An unstable dynamical system associated with model reference adaptive control

It is shown that a certain system of differential equations of importance to the proof of stability of the adaptive system proposed in [1], admit unbounded solutions. The implication of this result is that a much more elaborate argument than heretofore thought necessary is required to prove that the adaptive system of [1] is stable.     

Fuzzy-identification-based adaptive backstepping control using a self-organizing fuzzy system

In this paper, a fuzzy-identification-based adaptive backstepping control (FABC) scheme is proposed. The FABC system is composed of a backstepping controller and a robust controller. The backstepping controller, which uses a self-organizing fuzzy system (SFS) with the structure and parameter learning phases to on-line estimate the controlled system dynamics, is the principal controller, and the robust controller is designed to dispel the effect of approximation error introduced by the SFS. The developed SFS automatically generates and prunes the fuzzy rules by the proposed structure adaptation algorithm and the parameters of the fuzzy rules and membership functions tunes on-line in the Lyapunov sense. Thus, the overall closed-loop FABC system can guarantee that the tracking error and parameter estimation error are uniformly ultimately bounded; and the tracking error converges to a desired small neighborhood around zero. Finally, the proposed FABC system is applied to a chaotic dynamic system to show its effectiveness. The simulation results verify that the proposed FABC system can achieve favorable tracking performance even with unknown controlled system dynamics.     

非线性系统的自组织多模型自适应逆控制

针对离散时间非线性系统,在分析基于自组织映射神经网络的多模型控制方法的基础上,提出了一种自组织多模型直接逆控制方法.并分析了控制误差的有界性.进一步,借鉴参数空间多模型方法的切换一自适应策略,在固定模型的基础上增加一个参数可调节的自适应逆模型.提高了稳态控制性能.仿真实例表明,对于变化较快的信号,自组织多模型直接逆控制器和自组织多模型自适应逆控制器都能进行有界跟踪,对于稳态信号,自组织多模型自适应逆控制器还能进行渐近跟踪.     

Parallel, self-organizing, hierarchical neural networks

A new neural-network architecture called the parallel, self-organizing, hierarchical neural network (PSHNN) is presented. The new architecture involves a number of stages in which each stage can be a particular neural network (SNN). At the end of each stage, error detection is carried out, and a number of input vectors are rejected. Between two stages there is a nonlinear transformation of input vectors rejected by the previous stage. The new architecture has many desirable properties, such as optimized system complexity (in the sense of minimized self-organizing number of stages), high classification accuracy, minimized learning and recall times, and truly parallel architectures in which all stages operate simultaneously without waiting for data from other stages during testing. The experiments performed indicated the superiority of the new architecture over multilayered networks with back-propagation training.     

Minimax program control for the approach process in a two-level hierarchical discrete dynamical system

We consider a dynamical system consisting of three objects whose dynamics is given by vector linear discrete recurrent equations. The system contains two levels of managerial decision making, basic and secondary, that have different operational criteria and are united by informational and managerial connections defined in advance. For the dynamical system in question, we propose a mathematical formalization in the form of solving a multistage problem of two-level hierarchical minimax program control over the approach process with incomplete information and give a general scheme for its solution.     

An adaptive predictive control system for random signals

A predictive system was described by Chestnut, et al. [4]. The purpose of this work is to increase the types of plants which can be controlled by such systems by making the fast time model adaptive, and to experimentally compare the random signal behavior of the resultant system with various other types of controllers. These controllers include a relay controller adjusted to switch when the error is zero, and a linear controller. According to the criteria of the minimum integral of the absolute error, the adaptive predictive controller delivered the most satisfactory-responses for second- and third-order systems.     

Comparisons of practical hierarchical control methods for interconnected dynamical systems

This paper gives a brief survey of possible methods which can be used for the practical control of large interconnected dynamical systems. The development is in two parts, i.e. optimal methods and suboptimal methods. In the first part, a brief outline is given of infeasible methods like Goal co-ordination and the Takara-Sage algorithm. In the general study of infeasible methods, Tamura's three-level method, Tamura's time-delay method and Pearson's pseudo-model co-ordination method are also included. It is seen that both the algorithms of Tamura as well as the Takahara-Sage method are particularly suited to systems with slow dynamics whereas Pearson's pseudo-model co-ordination method could be used advantageously for systems with fast dynamics.A practical example is then given of optimal traffic control using an infeasible method, in this case the time-delay method of Tamura. The main conclusion to emerge from this part is that optimal methods will require multiple processors for on-line dynamic optimization although for systems with slow dynamics like the traffic example, fairly large problems could nevertheless be tackled using only one processor.There are certain classes of systems for which it may be possible to obtain virtually optimal control using only a single processor even when the number of subsystems is very large. One such class of problems is of serially connected dynamical systems. In the second part of this paper a suboptimal approach is described for the control of serial systems and the method is demonstrated using river pollution as an example. Finally, a new method is developed which enables a significant improvement to be made for serial systems with conflicts between the subsystems and an example illustrates this approach.     

Indirect adaptive self-organizing RBF neural controller design with a dynamical training approach

This study proposes an indirect adaptive self-organizing RBF neural control (IASRNC) system which is composed of a feedback controller, a neural identifier and a smooth compensator. The neural identifier which contains a self-organizing RBF (SORBF) network with structure and parameter learning is designed to online estimate a system dynamics using the gradient descent method. The SORBF network can add new hidden neurons and prune insignificant hidden neurons online. The smooth compensator is designed to dispel the effect of minimum approximation error introduced by the neural identifier in the Lyapunov stability theorem. In general, how to determine the learning rate of parameter adaptation laws usually requires some trial-and-error tuning procedures. This paper proposes a dynamical learning rate approach based on a discrete-type Lyapunov function to speed up the convergence of tracking error. Finally, the proposed IASRNC system is applied to control two chaotic systems. Simulation results verify that the proposed IASRNC scheme can achieve a favorable tracking performance.     

Decentralized control scheme for adaptive earthworm locomotion using continuum-model-based analysis

Crawling locomotion has been the focus of attention in the field of robotics because various applications of it are expected. However, the design methodologies for crawling robots, which can be applied in various environments, are not yet established. Therefore, we considered an earthworm as our model and employed an unconventional approach: we analyzed the motion of the earthworm with a continuum model and derived an optimal force distribution for its efficient propulsion, based on which we proposed an autonomous decentralized control scheme. The validity of the proposed control scheme was confirmed via simulations.     

Identification and control of dynamical systems using the self-organizing map.

In this paper, we introduce a general modeling technique, called vector-quantized temporal associative memory (VQTAM), which uses Kohonen's self-organizing map (SOM) as an alternative to multilayer perceptron (MLP) and radial basis function (RBF) neural models for dynamical system identification and control. We demonstrate that the estimation errors decrease as the SOM training proceeds, allowing the VQTAM scheme to be understood as a self-supervised gradient-based error reduction method. The performance of the proposed approach is evaluated on a variety of complex tasks, namely: i) time series prediction; ii) identification of SISO/MIMO systems; and iii) nonlinear predictive control. For all tasks, the simulation results produced by the SOM are as accurate as those produced by the MLP network, and better than those produced by the RBF network. The SOM has also shown to be less sensitive to weight initialization than MLP networks. We conclude the paper by discussing the main properties of the VQTAM and their relationships to other well established methods for dynamical system identification. We also suggest directions for further work.     

Neural network adaptive control for nonlinear nonnegative dynamical systems

Nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in engineering and life sciences and typically involve the exchange of nonnegative quantities between subsystems or compartments wherein each compartment is assumed to be kinetically homogeneous. In this paper, we develop a full-state feedback neural adaptive control framework for adaptive set-point regulation of nonlinear uncertain nonnegative and compartmental systems. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains. In addition, the neural adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state-space for nonnegative initial conditions.     

An adaptive system for process control using genetic algorithms

Researchers at the U.S. Bureau of Mines have developed adaptive process control systems in which genetic algorithms (GAs) are used to augment fuzzy logic controllers (FLCs). GAs are search algorithms that rapidly locate near-optimum solutions to a wide spectrum of problems by modeling the search procedures of natural genetics. FLCs are rule based systems that efficiently manipulate a problem environment by modeling the “rule-of-thumb” strategy used in human decision making. Together, GAs and FLCs possess the capabilities necessary to produce powerful, efficient, and robust adaptive control systems. To perform efficiently, such control systems require a control element to manipulate the problem environment, an analysis element to recognize changes in the problem environment, and a learning element to adjust to the changes in the problem environment. Details of an overall adaptive control system are discussed. A specific laboratory acid-base pH system is used to demonstrate the ideas presented.     

Robust adaptive control of a bio-inspired robot manipulator using bat algorithm

This paper proposes a novel adaptive fractional order PID sliding mode controller (AFOPIDSMC) using a Bat algorithm to control of a Caterpillar robot manipulator. A fractional order PID (FOPID) control is applied to improve both trajectory tracking and robustness. Sliding mode controller (SMC) is one of the control methods which provides high robustness and low tracking error. Using hybridization, a new combined control law is proposed for chattering reduction by means of FOPID controller and high trajectory tracking through using SMC. Then, an adaptive controller design motivated from the SMC is applied for updating FOPID parameters. A metaheuristic approach, the Bat search algorithm based on the echolocation behavior of bats is applied for optimal design of the Caterpillar robot in order to tune the parameter AFOPIDSMC controllers (BA-AFOPIDSMC). To study the effectiveness of Bat algorithm, its performance is compared with five other controllers such as PID, FOPID, SMC, AFOPIDSMC and PSO-AFOPIDSMC. The stability of the AFOPIDSMC controller is proved by Lyapunov theory. Numerical simulation results completely indicate the advantage of BA-AFOPIDSMC for trajectory tracking and chattering reduction.     

Hierarchical control structure of a multilegged robot for environmental adaptive locomotion

We propose a biomimetic, two-layered, hierarchical control structure for adaptive locomotion of a hexapod robot. In this structure, the lower layer consists of six uniform subsystems. Each subsystem interacts locally with its neighboring subsystems, and autonomously controls its own leg movements according to the weighted sum of three basic vector fields that represent the three basic motion patterns of the robot body. The upper-layer controller decides the intended body movement, and sends the lower-layer controllers three variables as the weights of each basic vector field. This approach greatly reduces the communication between the two layers, and contributes to real-time adaptive locomotion. 3D dynamic simulations, as well as experiments with a real modularized hexapod robot, show the effectiveness of this hierarchical structure. This work was presented, in part, at the Sixth International Symposium on Artificial Life and Robotics, Tokyo, Japan, January 15–17, 2001     

AH-questionnaire: An adaptive hierarchical questionnaire for learning styles

One of the main concerns when providing learning style adaptation in Adaptive Educational Hypermedia Systems is the number of questions the students have to answer. Most of the times, adaptive material available will discriminate among a few categories for each learning style dimension. Consequently, it is only needed to take into account the general tendency of the student and not the specific score obtained in each dimension. In this context, we present AH-questionnaire, a new approach to minimize the number of questions needed to classify student Learning Styles. Based on the Felder-Silverman’s Learning Style Model, it aims at classifying students into categories in spite of providing precise scores. The results obtained in a case study with 330 students are very promising. It was possible to predict students’ learning style preference with high accuracy and only a few questions.     

Mapping and hierarchical self-organizing neural networks for VLSIplacement

We have developed mapping and hierarchical self-organizing neural networks for placement of very large scale integrated (VLST) circuits. In this paper, we introduce MHSO and MHSO2 as two versions of mapping and hierarchical self-organizing network (MHSO) algorithms. By using the MHSO, each module in the placement wins the competition with a probability density function that is defined according to different design styles, e.g., the gate arrays and standard cell circuits. The relation between a placement carrier and movable modules is met by the algorithm's ability to map an input space (somatosensory source) into an output space where the circuit modules are located, MHSO2 is designed for macro cell circuits. In this algorithm, the shape and dimension of each module is simultaneously considered together with the wire length by a hierarchical order. In comparison with other conventional placement approaches, the MHSO algorithms have shown their distinct advantages. The results for benchmark circuits so far obtained are quite comparable to simulated annealing (SA), but the computation time is about eight-ten times faster than with SA.     

Clustering properties of hierarchical self-organizing maps

A multilayer hierarchical self-organizing map (HSOM) is discussed as an unsupervised clustering method. The HSOM is shown to form arbitrarily complex clusters, in analogy with multilayer feedforward networks. In addition, the HSOM provides a natural measure for the distance of a point from a cluster that weighs all the points belonging to the cluster appropriately. In experiments with both artificial and real data it is demonstrated that the multilayer SOM forms clusters that match better to the desired classes than do direct SOM's, classical k-means, or Isodata algorithms.     

Nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors

This paper exploits a nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors subject to thrust constraint and inertial parameter uncertainty to accomplish trajectory tracking missions. Because of under‐actuated nature of the quadrotor, a hierarchical control strategy is available; and position and attitude loop controllers are synthesized according to adaptive sliding mode control projects, where adaptive updates with projection algorithm are developed to ensure bounded estimations for uncertain inertial parameters. Further, during the position loop controller development, an auxiliary dynamic system is introduced, and selection criteria for controller parameters are established to maintain the thrust constraint and to ensure the non‐singular requirement of command attitude extraction. It has demonstrated that, the asymptotically stable trajectory tracking can be realized by the asymptotically stable cascaded closed‐loop system and auxiliary dynamic system. Simulations validate and highlight the proposed control approach. Copyright © 2016 John Wiley & Sons, Ltd.     

On-line tuning of fuzzy-neural network for adaptive control ofnonlinear dynamical systems

The adaptive fuzzy-neural controllers tuned online for a class of unknown nonlinear dynamical systems are proposed. To approximate the unknown nonlinear dynamical systems, the fuzzy-neural approximator is established. Furthermore, the control law and update law to tune on-line both the B-spline membership functions and the weighting factors of the adaptive fuzzy-neural controller are derived. Therefore, the control performance of the controller is improved. Several examples are simulated in order to confirm the effectiveness and applicability of the proposed methods in this paper.