Measurements, Models, Systems and Design

531 s.

Stability analysis for periodic solutions of fuzzy shunting inhibitory CNNs with delays

https://advancesindifferenceequations.springeropen.com/articles/10.1186/s13662-019-2321-z#rightslinkWe consider fuzzy shunting inhibitory cellular neural networks (FSICNNs) with time-varying coefficients and constant delays. By virtue of continuation theorem of coincidence degree theory and Cauchy–Schwartz inequality, we prove the existence of periodic solutions for FSICNNs. Furthermore, by employing a suitable Lyapunov functional we establish sufficient criteria which ensure global exponential stability of the periodic solutions. Numerical simulations that support the theoretical discussions are depicted

Existence, Uniqueness, and Stability Analysis of Impulsive Neural Networks with Mixed Time Delays

We study a class of impulsive neural networks with mixed time delays and generalized activation functions. The mixed delays include time-varying transmission delay, bounded time-varying distributed delay, and discrete constant delay in the leakage term. By using the contraction mapping theorem, we obtain a sufficient condition to guarantee the global existence and uniqueness of the solution for the addressed neural networks. In addition, a delay-independent sufficient condition for existence of an equilibrium point and some delay-dependent sufficient conditions for stability are derived, respectively, by using topological degree theory and Lyapunov-Krasovskii functional method. The presented results require neither the boundedness, monotonicity, and differentiability of the activation functions nor the differentiability (even differential boundedness) of time-varying delays. Moreover, the proposed stability criteria are given in terms of linear matrix inequalities (LMI), which can be conveniently checked by the MATLAB toolbox. Finally, an example is given to show the effectiveness and less conservativeness of the obtained results

A non-linear approach to modelling and control of electrically stimulated skeletal muscle

This thesis is concerned with the development and analysis of a non-linear approach to modelling and control of the contraction of electrically stimulated skeletal muscle. For muscle which has lost nervous control, artificial electrical stimulation can be used as a technique aimed at providing muscular contraction and producing a functionally useful movement. This is generally referred to as Functional Electrical Stimulation (FES) and is used in different application areas such as the rehabilitation of paralysed patient and in cardiac assistance where skeletal muscle can be used to support a failing heart. For both these FES applications a model of the muscle is essential to develop algorithms for the controlled stimulation. For the identification of muscle models, real data are available from experiments with rabbit muscle. Data for contraction with constant muscle length were collected from two muscle with very different characteristics. An empirical modelling approach is developed which is suitable for both muscles. The approach is based on a decomposition of the operating space into smaller sub-regions which are then described by local models of simple, possibly linear structure. The local models are blended together by a scheduler, and the resulting non-linear model is called a Local Model Network (LMN). It is shown how a priori knowledge about the system can be used directly when identifying Local Model Networks. Aspects of the structure selection are discussed and algorithms for the identification of the model parameters are presented. Tools of the analysis of Local Model Networks have been developed and are used to validate the models. The problem of designing a controller based on the LMN structure is discussed. The structure of Local Controller Networks is introduced. These can be derived directly from Local Model Networks. Design techniques for input-output and for state feedback controllers, based on pole placement, are presented. Aspects of the generation of optimal stimulation patterns (which are defined as stimulation patterns which deliver the smallest number of pulses to obtain a desired contraction) are discussed, and various techniques to generate them are presented. In particular, it is shown how a control structure can be used to generate optimal stimulation patterns. A Local Controller Network is used as the controller with a design based on a non-linear LMN model of muscle. Experimental data from a non-linear heat transfer process have been collected and are used to demonstrate the basic modelling and control principles throughout the first part of the thesis

Dynamic modelling and control of a flexible manoeuvring system.

In this research a twin rotor multi-input multi-output system (TRMS), which is a laboratory platform with 2 degrees of freedom (DOF) is considered. Although, the TRMS does not fly, it has a striking similarity with a helicopter, such as system nonlinearities and cross-coupled modes. Therefore, the TRMS can be perceived as an unconventional and complex "air vehicle" that poses formidable challenges in modelling, control design and analysis, and implementation. These issues constitute the scope of this research. Linear and nonlinear models for the vertical movement of the TRMS are obtained via system identification techniques using black-box modelling. The approach yields input-output models without a priori defined model structure or specific parameter settings reflecting any physical attributes of the system. Firstly, linear parametric models, characterising the TRMS in its hovering operation mode, are obtained using the potential of recursive least squares (RLS) estimation and genetic algorithms (GAs). Further, a nonlinear model using multi-layer perceptron (MLP) neural networks (NNs) is obtained. Such a high fidelity nonlinear model is often required for nonlinear system simulation studies and is commonly employed in the aerospace industry. Both time and frequency domain analyses are utilised to investigate and develop confidence in the models obtained. The frequency domain verification method is a useful tool in the validation of extracted parametric models. It allows high-fidelity verification of dynamic characteristics over a frequency range of interest. The resulting models are utilized in designing controllers for low frequency vibration suppression, development of suitable feedback control laws for set-point tracking, and design of augmented feedforward and feedback control schemes for both vibration suppression and set-point tracking performance. The modelling approaches presented here are shown to be suitable for modelling complex new generation air vehicles, whose flight mechanics are not well understood. Modelling of the TRMS revealed the presence of resonance modes, which are responsible for inducing unwanted vibrations in the system. Command shaping 11 control strategies are developed to reduce motion and uneven mass induced vibrations, produced by the main rotor during the vertical movement around the lateral axis of the TRMS rig. 2-impulse, 3-impulse and 4-impulse sequence input shapers and Iow-pass and band-stop digital filters are developed to shape the command signals such that the resonance modes are not overly excited. The effectiveness of this concept is then demonstrated in both simulation and real-time experimental environments in terms of level of vibration reduction using power spectral density profiles of the system response. Combinations of intelligent and conventional techniques are commonly used the control of complex dynamic systems. Such hybrid schemes have proved to be efficient and can overcome the deficiencies of conventional and intelligent controllers alone. The current study is confined to the development of two forms of hybrid control schemes that combine fuzzy control and conventional PID compensator for input tracking performance. The two hybrid control strategies comprising conventional PO control plus PlO compensator and PO-type fuzzy control plus PlO compensator are developed and implemented for set-point tracking control of the vertical movement of the TRMS rig. It is observed that the hybrid control schemes are superior to other feedback control strategies namely, PlO compensator, pure PO-type and PI-type fuzzy controllers in terms of time domain system behaviour. This research also witnesses investigations into the development of an augmented feedforward and feedback control scheme (AFFCS) for the control of rigid body motion and vibration suppression of the TRMS. The main goal of this framework is to satisfy performance objectives in terms of robust command tracking, fast system response and minimum residual vibration. The developed control strategies have been designed and implemented within both simulation and real-time environments of the TRMS rig. The employed control strategies are shown to demonstrate acceptable performances. The obtained results show that much improved tracking is achieved on positive and negative cycles of the reference signal, as compared to that without any control action. The system performance with the feedback controller is significantly improved when the feedforward control component is added. This leads to the conclusion that augmenting feedback control with feedforward method can lead to more practical and accurate control of flexible systems such as the TRMS

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

Impulsive Control of Dynamical Networks

Dynamical networks (DNs) consist of a large set of interconnected nodes with each node being a fundamental unit with detailed contents. A great number of natural and man-made networks such as social networks, food networks, neural networks, WorldWideWeb, electrical power grid, etc., can be effectively modeled by DNs. The main focus of the present thesis is on delay-dependent impulsive control of DNs. To study the impulsive control problem of DNs, we firstly construct stability results for general nonlinear time-delay systems with delayed impulses by using the method of Lyapunov functionals and Razumikhin technique. Secondly, we study the consensus problem of multi-agent systems with both fixed and switching topologies. A hybrid consensus protocol is proposed to take into consideration of continuous-time communications among agents and delayed instant information exchanges on a sequence of discrete times. Then, a novel hybrid consensus protocol with dynamically changing interaction topologies is designed to take the time-delay into account in both the continuous-time communication among agents and the instant information exchange at discrete moments. We also study the consensus problem of networked multi-agent systems. Distributed delays are considered in both the agent dynamics and the proposed impulsive consensus protocols. Lastly, stabilization and synchronization problems of DNs under pinning impulsive control are studied. A pinning algorithm is incorporated with the impulsive control method. We propose a delay-dependent pinning impulsive controller to investigate the synchronization of linear delay-free DNs on time scales. Then, we apply the pinning impulsive controller proposed for the delay-free networks to stabilize time-delay DNs. Results show that the delay-dependent pinning impulsive controller can successfully stabilize and synchronize DNs with/without time-delay. Moreover, we design a type of pinning impulsive controllers that relies only on the network states at history moments (not on the states at each impulsive instant). Sufficient conditions on stabilization of time-delay networks are obtained, and results show that the proposed pinning impulsive controller can effectively stabilize the network even though only time-delay states are available to the pinning controller at each impulsive instant. We further consider the pinning impulsive controllers with both discrete and distributed time-delay effects to synchronize the drive and response systems modeled by globally Lipschitz time-delay systems. As an extension study of pinning impulsive control approach, we investigate the synchronization problem of systems and networks governed by PDEs

Time-Delay Systems

Time delay is very often encountered in various technical systems, such as electric, pneumatic and hydraulic networks, chemical processes, long transmission lines, robotics, etc. The existence of pure time lag, regardless if it is present in the control or/and the state, may cause undesirable system transient response, or even instability. Consequently, the problem of controllability, observability, robustness, optimization, adaptive control, pole placement and particularly stability and robustness stabilization for this class of systems, has been one of the main interests for many scientists and researchers during the last five decades