Control Of Nonlinear Dynamical Systems Research Articles

Temperature Control using Fuzzy Logic

The aim of the temperature control is to heat the system up todelimitated temperature, afterwardholdit at that temperature in insured manner. Fuzzy Logic Controller (FLC) is best way in which this type of precision control can be accomplished b y controller. During past twenty yearssignificant amount of research using fuzzy logichas done in this field of control of non-linear dynamical system. Here we have developed temperature control system using fuzzy logic.Control theory techniques are the root from which convention controllers are deducted . The desired response of the output can be guarante ed by the feedback controller.

Nonlinear adaptive control using multiple models and dynamic neural networks

The adaptive control of nonlinear dynamic system using multiple models has emerged as a mathematically attractive and practically available method. It can be used to improve the transient response of adaptive control. In this paper, parallel dynamic neural networks (PDNNs) are used to identify the unknown dynamic system. Three kinds of combinations of adaptive model and fixed model are established to set up multiple model adaptive control (MMAC) by using an effective switching scheme. The stability and convergence of MMAC using multiple PDNNs are discussed by means of Lyapunov-like analysis. Considering the unmodeled dynamics, the new learning law ensures that the identification error converges to a bounded zone, and the proposed MMAC with PDNNs can improve the control property greatly. By simulation studies, the results of different combinations of fixed and adaptive models are compared, and the effectiveness of the proposed method can be seen.

Adaptive Control of Nonlinear Discrete-Time Systems by Using OS-ELM Neural Networks

As a kind of novel feedforward neural network with single hidden layer, ELM (extreme learning machine) neural networks are studied for the identification and control of nonlinear dynamic systems. The property of simple structure and fast convergence of ELM can be shown clearly. In this paper, we are interested in adaptive control of nonlinear dynamic plants by using OS-ELM (online sequential extreme learning machine) neural networks. Based on data scope division, the problem that training process of ELM neural network is sensitive to the initial training data is also solved. According to the output range of the controlled plant, the data corresponding to this range will be used to initialize ELM. Furthermore, due to the drawback of conventional adaptive control, when the OS-ELM neural network is used for adaptive control of the system with jumping parameters, the topological structure of the neural network can be adjusted dynamically by using multiple model switching strategy, and an MMAC (multiple model adaptive control) will be used to improve the control performance. Simulation results are included to complement the theoretical results.

Decentralised control of nonlinear dynamical systems

In this paper, we provide a simple novel approach to decentralised control design. Each subsystem of an interconnected interacting system is controlled in a decentralised manner using locally available information related only to the state of that particular subsystem. The method is developed in two steps. In the first step, we define what we call a ‘nominal system’, which consists of ‘nominal subsystems’. The nominal subsystems are assumed to be acted upon by forces that can be computed using only locally available information. We obtain an asymptotically stable control for each nominal subsystem which minimises a suitable, desired norm of the control effort at each instant of time. In the second step, we determine the control force that needs to be applied to the actual (interconnected) subsystem in addition to the control force calculated for the nominal subsystem, so each actual subsystem tracks the state of the controlled nominal subsystem as closely as desired. This additional compensating controller is obtained using the concept of a generalised sliding surface control. The design of this additional controller needs as its input an estimate of the bound on the mismatch between the nominal and the actual subsystems. Examples of non-autonomous, nonlinear, distributed systems are provided that demonstrate the efficacy and ease of implementation of the control method.

Wiener's Polynomial Chaos for the Analysis and Control of Nonlinear Dynamical Systems with Probabilistic Uncertainties [Historical Perspectives

One purpose of the "Historical Perspectives" column is to look back at work done by pioneers in control and related fields that has been neglected for many years but was later revived in the control literature. This column discusses the topic of Norbert Wiener's most cited paper, which proposed polynomial chaos expansions (PCEs) as a method for probabilistic uncertainty quantification in nonlinear dynamical systems. PCEs were almost completely ignored until the turn of the new millennium, when they rather suddenly attracted a huge amount of interest in the noncontrol literature. Although the control engineering community has studied uncertain systems for decades, all but a handful of researchers in the systems and control community have ignored PCEs. The purpose of this column is to present a concise introduction to PCEs, provide an overview of the theory and applications of PCE methods in the control literature, and to consider the question of why PCEs have only recently appeared in the control literature.

MULTIPLE VALUED ITERATIVE DYNAMICS MODELS OF NONLINEAR DISCRETE-TIME CONTROL DYNAMICAL SYSTEMS WITH DISTURBANCE

The study of nonlinear discrete-time control dynamical systems with disturbance is an important topic in control theory. In this paper, we concentrate our efforts to multiple valued iterative dynamical systems, which model the nonlinear discrete-time control dynamical systems with disturbance. After establishing the validity of such modeling, we study the invariant set theory of the multiple valued iterative dynamical systems, including the controllability/reachablity problems of the maximal invariant sets.

Lyapunov stabilizability for nonlinear dynamic control systems on time scales

In this paper we use an appropriate Lyapunov function and derive sufficient conditions for the nonlinear dynamic control system x Δ (t )= A(t)x(t )+ B(t)u(t )+ f (t,x(t),u(t)) ,t ∈ T on a time scale T to be uniformly stabilizable, uniformly exponentially stabilizable, and h− stabilizable. Here, A : T → R n×n is an n×n matrix

Some remarks concerning differential flatness and tangent systems

AbstractThe flatness properties of a nonlinear dynamical control system are completely characterized by its tangent approximation. The flat output of the nonlinear system can be obtained (at least from a theoretical point of view) by solving an integrability problem for the flat outputs of the tangent system. In the present contribution, this approach is used to easily obtain flatness conditions for two special classes of systems, namely systems with one input and systems with one input less than states. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Adaptive fuzzy control for non-linear dynamical systems based on differential flatness theory

A new approach to adaptive fuzzy control for uncertain non-linear dynamical systems, is proposed. The considered class of systems can be written in the Brunovsky (canonical) form after a transformation of their state variables and control input. The resulting control signal is shown to consist of non-linear elements, which in case of unknown system parameters can be approximated using neurofuzzy networks. An adaptation law for the neurofuzzy approximators can be computed using Lyapunov stability analysis. It is shown that the proposed adaptation law assures stability of the closed loop. Simulation experiments on benchmark non-linear dynamical systems are used to evaluate the performance of the proposed flatness-based adaptive fuzzy control scheme.

Adaptive critic design with graph Laplacian for online learning control of nonlinear systems

SUMMARYIn recent years, reinforcement learning (RL) and approximate dynamic programming (ADP) have been widely studied in the community of artificial intelligence and machine learning. As an important class of RL and ADP methods, adaptive critic designs (ACDs) with function approximation have been studied to realize online learning control of nonlinear dynamical systems. However, how to construct efficient feature representations for approximating value functions or policies is still a difficult problem. In this paper, ACDs with graph Laplacian (GL) are proposed by integrating manifold learning methods into feature representations of ACDs. An online learning control algorithm called graph Laplacian dual heuristic programming (GL‐DHP) is presented, and its performance is analyzed both theoretically and empirically. Because of the nonlinear approximation ability of feature representation with GL, the GL‐DHP method has much better performance than previous DHP methods with manually designed neural networks. Simulation results on learning control of a ball and plate system, which is a typical nonlinear dynamical system with continuous state and action spaces, demonstrate the effectiveness of the GL‐DHP method. Copyright © 2012 John Wiley & Sons, Ltd.

A derivative-free distributed filtering approach for sensorless control of nonlinear systems

This article examines the problem of sensorless control for nonlinear dynamical systems with the use of derivative-free Extended Information Filtering (EIF). The system is first subject to a linearisation transformation and next state estimation is performed by applying the standard Kalman Filter to the linearised model. At a second level, the standard Information Filter is used to fuse the state estimates obtained from local derivative-free Kalman filters running at the local information processing nodes. This approach has significant advantages because unlike the EIF (i) is not based on local linearisation of the nonlinear dynamics (ii) does not assume truncation of higher order Taylor expansion terms thus preserving the accuracy and robustness of the performed estimation and (iii) does not require the computation of Jacobian matrices. As a case study a robotic manipulator is considered and a cameras network consisting of multiple vision nodes is assumed to provide the visual information to be used in the control loop. A derivative-free implementation of the EIF is used to produce the aggregate state vector of the robot by processing local state estimates coming from the distributed vision nodes. The performance of the considered sensorless control scheme is evaluated through simulation experiments.

A dynamical inequality for the output of uncertain nonlinear systems

An important task in control theory is to study the limitations of feedback principle in dealing with uncertainties. Although some progresses have been achieved in this area, they are all focused on some special classes of linearly parameterized nonlinear uncertain systems. In this paper, we will present a dynamic inequality for the output process of a quite general class of nonlinear dynamical control systems with nonlinearly parameterized uncertain parameters. This inequality will be established using a stochastic imbedding approach based on a Cramer-Rao inequality for dynamical systems, and will be shown to play a crucial role in investigating the fundamental limitations of the feedback mechanism.

Computation of tight integral input-to-state stability bounds for nonlinear systems

Integral input-to-state stability (iISS) is a robust stability property of interest in the analysis and control of nonlinear dynamical systems affected by external inputs. The computation of tight comparison functions associated with this stability property is useful for assessing robustness in the iISS sense for specific systems. This paper presents a variational characterization of these tight comparison functions, along with an approach to computation via solution of an associated Hamilton–Jacobi–Bellman partial differential equation. A limiting case of relevance to the related input-to-state stability (ISS) property is also considered. An illustrative example highlights the application of this approach.

Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures

Computing globally efficient solutions is a major challenge in optimal control of nonlinear dynamical systems. This work proposes a method combining local optimization and motion planning techniques based on exploiting inherent dynamical systems structures, such as symmetries and invariant manifolds. Prior to the optimal control, the dynamical system is analyzed for structural properties that can be used to compute pieces of trajectories that are stored in a motion planning library. In the context of mechanical systems, these motion planning candidates, termed primitives, are given by relative equilibria induced by symmetries and motions on stable or unstable manifolds of e.g. fixed points in the natural dynamics. The existence of controlled relative equilibria is studied through Lagrangian mechanics and symmetry reduction techniques. The proposed framework can be used to solve boundary value problems by performing a search in the space of sequences of motion primitives connected using optimized maneuvers. The optimal sequence can be used as an admissible initial guess for a post-optimization. The approach is illustrated by two numerical examples, the single and the double spherical pendula, which demonstrates its benefit compared to standard local optimization techniques.

Extended and unscented kalman filters for artificial neural network modelling of a nonlinear dynamical system

Recently, artificial neural networks, especially feedforward neural networks, have been widely used for the identification and control of nonlinear dynamical systems. However, the determination of a suitable set of structural and learning parameter value of the feed-forward neural networks still remains a difficult task. This paper is concerned with the use of extended Kalman filter and unscented Kalman filter based feedforward neural networks training algorithms. The comparisons of the performances of both algorithms are discussed and illustrated using a simulated example. The simulation results show that in terms of mean squared errors, unscented Kalman filter algorithm is superior to the extended Kalman filter and back-propagation algorithms since there are improvements between 2.45–21.48% (for training) and 8.35–29.15% (for testing). This indicates that unscented Kalman filter based feedforward neural networks learning could be a good alternative in artificial neural network models based applications for nonlinear dynamical systems.

Postgraduate Education in Nonlinear Dynamical Systems and Automatic Control in Aerospace

This note deals with the postgraduate educational programmes offered by the Department of Mathematical Modeling (BMSTU) both in English and in Russian. They include the Masters and PhD programmes in control of nonlinear dynamical systems. The programmes are specifically focused on nonlinear control techniques. The students are provided both with the theoretical courses in modern nonlinear control theory and applied courses in control of spacecrafts, aircrafts and mobile robots. Application examples in aerospace control are considered.

Control Simulation Study Based on Recurrent Generalized Congruence Neural Network

In order to meet the real-time demand of neural network control system, the structure and algorithm of self-tuning PID control system based on recurrent generalized congruence neural network(RGCNN) with fast convergence are presented, in which the improved recurrent generalized congruence neural network is adopted for identifier, and the single generalized congruence neuron with three inputs is used as controller. The simulation results of nonlinear dynamical control system show that the proposed RGCNN control system responses quickly and is stable, i.e., the proposed control system based on RGCNN is effective and feasible.

Symmetries, stability, and control in nonlinear systems and networks

This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence analysis tools based on nonlinear contraction theory and virtual dynamical systems. This synergy between structural properties (symmetries) and convergence properties (contraction) is illustrated in the contexts of network motifs arising, for example, in genetic networks, from invariance to environmental symmetries, and from imposing different patterns of synchrony in a network.

Wavelet Fuzzy Neural Networks for Identification and Predictive Control of Dynamic Systems

This paper presents a wavelet fuzzy neural network (WFNN) structure for identifying and controlling nonlinear dynamic systems. The proposed WFNN is constructed on the base of a set of fuzzy rules. Each rule includes a wavelet function in the consequent part of the rules. A training algorithm adopting a gradient descent method is employed to identify the unknown parameters in the WFNN. For the control problem, a WFNN-based predictive control (WFNNPC) law is derived via a generalized predictive performance criterion, and the control algorithm is proven to guarantee the convergence of the WFNNPC controller. The conditions of the stability analysis of the resulting control system are presented based on the Lyapunov stability theorem. Finally, the WFNN is applied in numerical simulations and experiments (identification and control of nonlinear dynamic systems and a physical positioning mechanism). The results confirm the effectiveness of the WFNN.

Functional Evaluation and Rehabilitation Engineering

Life is complex and all about movement, which allows us to interact with the environment and communicate with each other. The human nervous system is capable of performing a simultaneous and integrated control of 100-150 mechanical degrees of freedom of movement in the body via tensions generated by about 700 muscles. In its widest context, movement is carried out by a sensory motor system comprising multiple sensors (visual,auditory, and proprioceptive),multiple actuators (muscles acting on the skeletal system),and an intermediary processor that can be summarized as a multiple-input–multiple-output nonlinear dynamic time-varying control system. This grand control system is capable of responding with remarkable accuracy,speed, appropriateness,versatility, and adaptability to a wide spectrum of continuous and discrete stimuli and conditions and is certainly orders of magnitude more complex and sophisticated than the most advanced robotic systems currently available. In the last decades,a great deal of research has been carried out in the fields of functional evaluation of human performance and rehabilitation engineering. These fields combine knowledge, concepts, and methods from across many disciplines (e.g., biomechanics,neuroscience, and physiology), with the aim of developing apparatuses and methods fort he measurement and analysis of complex sensory motor performance and the ultimate goal of enhancing the execution of different tasks in both healthy people and persons with reduced capabilities from different causes (injury, disease, amputation,and neural degeneration).