved by the optimal L₂ controller and the suboptimal H_∞ central controller. The case where the disturbance contains a constant term is also discussed. These bounds are shown to depend only on the function mapping the control input to the performance variable. This result is used to derive a robust control design for a special, but practically important, class of non-input affine nonlinear systems consisting of the series connection of a nonlinear state and input dependent map and of a nonlinear input affine dynamical system. Approximate inversion of the nonlinear static map leads to a robust control problem which fits into the framework. The effectiveness of the theoretical results is shown by its use for the robust control design of a diesel engine test bench.     

Attitude and handling improvements through gain-scheduled suspensions and brakes control

In this paper, the problem of comfort and handling improvements of a ground vehicle is treated through the joint control of the suspension and braking systems. Two H_∞ gain-scheduled controllers are synthesized to achieve attitude and yaw performances according to the driving situation, observed through a simple vehicle monitor. The proposed strategy tackles the nonlinear tire braking force in an original way and meets the situation dependent objectives of the vehicle in a unified framework. Simulations on a complex nonlinear full vehicle model, validated using experimental data obtained on a real vehicle, illustrate the improvements brought about by the proposed approach.     

Unification of independent and sequential procedures for decentralized controller design

This paper is concerned with decentralized control problems. There are two typical procedures to design decentralized controllers, ‘independent’ and ‘sequential’ design procedures. As the concepts and the techniques in these two approaches are too different from each other, there have been no attempts to unify these approaches. This paper proposes an iterative independent design procedure for decentralized control systems, which is a unified approach to these conventional approaches.     

Application of a new multi-agent Hybrid Co-evolution based Particle Swarm Optimisation methodology in ship design

In this paper, a multiple objective ‘Hybrid Co-evolution based Particle Swarm Optimisation’ methodology (HCPSO) is proposed. This methodology is able to handle multiple objective optimisation problems in the area of ship design, where the simultaneous optimisation of several conflicting objectives is considered. The proposed method is a hybrid technique that merges the features of co-evolution and Nash equilibrium with a ε-disturbance technique to eliminate the stagnation. The method also offers a way to identify an efficient set of Pareto (conflicting) designs and to select a preferred solution amongst these designs. The combination of co-evolution approach and Nash-optima contributes to HCPSO by utilising faster search and evolution characteristics. The design search is performed within a multi-agent design framework to facilitate distributed synchronous cooperation. The most widely used test functions from the formal literature of multiple objectives optimisation are utilised to test the HCPSO. In addition, a real case study, the internal subdivision problem of a ROPAX vessel, is provided to exemplify the applicability of the developed method.     

Incorporating historical control information into quantal bioassay with Bayesian approach

A Bayesian approach with an iterative reweighted least squares is used to incorporate historical control information into quantal bioassays to estimate the dose-response relationship, where the logit of the historical control responses are assumed to have a normal distribution. The parameters from this normal distribution are estimated from both empirical and full Bayesian approaches with a marginal likelihood function being approximated by Laplace’s Method. A comparison is made using real data between estimates that include the historical control information and those that do not. It was found that the inclusion of the historical control information improves the efficiency of the estimators. In addition, this logit-normal formulation is compared with the traditional beta-binomial for its improvement in parameter estimates. Consequently the estimated dose-response relationship is used to formulate the point estimator and confidence bands for ED(100p) for various values of risk rate p and the potency for any dose level.     

Obtaining more information from conjoint experiments by best-worst choices

Conjoint choice experiments elicit individuals’ preferences for the attributes of a good by asking respondents to indicate repeatedly their most preferred alternative in a number of choice sets. However, conjoint choice experiments can be used to obtain more information than that revealed by the individuals’ single best choices. A way to obtain extra information is by means of best-worst choice experiments in which respondents are asked to indicate not only their most preferred alternative but also their least preferred one in each choice set. To create D-optimal designs for these experiments, an expression for the Fisher information matrix for the maximum-difference model is developed. Semi-Bayesian D-optimal best-worst choice designs are derived and compared with commonly used design strategies in marketing in terms of the D-optimality criterion and prediction accuracy. Finally, it is shown that best-worst choice experiments yield considerably more information than choice experiments.     

A study of Gaussian mixture models of color and texture features for image classification and segmentation

The aims of this paper are two-fold: to define Gaussian mixture models (GMMs) of colored texture on several feature spaces and to compare the performance of these models in various classification tasks, both with each other and with other models popular in the literature. We construct GMMs over a variety of different color and texture feature spaces, with a view to the retrieval of textured color images from databases. We compare supervised classification results for different choices of color and texture features using the Vistex database, and explore the best set of features and the best GMM configuration for this task. In addition we introduce several methods for combining the ‘color’ and ‘structure’ information in order to improve the classification performances. We then apply the resulting models to the classification of texture databases and to the classification of man-made and natural areas in aerial images. We compare the GMM model with other models in the literature, and show an overall improvement in performance.     

Fuzzy and possibilistic clustering for fuzzy data

The Fuzzy k-Means clustering model (FkM) is a powerful tool for classifying objects into a set of k homogeneous clusters by means of the membership degrees of an object in a cluster. In FkM, for each object, the sum of the membership degrees in the clusters must be equal to one. Such a constraint may cause meaningless results, especially when noise is present. To avoid this drawback, it is possible to relax the constraint, leading to the so-called Possibilistic k-Means clustering model (PkM). In particular, attention is paid to the case in which the empirical information is affected by imprecision or vagueness. This is handled by means of LR fuzzy numbers. An FkM model for LR fuzzy data is firstly developed and a PkM model for the same type of data is then proposed. The results of a simulation experiment and of two applications to real world fuzzy data confirm the validity of both models, while providing indications as to some advantages connected with the use of the possibilistic approach.     

Smooth semiparametric and nonparametric Bayesian estimation of bivariate densities from bivariate histogram data

Penalized B-splines combined with the composite link model are used to estimate a bivariate density from a histogram with wide bins. The goals are multiple: they include the visualization of the dependence between the two variates, but also the estimation of derived quantities like Kendall’s tau, conditional moments and quantiles. Two strategies are proposed: the first one is semiparametric with flexible margins modeled using B-splines and a parametric copula for the dependence structure; the second one is nonparametric and is based on Kronecker products of the marginal B-spline bases. Frequentist and Bayesian estimations are described. A large simulation study quantifies the performances of the two methods under different dependence structures and for varying strengths of dependence, sample sizes and amounts of grouping. It suggests that Schwarz’s BIC is a good tool for classifying the competing models. The density estimates are used to evaluate conditional quantiles in two applications in social and in medical sciences.     

A discrete-time stable controller for an omni-directional mobile robot based on an approximated model

An adaptive controller based on multi-input fuzzy rules emulated networks (MIFRENs) is introduced for omni-directional mobile robot systems in the discrete-time domain without any kinematic or dynamic models. An approximated model for unknown systems is developed by using two MIFRENs with an online learning algorithm in addition to the stability analysis. The main theorem in this model is proposed to guarantee closed-loop performance and system robustness for all adjustable parameters inside MIFRENs. The system is validated by an experimental setup with a FESTO omni-directional mobile robot called Robotino^®. The proposed algorithm is shown to have superior performance compared to that of an algorithm that uses only an embedded controller. The advantage of the MIFREN initial setting is verified comparing its results with those of a controller that is based on neural networks.     

Online computation with advice

We consider a model for online computation in which the online algorithm receives, together with each request, some information regarding the future, referred to as advice. The advice is a function, defined by the online algorithm, of the whole request sequence. The advice provided to the online algorithm may allow an improvement in its performance, compared to the classical model of complete lack of information regarding the future. We are interested in the impact of such advice on the competitive ratio, and in particular, in the relation between the size b of the advice, measured in terms of bits of information per request, and the (improved) competitive ratio. Since b=0 corresponds to the classical online model, and b=⌈log∣A∣⌉, where A is the algorithm’s action space, corresponds to the optimal (offline) one, our model spans a spectrum of settings ranging from classical online algorithms to offline ones.In this paper we propose the above model and illustrate its applicability by considering two of the most extensively studied online problems, namely, metrical task systems (MTS) and the k-server problem. For MTS we establish tight (up to constant factors) upper and lower bounds on the competitive ratio of deterministic and randomized online algorithms with advice for any choice of 1≤b≤Θ(logn), where n is the number of states in the system: we prove that any randomized online algorithm for MTS has competitive ratio Ω(log(n)/b) and we present a deterministic online algorithm for MTS with competitive ratio O(log(n)/b). For the k-server problem we construct a deterministic online algorithm for general metric spaces with competitive ratio k^O(1/b) for any choice of Θ(1)≤b≤logk.     

A class of aggregation functions encompassing two-dimensional OWA operators

In this paper we prove that, under suitable conditions, Atanassov’s K_α operators, which act on intervals, provide the same numerical results as OWA operators of dimension two. On one hand, this allows us to recover OWA operators from K_α operators. On the other hand, by analyzing the properties of Atanassov’s operators, we can generalize them. In this way, we introduce a class of aggregation functions - the generalized Atanassov operators - that, in particular, include two-dimensional OWA operators. We investigate under which conditions these generalized Atanassov operators satisfy some properties usually required for aggregation functions, such as bisymmetry, strictness, monotonicity, etc. We also show that if we apply these aggregation functions to interval-valued fuzzy sets, we obtain an ordered family of fuzzy sets.     

Arithmetic operators in interval-valued fuzzy set theory

We introduce the addition, subtraction, multiplication and division on L^I, where L^I is the underlying lattice of both interval-valued fuzzy set theory [R. Sambuc, Fonctions Φ-floues. Application à l’aide au diagnostic en pathologie thyroidienne, Ph.D. Thesis, Université de Marseille, France, 1975] and intuitionistic fuzzy set theory [K.T. Atanassov, Intuitionistic fuzzy sets, 1983, VII ITKR’s Session, Sofia (deposed in Central Sci. Technical Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian)]. We investigate some algebraic properties of these operators. We show that using these operators the pseudo-t-representable extensions of the ?ukasiewicz t-norm and the product t-norm on the unit interval to L^I and some related operators can be written in a similar way as their counterparts on ([0,1],?).     

Unified approach to coefficient-based regularized regression

In this paper, we consider the coefficient-based regularized least-squares regression problem with the l^q-regularizer (1≤q≤2) and data dependent hypothesis spaces. Algorithms in data dependent hypothesis spaces perform well with the property of flexibility. We conduct a unified error analysis by a stepping stone technique. An empirical covering number technique is also employed in our study to improve sample error. Comparing with existing results, we make a few improvements: First, we obtain a significantly sharper learning rate that can be arbitrarily close to O(m⁻¹) under reasonable conditions, which is regarded as the best learning rate in learning theory. Second, our results cover the case q=1, which is novel. Finally, our results hold under very general conditions.     

Negative selection algorithms on strings with efficient training and linear-time classification

A string-based negative selection algorithm is an immune-inspired classifier that infers a partitioning of a string space Σ^? into “normal” and “anomalous” partitions from a training set S containing only samples from the “normal” partition. The algorithm generates a set of patterns, called “detectors”, to cover regions of the string space containing none of the training samples. Strings that match at least one of these detectors are then classified as “anomalous”. A major problem with existing implementations of this approach is that the detector generating step needs exponential time in the worst case. Here we show that for the two most widely used kinds of detectors, the r-chunk and r-contiguous detectors based on partial matching to substrings of length r, negative selection can be implemented more efficiently by avoiding generating detectors altogether: for each detector type, training set S⊆Σ^? and parameter r≤? one can construct an automaton whose acceptance behaviour is equivalent to the algorithm’s classification outcome. The resulting runtime is O(|S|?r|Σ|) for constructing the automaton in the training phase and O(?) for classifying a string.     

Experimental investigation on adaptive robust controller designs applied to a free-floating space manipulator

This paper aims to formulate and investigate the application of various nonlinear H_∞ control methods to a free-floating space manipulator subject to parametric uncertainties and external disturbances. From a tutorial perspective, a model-based approach and adaptive procedures based on linear parametrization, neural networks and fuzzy systems are covered by this work. A comparative study is conducted based on experimental implementations performed with an actual underactuated fixed-base planar manipulator which is, following the DEM concept, dynamically equivalent to a free-floating space manipulator.     

Hierarchical trajectory refinement for a class of nonlinear systems

Trajectory generation for nonlinear control systems is an important and difficult problem. In this paper, we provide a constructive method for hierarchical trajectory refinement. The approach is based on the recent notion of φ-related control systems. Given a control affine system satisfying certain assumptions, we construct a φ-related control system of smaller dimension. Trajectories designed for the smaller, abstracted system are guaranteed, by construction, to be feasible for the original system. Constructive procedures are provided for refining trajectories from the coarser to the more detailed system.     

On using prototype reduction schemes to enhance the computation of volume-based inter-class overlap measures

In most pattern recognition (PR) applications, it is advantageous if the accuracy (or error rate) of the classifier can be evaluated or bounded prior to testing it in a real-life setting. It is also well known that if the two class-conditional distributions have a large overlapping volume (almost all the available work on “overlapping of classes” deals with the case when there are only two classes), the classification accuracy is poor. This is because if we intend to use the classification accuracy as a criterion for evaluating a PR system, the points within the overlapping volume tend to lead to maximal misclassification. Unfortunately, the computation of the indices which quantify the overlapping volume is expensive. In this vein, we propose a strategy of using a prototype reduction scheme (PRS) to approximately, but quickly, compute the latter. In this paper, we demonstrate, first of all, that this is an extremely expedient proposition. Indeed, we show that by completely discarding (we are not aware of any reported scheme which discards “irrelevant” sample (training) points, and which simultaneously attains to an almost-comparable accuracy) the points not included by the PRS, we can obtain a reduced set of sample points, using which, in turn, the measures for the overlapping volume can be computed. The value of the corresponding figures is comparable to those obtained with the original training set (i.e., the one which considers all the data points) even though the computations required to obtain the prototypes and the corresponding measures are significantly less. The proposed method has been rigorously tested on artificial and real-life datasets, and the results obtained are, in our opinion, quite impressive—sometimes faster by two orders of magnitude.