Dynamic economic load dispatch (DELD) is one of the most important steps in power system operation. Various optimisation algorithms for solving the problem have been developed; however, due to the non-convex characteristics and large dimensionality of the problem, it is necessary to explore new methods to further improve the dispatch results and minimise the costs. This article proposes a hybrid differential evolution (DE) algorithm, namely clonal selection-based differential evolution (CSDE), to solve the problem. CSDE is an artificial intelligence technique that can be applied to complex optimisation problems which are for example nonlinear, large scale, non-convex and discontinuous. This hybrid algorithm combines the clonal selection algorithm (CSA) as the local search technique to update the best individual in the population, which enhances the diversity of the solutions and prevents premature convergence in DE. Furthermore, we investigate four mutation operations which are used in CSA as the hyper-mutation operations. Finally, an efficient solution repair method is designed for DELD to satisfy the complicated equality and inequality constraints of the power system to guarantee the feasibility of the solutions. Two benchmark power systems are used to evaluate the performance of the proposed method. The experimental results show that the proposed CSDE/best/1 approach significantly outperforms nine other variants of CSDE and DE, as well as most other published methods, in terms of the quality of the solution and the convergence characteristics.

A number of neural networks can be formulated as the linear-in-the-parameters models. Training such networks can be transformed to a model selection problem where a compact model is selected from all the candidates using subset selection algorithms. Forward selection methods are popular fast subset selection approaches. However, they may only produce suboptimal models and can be trapped into a local minimum. More recently, a two-stage fast recursive algorithm (TSFRA) combining forward selection and backward model refinement has been proposed to improve the compactness and generalization performance of the model. This paper proposes unified two-stage orthogonal least squares methods instead of the fast recursive-based methods. In contrast to the TSFRA, this paper derives a new simplified relationship between the forward and the backward stages to avoid repetitive computations using the inherent orthogonal properties of the least squares methods. Furthermore, a new term exchanging scheme for backward model refinement is introduced to reduce computational demand. Finally, given the error reduction ratio criterion, effective and efficient forward and backward subset selection procedures are proposed. Extensive examples are presented to demonstrate the improved model compactness constructed by the proposed technique in comparison with some popular methods.

The Takagi–Sugeno–Kang-type rule-based fuzzy model has found many applications in different fields; a major challenge is, however, to build a compact model with optimized model parameters which leads to satisfactory model performance. To produce a compact model, most existing approaches mainly focus on selecting an appropriate number of fuzzy rules. In contrast, this paper considers not only the selection of fuzzy rules but also the structure of each rule premise and consequent, leading to the development of a novel compact rule-based fuzzy model. Here, each fuzzy rule is associated with two sets of input attributes, in which the first is used for constructing the rule premise and the other is employed in the rule consequent. A new hybrid learning method combining the modified harmony search method with a fast recursive algorithm is hereby proposed to determine the structure and the parameters for the rule premises and consequents. This is a hard mixed-integer nonlinear optimization problem, and the proposed hybrid method solves the problem by employing an embedded framework, leading to a significantly reduced number of model parameters and a small number of fuzzy rules with each being as simple as possible. Results from three examples are presented to demonstrate the compactness (in terms of the number of model parameters and the number of rules) and the performance of the fuzzy models obtained by the proposed hybrid learning method, in comparison with other techniques from the literature.

The majority of reported learning methods for Takagi-Sugeno-Kang (TSK) fuzzy neural models to date mainly focus on improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behavior when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, identify the corresponding consequent models which can be directly explained in terms of system behavior, presents a critical step in fuzzy neural modeling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practiced in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. Thus, a new Jacobian matrix is proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues regarding the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.

The construction of a radial basis function (RBF) network involves the determination of the model size, hidden nodes, and output weights. Least squares-based subset selection methods can determine a RBF model size and its parameters simultaneously. Although these methods are robust, they may not achieve optimal results. Alternatively, gradient methods are widely used to optimize all the parameters. The drawback is that most algorithms may converge slowly as they treat hidden nodes and output weights separately and ignore their correlations. In this paper, a new discrete-continuous algorithm is proposed for the construction of a RBF model. First, the orthogonal least squares (OLS)-based forward stepwise selection constructs an initial model by selecting model terms one by one from a candidate term pool. Then a new Levenberg-Marquardt (LM)-based parameter optimization is proposed to further optimize the hidden nodes and output weights in the continuous space. To speed up the convergence, the proposed parameter optimization method considers the correlation between the hidden nodes and output weights, which is achieved by translating the output weights to dependent parameters using the OLS method. The correlation is also used by the previously proposed continuous forward algorithm (CFA). However, unlike the CFA, the new method optimizes all the parameters simultaneously. In addition, an equivalent recursive sum of squared error is derived to reduce the computation demanding for the first derivatives used in the LM method. Computational complexity is given to confirm the new method is much more computationally efficient than the CFA. Different numerical examples are presented to illustrate the effectiveness of the proposed method. Further, Friedman statistical tests on 13 classification problems are performed, and the results demonstrate that RBF networks built by the new method are very competitive in comparison with some popular classifiers.

This paper proposes a new methodology for solving the unmanned multi-vehicle formation control problem. It employs a unique “extension-decomposition-aggregation” scheme to transform the overall complex formation control problem to a group of sub-problems which work via boundary interactions. The H∞robust control strategy is applied to design the decentralised formation controllers to reject the interactions and work jointly to maintain the stability of the overall formation. Simulation studies have been performed to verify its performance and effectiveness.

Fuzzy-neural-network-based inference systems are well-known universal approximators which can produce linguistically interpretable results. Unfortunately, their dimensionality can be extremely high due to an excessive number of inputs and rules, which raises the need for overall structure optimization. In the literature, various input selection methods are available, but they are applied separately from rule selection, often without considering the fuzzy structure. This paper proposes an integrated framework to optimize the number of inputs and the number of rules simultaneously. First, a method is developed to select the most significant rules, along with a refinement stage to remove unnecessary correlations. An improved information criterion is then proposed to find an appropriate number of inputs and rules to include in the model, leading to a balanced tradeoff between interpretability and accuracy. Simulation results confirm the efficacy of the proposed method.

This paper presents two new approaches for use in complete process monitoring. The first concerns the identification of nonlinear principal component models. This involves the application of linear principal component analysis (PCA), prior to the identification of a modified autoassociative neural network (AAN) as the required nonlinear PCA (NLPCA) model. The benefits are that (i) the number of the reduced set of linear principal components (PCs) is smaller than the number of recorded process variables, and (ii) the set of PCs is better conditioned as redundant information is removed. The result is a new set of input data for a modified neural representation, referred to as a T2T network. The T2T NLPCA model is then used for complete process monitoring, involving fault detection, identification and isolation. The second approach introduces a new variable reconstruction algorithm, developed from the T2T NLPCA model. Variable reconstruction can enhance the findings of the contribution charts still widely used in industry by reconstructing the outputs from faulty sensors to produce more accurate fault isolation. These ideas are illustrated using recorded industrial data relating to developing cracks in an industrial glass melter process. A comparison of linear and nonlinear models, together with the combined use of contribution charts and variable reconstruction, is presented. © 2008 Wiley Periodicals, Inc.

This paper investigates the learning of a wide class of single-hidden-layer feedforward neural networks (SLFNs) with two sets of adjustable parameters, i.e., the nonlinear parameters in the hidden nodes and the linear output weights. The main objective is to both speed up the convergence of second-order learning algorithms such as Levenberg-Marquardt (LM), as well as to improve the network performance. This is achieved here by reducing the dimension of the solution space and by introducing a new Jacobian matrix. Unlike conventional supervised learning methods which optimize these two sets of parameters simultaneously, the linear output weights are first converted into dependent parameters, thereby removing the need for their explicit computation. Consequently, the neural network (NN) learning is performed over a solution space of reduced dimension. A new Jacobian matrix is then proposed for use with the popular second-order learning methods in order to achieve a more accurate approximation of the cost function. The efficacy of the proposed method is shown through an analysis of the computational complexity and by presenting simulation results from four different examples.

In neural network optimization, multiple goals and constraints cannot be handled independently of the underlying optimizer. While "better" solutions should be rated higher than "worse" ones, the resulting cost landscapes must also comply with requirements such as continuity and differentiability of the cost surface. The genetic algorithm (GA), which has found application in many areas not amenable to optimization by other methods, is a random search technique which requires the assignment of a scalar measure of quality, or fitness, to candidate solutions. This paper proposes that the fitness assignment be interpreted as, or at least related to, a multicriterion decision process. A suitable decision-making framework, based on goals and priority, is subsequently formulated in term of fuzzy reasoning and shown to encompass a number of simpler decision strategies. Since the GA is a random search process and therefore takes more time to find a solution in the problem domain, a proper search direction is required in order to produce an optimum result. Fuzzy logic cannot provide an exact solution but can be used as a useful tool for reasoning. In this paper, the reasoning capability of fuzzy logic is used to provide a proper direction for genetic search in a problem domain and thus to achieve faster convergence in the GA. The effectiveness of this is shown in neural network optimization applied to dynamic modelling of an experimental flexible manipulator. The results show that the new fuzzy logic approach is superior to conventional exploration of the genetic search region.

In this letter, a standard postnonlinear blind source separation algorithm is proposed, based on the MISEP method, which is widely used in linear and nonlinear independent component analysis. To best suit a wide class of postnonlinear mixtures, we adapt the MISEP method to incorporate a priori information of the mixtures. In particular, a group of three-layered perceptrons and a linear network are used as the unmixing system to separate sources in the postnonlinear mixtures, and another group of three-layered perceptron is used as the auxiliary network. The learning algorithm for the unmixing system is then obtained by maximizing the output entropy of the auxiliary network. The proposed method is applied to postnonlinear blind source separation of both simulation signals and real speech signals, and the experimental results demonstrate its effectiveness and efficiency in comparison with existing methods.

This paper deals with reinforcement learning for process modeling and control using a model-free, action- dependent adaptive critic (ADAC). A new modified recursive Levenberg Marquardt (RLM) training algorithm, called temporal difference RLM, is developed to improve the ADAC performance. Novel application results for a simulated continuously-stirred-tank-reactor process are included to show the superiority of the new algorithm to conventional temporal-difference stochastic backpropagation.

A new chromosome encoding method, named fuzzy coding, is proposed for representing real number parameters in a genetic algorithm. Fuzzy coding provides the value of a parameter on the basis of the optimum number of selected fuzzy sets and their effectiveness in terms of degree of membership. Thus, it represents the knowledge associated with each parameter and is an indirect method of encoding compared with alternatives, where the parameters are directly represented in the encoding. Fuzzy coding is described and compared with conventional binary coding, gray coding, and floating-point coding. Two test examples, along with neural identification of a nonlinear pH process from experimental data, are studied. It is shown that fuzzy coding is better than the conventional methods and is effective for parameter optimization in problems where the search space is complicated.

Virtual reality can be a very useful tool for complicated programming, planning, controlling and teleoperating robots. As yet the application of virtual reality to cooperation and conflict resolution between multiple robots has received little attention. In the paper, an event-driven virtual reality system for two robots is proposed and implemented. This system uses a standard VR package to implement the environment, thus allowing easier development of tasks, skills and behaviours. The assemblies in the virtual scene, i.e. CAD counterparts of these two robots, act like an outer protective skin to events from the variable environment around them such as collisions. Thus the corresponding safety actions can then be taken. The virtual and real environments are physically connected through a LAN using the TCP/IP protocol. Once the virtual assemblies are placed in safe and desirable goal locations, the real links update their locations using recorded trajectory points through path planning and collision avoidance. This approach prevents the VR from causing collisions between two real links, and between the real links and their environment. This system has provided a useful extension to current virtual reality systems for single robots. Also this system has application potential in multiple robot teleoperation tasks.

This paper describes a novel means for creating a nonlinear extension of principal component analysis (PCA) using radial basis function (RBF) networks. This algorithm comprises two distinct stages: projection and self-consistency. The projection stage contains a single network, trained to project data from a high- to a low-dimensional space. Training requires solution of a generalized eigenvector equation. The second stage, trained using a novel hybrid nonlinear optimization algorithm, then performs the inverse transformation. Issues relating to the practical implementation of the procedure are discussed, and the algorithm is demonstrated on a nonlinear test problem. An example of the application of the algorithm to data from a benchmark simulation of an industrial overheads condenser and reflux drum rig is also included. This shows the usefulness of the procedure in detecting and isolating both sensor and process faults. Pointers for future research in this area are also given.

Where two robot arms hold a common object and their usable space is limited such as inside an automatic instrument it is important to determine its maximum extreme distance or reachable workspace. Obviously, the grasping orientations and placement of the two arms are crucial to maximising the distance and workspace. To date, these factors have been ignored. This problem is much more difficult than that for a single arm and many methods for a single arm are no longer applicable, due to many extra constraints, variables and joint configurations. Here, a new approach to this problem is proposed. The problem is formulated as a multivariable nonlinear constrained optimisation problem and it is solved using sequential quadratic programming (SQP). With this method, the optimal grasping with optimal placement of the two arms, the extreme joint configurations and the maximum extreme distance can be obtained The computational results show that the distance takes its maximum where a small number of joint configurations are at their singularities, which is quite different from the situations of a single arm and from intuition. This method is illustrated using an example, where a rod is held by the two-finger grippers of two SCARA-type robot arms. Objects of different shapes, such as a plate, can be treated as special cases of the rod.

This paper presents a new hybrid optimization strategy for training feedforward neural networks. The algorithm combines gradient-based optimization of nonlinear weights with singular value decomposition (SVD) computation of linear weights in one integrated routine. It is described for the multilayer perceptron (MLP) and radial basis function (RBF) networks and then extended to the local model network (LMN), a new feedforward structure in which a global nonlinear model is constructed from a set of locally valid submodels. Simulation results are presented demonstrating the superiority of the new hybrid training scheme compared to second-order gradient methods. It is particularly effective for the LMN architecture where the linear to nonlinear parameter ratio is large.

The objective of inspection task sequence planning for two robot arms is not only to find a series of common optimal final configurations, but to find a time-optimal task sequence of inspection points. The time-suboptimal final configurations are solved using a (continuous) nonlinear optimization method. The task sequence planning is formulated as a variation of the travelling salesman problem (an integer optimization) and is solved by simulated annealing. The time-suboptimal task sequence planning and time-efficient trajectory planning are integrated and the related computational problems are addressed and solved. The proposed method is applied to an environment containing two cooperative SCARA type inspection robot arms. Computations have been carried out for 4-20 moving points/cities in a route where both arms move. This is compared with completing the task with the same goal points in a route where only one arm moves. The conclusion is that it is much more efficient if two robot arms work in cooperative mode. Experiments have also been conducted on an experimental system, this gave satisfactory results which are consistent with those obtained by simulation.

Planning for effective manipulation of single, redundant or multiple robot systems requires the consideration of the DOF, dexterity, tasks and constraints. A new approach to redundancy resolution for multiple cooperative robots is proposed. A relative Jacobian, thus relative dexterity, is clearly defined and derived for multiple robots. Sequential quadratic programming (SQP) is used to optimize the relative dexterity of the robots whilst satisfying task requirements and limits on joint angles. With this approach it is not necessary to balance the weightings between the performance index and those constraint terms in the cost function. Further the resulting joint configurations are globally optimal with respect to the specified cost. An illustrative example is included to demonstrate the usefulness of this approach. From this example, the relative dexterity of the arms has been found to be more useful than individual arm dexterities in planning the cooperative task.

This paper investigates in detail the possible application of neural networks to the modeling and adaptive control of nonlinear systems. Nonlinear neural-network-based plant modeling is first discussed, based on the approximation capabilities of the multilayer perceptron. A structure is then proposed to utilize feedforward networks within a direct model reference adaptive control strategy. The difficulties involved in training this network, embedded within the closed-loop are discussed and a novel neural-network-based sensitivity modeling approach proposed to allow for the backpropagation of errors through the plant to the neural controller. Finally, a novel nonlinear internal model control (IMC) strategy is suggested, that utilizes a nonlinear neural model of the plant to generate parameter estimates over the nonlinear operating region for an adaptive linear internal model, without the problems associated with recursive parameter identification algorithms. Unlike other neural IMC approaches the linear control law can then be readily designed. A continuous stirred tank reactor was chosen as a realistic nonlinear case study for the techniques discussed in the paper.

Various approaches to the parallel implementation of second-order gradient-based multilayer perceptron training algorithms are described. Two main classes of algorithm are defined involving Hessian and conjugate gradient-based methods. The limited- and full-memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithms are selected as representative examples and used to show that the step size and gradient calculations are critical components. For larger problems the matrix calculations in the full-memory algorithm are also significant. Various strategies are considered for parallelization, the best of which is implemented on parallel virtual machine (PVM) and transputer-based architectures. Results from a range of problems are used to demonstrate the performance achievable with each architecture. The transputer implementation is found to give excellent speed-ups but the problem size is limited by memory constraints. The speed-ups achievable with the PVM implementation are much poorer because of inefficient communication, but memory is not a difficulty.

A practical approach to time-efficient trajectory planning for two cooperative industrial robots with free final configurations is presented. A time-efficient trajectory planning problem is then formulated which uses time-efficient acceleration profiles and is subject to limits on joint positions, velocities, accelerations and jerks. The formula is further simplified by suitably choosing the time intervals of the profile. The optimization problem is solved using a nonlinear optimization method, sequential quadratic programming (SQP). The computation problem arising thereby is successfully dealt with. The proposed method is applied to an environment containing two RTX SCARA type robot arms where their final configurations are relatively given with respect to each other, e.g. in a tool/workpiece operation, and are free with respect to the world frame. The problem is solved in almost real-time. For each robot arm, at least one of the resulting joint trajectories reaches its limit velocity. These joint trajectories are used as reference inputs to a robot control system for the two RTX arms realised on a transputer network. Experiments demonstrating feasibility of this method are conducted.

In this paper time-optimal, smooth and collision-free cubic spline path planning in an environment with two industrial robot arms is implemented. A suitable objective function combining the requirements of time optimality and smoothness of paths is put forward which is subject to the continuity of joint positions, velocities, and accelerations, the limits on their rates of change and collision-free constraints. A fast and effective collision detection method is used. A nonlinear optimization method is used to solve this problem. The resulting joint trajectories or spatial Cartesian paths are time-optimal, smooth and collision-free. The feasibility of this method is illustrated both by simulation and by experimental results with two RTX SCARA type robot arms. Further fast parallel implementation is outlined.

In this paper a new approach to time-optimal and smooth constrained path (continuous path) planning for robot manipulators is presented. A suitable objective function to combine time-optimal and smooth trajectory planning is found. The optimization process involves first obtaining smooth and time-suboptimal joint paths by minimizing the objective function, and then contracting travelling time by scaling the resulting time intervals for time-optimal joint paths so that the resulting velocities or accelerations or joints at some knots of die paths are maximal within their limitations. The resulting joint paths are smooth, time-optimal with optimal velocity profiles and therefore suitable for robotic motion. The feasibility of this method is illustrated by simulation and experimental results with an RTX SCARA type robot.>

A neural network (NN) based regulator for nonlinear, multivariable turbogenerator control is presented. A hierarchical architecture of an NN is proposed for regulator design, consisting of two subnetworks which are used for input-output (I-O) mapping and control, respectively, based on the back-propagation (BP) algorithm. The regulator has the flexibility for accepting more sensory information to cater to multi-input, multioutput systems. Its operation does not require a reference model or inverse system model and it can produce more acceptable control signals than are obtained by using sign of plant errors during training I-O mapping of turbogenerator systems using NNs has been investigated and the regulator has been implemented on a complex turbogenerator system model. Simulation results show satisfactory control performance and illustrate the potential of the NN regulator in comparison with an existing adaptive controller.