Mixed H∞ and passive control for a class of nonlinear switched systems with average dwell time via hybrid control approach

This paper investigates the mixed H_∞ and passive control problem for a class of nonlinear switched systems based on a hybrid control strategy. To solve this problem, firstly, using the Takagi–Sugeno (T–S) fuzzy model to approximate every nonlinear subsystem, the nonlinear switched systems are modeled as the switched T–S fuzzy systems. Secondly, the hybrid controllers are used to stabilize the switched T–S fuzzy systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. Thirdly, a new performance index is proposed for switched systems. This new performance index can be viewed as the mixed weighted H_∞ and passivity performance. Based on this new performance index, the weighted H_∞ control problem and the passive control problem for switched T–S fuzzy systems via the hybrid control strategy are solved in a unified framework. Together the multiple Lyapunov functions (MLFs) approach with the average dwell time (ADT) technique, new design conditions for the hybrid controllers are obtained. Under these conditions, the closed-loop switched T–S fuzzy systems are globally uniformly asymptotically stable with a prescribed mixed H_∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the obtained results is illustrated by a numerical example.     

H∞ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance

Finite-time stability concerns the boundness of system during a fixed finite-time interval. For switched systems, finite-time stability property can be affected significantly by switching behavior; however, it was neglected by most previous research. In this paper, the problems of finite-time stability analysis and stabilization for switched nonlinear discrete-time systems are addressed. First, sufficient conditions are given to ensure a class of switched nonlinear discrete-time system subjected to norm bounded disturbance finite-time bounded under arbitrary switching, and then the results are extended to H_∞ finite-time boundness of switched nonlinear discrete-time systems. Finally based on the results on finite-time boundness, the state feedback controller is designed to H_∞ finite-time stabilize a switched nonlinear discrete-time system. A numerical design example is given to illustrate the proposed results within this paper.     

Vector incremental L2-gain and incremental stability for switched nonlinear systems

This paper studies vector incremental L₂-gain and incremental stability for switched nonlinear systems using individual incremental gains and multiple storage functions. Firstly, a vector incremental L₂-gain concept for switched nonlinear systems is proposed. Each subsystem is not required to have incremental L₂-gain, but it has its own incremental L₂-gain and the related storage function, when it is active. The transformation of “energy” from the active subsystem to each inactive subsystem is characterized by cross-supply rates. Then, we show that a switched nonlinear system who has vector incremental L₂-gain can be incrementally stabilized under some constraints on the energy change of inactive subsystems. Secondly, a state-dependent switching law is designed to achieve vector incremental L₂-gain, even if each subsystem does not have incremental L₂-gain in the classic sense. Thirdly, each switched system is not required to have vector incremental L₂-gain, but the feedback interconnection of switched nonlinear systems is incrementally stabilized by the design of a composite switching law. The switching law allows the two switched systems switch asynchronously. Two examples are provided to verify the effectiveness of the proposed method.     

Backstepping-based decentralized adaptive neural H∞ tracking control for a class of large-scale nonlinear interconnected systems

The decentralized tracking control methods for large-scale nonlinear systems are investigated in this paper. A backstepping-based robust decentralized adaptive neural H_∞ tracking control method is addressed for a class of large-scale strict feedback nonlinear systems with uncertain disturbances. Under the condition that the nonlinear interconnection functions in subsystems are unknown and mismatched, the decentralized adaptive neural network H_∞ tracking controllers are designed based on backstepping technology. Neural networks are used to approximate the packaged multinomial including the unknown interconnections and nonlinear functions in the subsystems as well as the derivatives of the virtual controls. The effect of external disturbances and approximation errors is attenuated by H_∞ tracking performance. Whether the external disturbances occur or not, the output tracking errors of the close-loop system are guaranteed to be bounded. A practical example is provided to show the effectiveness of the proposed control approach.     

H∞ filtering for nonlinear systems via neural networks

A novel H_∞ filter design methodology has been presented for a general class of nonlinear systems. Different from existing nonlinear filtering design, the nonlinearities are approximated using neural networks, and then are modeled based on linear difference inclusions, which makes the structure of the desired filter simpler and parameter turning easier and has the advantages of guaranteed stability, numeral robustness, bounded estimation accuracy. A unified framework is established to solve the addressed H_∞ filtering problem by exploiting linear matrix inequality (LMI) approach. A numerical example shows that the filtering error systems will work well against bounded error between a nonlinear dynamical system and a multilayer neural network.     

Input-to-state stability of switched stochastic delayed systems with Lévy noise

This paper focuses on input-to-state stability of a class of switched stochastic delayed systems which are drived by Lévy noise. By multiple Lyapunov function and average dwell time approach, the sufficient conditions of the ψ^λ(t)-weighted input-to-state stability can be obtained if all the subsystems are input-to-state stable. Then utilizing comparison principle and the method of constant variation, the sufficient criteria of the e^λt-weighted input-to-state stability of the switched stochastic delayed systems containing both input-to-state stable subsystems and non-input-to-state stable subsystems can also be derived. Finally, an example is given to illustrate the effectiveness of the proposed results.     

Incremental H∞ performance for a class of stochastic switched nonlinear systems

In this paper, we investigate the incremental H_∞ performance problem for a class of stochastic switched nonlinear systems by using a state-dependent switching law and the maximum and minimum dwell time approach. By resorting to the state-dependent switching law, some sufficient conditions are provided to cope with the incremental H_∞ performance problem, which can be applied even if all subsystems are unstable. Then, based on the maximum and minimum dwell time scheme, the incremental H_∞ performance problem to be solvable is derived for two cases: one is all subsystems are incrementally globally asymptotically stable in the mean(IGASiM), another is both IGASiM subsystems and unstable subsystems coexist. When all subsystems are IGASiM, the stochastic switched nonlinear system is IGASiM and possesses a incremental L₂-gain under given conditions. When both IGASiM subsystems and unstable subsystems coexist, if the activation time ratio between IGASiM subsystems and unstable ones is not less than a specified constant, the sufficient conditions for the incremental H_∞ performance of the stochastic switched nonlinear system are given. Two numerical examples are given to illustrate the validity of methods proposed.     

Adaptive neural control for nonlinear switched systems with improved MDADT and its applications

In this paper, a new framework of the robust adaptive neural control for nonlinear switched stochastic systems is established in the presence of external disturbances and system uncertainties. In the existing works, the design of robust adaptive control laws for nonlinear switched systems mainly relies on the average dwell time method, while the design and analysis based on the model-dependent average dwell time (MDADT) method remains a challenge. An improved MDADT method is developed for the first time, which greatly relaxes the requirements of Lyapunov functions of any two subsystems. Benefiting from the improved MDADT, a switched disturbance observer for discontinuous disturbances is proposed, which realizes the real-time gain adjustment. For known and unknown piecewise continuous nonlinear functions, a processing method based on the tracking differentiator and the neural network is proposed, which skillfully guarantees the continuity of the control law. The theoretical proof shows that the semiglobal uniform ultimate boundedness of all closed-loop signals can be guaranteed under switching signals with MDADT property, and simulation results of the longitudinal maneuvering control at high angle of attack are given to further illustrate the effectiveness of the proposed framework.     

Adaptive fractional order sliding mode controller with neural estimator

In this study, an adaptive fractional order sliding mode controller with a neural estimator is proposed for a class of systems with nonlinear disturbances. Compared with traditional sliding mode controller, the new proposed fractional order sliding mode controller contains a fractional order term in the sliding surface. The fractional order sliding surface is used in adaptive laws which are derived in the framework of Lyapunov stability theory. The bound of the disturbances is estimated by a radial basis function neural network to relax the requirement of disturbance bound. To investigate the effectiveness of the proposed adaptive neural fractional order sliding mode controller, the methodology is applied to a Z-axis Micro-Electro-Mechanical System (MEMS) gyroscope to control the vibrating dynamics of the proof mass. Simulation results demonstrate that the proposed control system can improve tracking performance as well as parameter identification performance.     

Semi-globally/globally stable adaptive NN backstepping control for uncertain MIMO systems with tracking accuracy known a priori

This paper focuses on the problem of direct adaptive neural network (NN) tracking control for a class of uncertain nonlinear multi-input/multi-output (MIMO) systems by employing backstepping technique. Compared with the existing results, the outstanding features of the two proposed control schemes are presented as follows. Firstly, a semi-globally stable adaptive neural control scheme is developed to guarantee that the ultimate tracking errors satisfy the accuracy given a priori, which cannot be carried out by using all existing adaptive NN control schemes. Secondly, we propose a novel adaptive neural control approach such that the closed-loop system is globally stable, and in the meantime the ultimate tracking errors also achieve the tracking accuracy known a priori, which is different from all existing adaptive NN backstepping control methods where the closed-loop systems can just be ensured to be semi-globally stable and the ultimate tracking accuracy cannot be determined a priori by the designers before the controllers are implemented. Thirdly, the main technical novelty is to construct three new nth-order continuously differentiable switching functions such that multiswitching-based adaptive neural backstepping controllers are designed successfully. Fourthly, in contrast to the classic adaptive NN control schemes, this paper adopts Barbalat׳s lemma to analyze the convergence of tracking errors rather than Lyapunov stability theory. Consequently, the accuracy of ultimate tracking errors can be determined and adjusted accurately a priori according to the real-world requirements, and all signals in the closed-loop systems are also ensured to be uniformly ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness and merits of the two proposed adaptive NN control schemes.     

Backstepping-based decentralized bounded-H∞ adaptive neural control for a class of large-scale stochastic nonlinear systems

In this paper, a novel decentralized adaptive neural control approach based on the backstepping technique is proposed to design a decentralized H_∞ adaptive neural controller for a class of stochastic large-scale nonlinear systems with external disturbances and unknown nonlinear functions. RBF neural networks are utilized to approximate the packaged unknown nonlinearities. A novel concept with regard to bounded-H_∞ performance is proposed. It can be applied to solve an H_∞ control problem for a class of stochastic nonlinear systems. The constant terms appeared in stability analysis are dealt with by using Gronwall inequality, so that H_∞ performance criterion is satisfied. The assumption that the approximation errors of neural networks must be square-integrable in some literature can be eliminated. The design process for decentralized bounded-H_∞ controllers is given. The proposed control scheme guarantees that all the signals in the resulting closed-loop large-scale system are uniformly ultimately bounded in probability, and each subsystem possesses disturbance attenuation performance for external disturbances. Finally, the simulation results are provided to illustrate the effectiveness and feasibility of the proposed approach.     

The improvement of the hardware design of artificial CNN and a fast algorithm of CNN component detector

Cellular neural network (CNN) is a type of analog, nonlinear, real-time parallel processing network. The paper studies an implementation of the integrated operational amplifier used in the design of an artificial CNN. It improves the implementation of CNN proposed by Chua. A 4 x 4 artificial CNN circuit is designed, obtaining a better characteristic of a CNN connected component detector. Finally, a fast algorithm for a CNN component detector is given which proves to be very simple and quite convenient.     

Some network thermodynamic models of coupled,dynamic physiological systems

A network thermodynamic method is presented which utilizes SPICE2, a computer program for simulating nonlinear electrical circuits, to model and simulate a number of nonlinear, dynamic physiological systems. Ordinary circuit diagrams are presented along with bond graph representations to facilitate translation into the simulation language. Examples discussed are a compartmental model of sodium flow in frog skin, coupled salt and volume flow in kidney proximal tubule and a cancer chemotherapeutic agent's permeation and metabolism in a cancer cell.     

Characteristics of small grid-controlled hot-cathode mercury arcs or thyratrons

The principle of the grid-controlled arc or thyratron is briefly described and the norminal ratings as regards filament current, maximum plate current etc. of four important thyratrns are given in table form. Methods of measuring the grid current, critical grid potential, etc., with D.C. power supply are given along with the results obtained on the General Electric Company thyratrons FG-₁₇, FG-₂₇ and FG-₆₇. Characteristics obtained with A.C. power supply are also shown for these thyratrons and some of the relative advantages of the “phase-shift” and the “critical potential” methods of control are discussed when used in connection with photoelectric cell circuits. The A.C. measurements seem to show that a time of 10^?3 second is required to start a thyratron. An amplifier circuit is shown by which it is theoretically possible to control a thyratron circuit using an input current to the amplifier of 10^?11 ampere.     

Optimal design of probabilistically robust PIλDμ controller to improve small signal stability of PV integrated power system

With the rapidly increasing penetration level of power generated by large scale photovoltaic (PV) units into the power systems, the effect of the variable output power of the PV unit on the stability of the system cannot be ignored. This paper presents a mathematical approach to study the effect of high infiltration of PV power plant on the small signal stability of a power network and design of optimal fractional order PID (PI^λD^μ) controller for improving the probabilistic small signal stability of the power systems, taking into consideration the uncertainty of system operating conditions. Due to the probabilistic characteristics of large scale PV power generation, deterministic analysis approaches are not able to fully reveal the impact of high-level PV penetration. At first, this work introduces the main module and mathematical modeling of the large scale PV generation jointly with the single-machine infinite-bus power system. In the following, the paper proposes an efficient method that tunes power system stabilizer (PSS) to have the robustness for damping electro-mechanical oscillations in power systems with incorporated random PV power. For this reason, a robust PSS based on hybridization of PI^λD^μ controller and Non-dominated Sorting Genetic Algorithm (NSGAII) is designed. This paper targets at finding the optimal gain scheduling of the PI^λD^μ through the use of the advanced heuristic optimization technique with two objective functions in PV-grid connected systems. The performance of the proposed NSGAII-based PI^λD^μ controller (NSGAII- PI^λD^μ) under different solar irradiation, temperature conditions and disturbances is tested. Simulation results illustrate that the model presented can be used in designing of essential controllers for large scale PV power plant.     

Iterative learning control for fractional-order multi-agent systems

In this paper, we apply iterative learning control to both linear and nonlinear fractional-order multi-agent systems to solve consensus tacking problem. Both fixed and iteration-varying communicating graphs are addressed in this paper. For linear systems, a PD^α-type update law with initial state learning mechanism is introduced by virtue of the memory property of fractional-order derivative. For nonlinear systems, a D^α-type update law with forgetting factor and initial state learning is designed. Sufficient conditions for both linear and nonlinear systems are established to guarantee all agents achieving the asymptotic output consensus. Simulation examples are provided to verify the proposed schemes.     

Biorthogonal wavelet trees in the classification of embedded signal classes for intelligent sensors using machine learning applications

The paper deals with a method of constructing orthonormal bases of coordinates which maximize, through redundant dictionaries (frames) of biorthogonal bases, a class separability index or distances among classes. The method proposes an algorithm which consists of biorthogonal expansions over two redundant dictionaries. Embedded classes are often present in multiclassification problems. It is shown how the biorthogonality of the expansion can really help to construct a coordinate system which characterizes the classes. The algorithm is created for training wavelet networks in order to provide an efficient coordinate system maximizing the Cross Entropy function between two complementary classes. Sine and cosine wavelet packets are basis functions of the network. Thanks to their packet structure, once selected the depth of the tree, an adaptive number of basis functions is automatically chosen. The algorithm is also able to carry out centering and dilation of the basis functions in an adaptive way. The algorithm works with a preliminary extracted feature through shrinkage technique in order to reduce the dimensionality of the problem. In particular, our attention is pointed out for time-frequency monitoring, detection and classification of transients in rail vehicle systems and the outlier problem. In the former case the goal is to distinguish transients as inrush current and no inrush current and a further distinction between the two complementary classes: dangerous inrush current and no dangerous inrush current. The proposed algorithm is used on line in order to recognize the dangerous transients in real time and thus shut-down the vehicle. The algorithm can also be used in a general application of the outlier detection. A similar structure is used in developed algorithms which are currently integrated in the inferential modeling platform of the unit responsible for Advanced Control and Simulation Solutions within ABB's (Asea Brown Boveri) industry division. It is shown how impressive and rapid performances are achieved with a limited number of wavelets and few iterations. Real applications using real measured data are included to illustrate and analyze the effectiveness of the proposed method.     

Decentralized event-triggered H∞ control for switched systems with network communication delay

This paper is concerned with the decentralized event-triggered H_∞ control for switched systems subject to network communication delay and exogenous disturbance. Depending on different physical properties, the system state is divided into multiple communication channels and decentralized sensors are employed to collect signals on these channels. Furthermore, decentralized event-triggering mechanisms (DETMs) with a switching structure are proposed to determine whether the sampled data needs to be transmitted. In particular, an improved data buffer is presented which can guarantee more timely utilization of the sampled data. Then, with the proposed DETMs and data buffer, a time-delay closed-loop switched system is developed. After that, sufficient conditions are presented to guarantee the H_∞ performance of the closed-loop switched system by utilizing the average dwell time and piecewise Lyapunov functional method. Since the event-triggered instants and the switching instants may stagger with each other, the influence of their coupling on the H_∞ performance analysis is systematically discussed. Subsequently, sufficient conditions for designing the event-triggered state feedback controller gains are provided. Finally, numerical simulations are given to verify the effectiveness of the proposed method.     

Overdamped and Underdamped Linear Dynamical Systems

Conditions are given for underdamped or overdamped linear dynamical systems in terms of loop matrix parameters, (√(C)R√(C)g,g)² ? 4(√(C)L√(C)g,g) for all [boxV]g[boxV] = 1, g ∈ H. These criteria are looked upon as natural generalizations of the elementary one-loop RLC series scalar criteria (R/2L)² ? 1/LC, when written in the more suggestive form: (√(C)R√(C))² ? 4√(C)L√(C). A simplified test for determining dynamical systems with all complex natural modes or all real modes are presented with additional comments.