Self-suppression of limit cycles in non-linear sampled-data systems with transportation lag†

This paper extends the principle of self-suppression of oscillations employed in continuous systems to non-linear sampled-data systems with transportation lag. The principle is based on the proper design of a. minor feedback loop to generate an oscillation with the desired frequency and amplitude. The type of response of the system is shown to depend entirely on the gain of the inner feedback path. Further it is shown that larger values of delay require larger gains to be employed in the inner feedback path to suppress the inherent oscillation. The results clearly indicate that by proper adjustment of the gain a response said to be optimum in regard to Borne performance index can be obtained.     

On the determination of limit cycles in relay control systems with additional saturation type non-linear elements†

Exact and approximate methods of determination of limit cycles in a relay control system including an actuator with PI transfer function and limited output are given. No restrictions are imposed on the order of the plant transfer function. The stability of the limit cycles may be checked using one of the well-known methods, using the describing function concept. With the help of an example it is indicated that the methods suggested give reliable results in eases where the use of the conventional describing function fails.     

Generalized Lyapunov function for Liénard-type non-linear systems

A systematic procedure for the derivation of Lyapunov functions for non-linear systems given by Liénard's equation is proposed. To establish the procedure, a similar system is derived first, by multiplying both sides of the system by a transformation matrix. Then, stability criteria for the system, which introduce a generalized Lyapunov function, are presented. The Lyapunov function obtained is used to estimate the stability region of the system. The superiority of the proposed method is illustrated by applying it to a single-machine system, which includes the variable damping effect, comparing the results with those obtained by conventional methods.     

On infinitesimal transformations and limit cycles†

A necessary condition for the existence of the limit cycle(s) of a second-order autonomous system, which can be reduced to a first-order system invariant under an infinitesimal transformation, is discussed in this paper. A method for obtaining an expression which will always include any limit cycle of the system that may exist is also shown.     

混沌的Liénard系统的鲁棒同步及应用

应用非线性系统的自适应控制技术及非自治动力系统的稳定性理论,给出了具有外界干扰的二阶混沌的Léinard系统的鲁棒同步的充分条件,并将所获结果应用到控制混沌的Duffing振子.最后,计算机数值模拟表明了所获理论结果的正确性及控制方法的有效性.     

Solvability of infinite systems of singular integral equations in Fréchet space of continuous functions

The aim of this paper is to show how some measures of noncompactness in the Fréchet space of continuous functions defined on an unbounded interval can be applied to an infinite system of singular integral equations. The results obtained generalize and improve several ones.     

A feedback control synthesis for the Rayleigh-Bénard convection by means of mode reduction

A state feedback controller is derived to suppress the Rayleigh-Bénard convection in a finite domain by adjusting heat flux profile at the bottom of the system under the constraint of constant heat input. The Karhunen-Loe've Galerkin procedure is employed to convert the Boussinesq equation to a reduced order model, from which an extended Kalman filter and the state optimal feedback controller are constructed. The number of measurement locations employed in the Kalman filter determines the number of reliable eigenmodes to be adopted in the feedback controller. With the feedback controller constructed by employing only the reliable dominant eigenmodes, it is found that there exists a threshold Rayleigh number beyond which the suppressed state becomes unstable to evolve to a new stationary convection state. The linear stability analysis is used to investigate the effect of a number of eigenmodes employed in the feedback controller on the threshold Rayleigh number.     

Approximate controllability of stochastic differential systems driven by a Lévy process

In this paper, we are concerned with the approximate controllability of stochastic differential systems driven by Teugels martingales associated with a Lévy process. We derive the approximate controllability with the coefficients in the system satisfying some non-Lipschitz conditions, which include classic Lipschitz conditions as special cases. The desired result is established by means of standard Picard’s iteration.     

Thermodynamic description of the Ag–(Ca,Li, Zn) and Ca–(In,Li) binary systems

Critical evaluations and thermodynamic modeling of the Ag-(Ca, Li, and Zn) and Ca-(In, Li) binary systems are presented. Thermodynamic optimization of the Ag–Li binary system was carried out in the present work at first. Thermodynamic re-optimizations of the Ag–Ca, Ag–Zn, Ca–In and Ca–Li binary systems were carried out in the present work, which presents improvements in comparison with previous works. The Modified Quasichemical Model in the Pair Approximation (MQMPA) was used for the liquid solution; this model is particularly suited for liquid which exhibits a high degree of short-range order. The intermetallic compounds are modeled with the Compound Energy Formalism (CEF), and terminal solid solutions are modeled with Bragg–Williams model (BWM) with sub-regular solution approximation. All available and reliable experimental data are reproduced within experimental error limits. A self-consistent thermodynamic database was constructed for the Ag–(Ca, Li, and Zn) and Ca–(In, Li) binary systems, which as a part of the thermodynamic database of the Mg–X (X: Ag, Ca, In, Li, Na, Sn, Sr, and Zn) multi-component system shall facilitate the development of Mg alloys for practical industrial purposes.     

pth moment asymptotic stability of stochastic delayed hybrid systems with Lévy noise

The problem of pth moment asymptotic stability analysis is considered for stochastic delayed hybrid systems with Lévy noise. By virtue of Itô’s formula and M-matrix theories, we propose some sufficient conditions to guarantee the asymptotic stability and exponential stability of the system. The criterion of mean square asymptotic stability is derived as well for delayed neural networks with Lévy noise. A numerical example is provided to show the usefulness of the proposed asymptotic stability criterion.     

Predictive control,embedded cyberphysical systems and systems of systems – A perspective

Today’s world is changing rapidly due to advancements in information technology, computation and communication. Actuation, communication, sensing, and control are becoming ubiquitous. These technological advancements have led to the widespread availability of information and the possibility to connect systems in unforeseen manner. There is a strong desire for smart(er) cities, buildings, devices, factories, health monitoring – a smarter world. However, designing such a smarter world requires addressing also many challenges resulting from the emerging complex interactions and interoperation of systems. How is it possible to handle the increasing complexity during design and maintenance of such systems? How can one guarantee safety and performance of systems operating over networks which are subject to erroneous communication, delays, and failures of sensors and actuators? Is it possible to design control systems which allow for easy reconfiguration or even self-organization, for example by letting subsystems join and leave larger systems via plug and play strategies? Can one guarantee privacy of the controlled subsystems while exchanging information, which is necessary for maintaining overall system performance? We believe that predictive control is a well suited control approach to tackle some of these challenges due to its flexibility with respect to the formulation of the problem and the possibility to directly take constraints, preview information, as well as models of different complexity of the physical world into account. In this perspective we limit our attention to three areas we believe predictive control methods can provide a basis to tackle the appearing challenges: the efficient and easy implementation of predictive control on omnipresent embedded computation hardware, the question of resource and network aware control, as well as control on the network level of systems of systems. We briefly summarize results from these fields and outline some ideas on challenges, which arise.     

Stabilization of non-linear systems†

The problem of stabilizing a discrete-time non-linear system is considered. For a rather large class of common stabilizable non-linear systems, a procedure leading to the stabilization of a given non-linear system Σ belonging to that class is derived. In this procedure, a pair of compensators is constructed, consisting of a precompensator and an output feedback compensator, which, when connected in closed loop around the system Σ, yield a closed-loop system that is internally stable for bounded input sequences. The procedure allows the construction of infinitely many different pairs of such compensators, thus facilitating the choice of a convenient one.     

Vulnerability of dynamic systems†

The purpose of this paper is to formulate and partially resolve the problem of vulnerability of dynamic systems in the context of the theory of directed graphs. A system is considered vulnerable if its structural properties such as input (output) reachability or structural controllability (observability) is destroyed by a perturbation characterized as removal of a line, or set of lines, from the corresponding graph. Graph-theoretic procedures are developed to identify the minimal sets of lines which are essential for preserving the structural properties of the system.     

Probability representations of fuzzy systems

1 Background of birth of fuzzy systems As is well-known, just considering the great uncertainties of many systems, Zadeh put forward the notion of fuzzy sets and advanced the idea of the fuzzy reasoning by means of fuzzy sets which could describe a system approximately[1]. Those systems that are constructed on the basis of fuzzy reasoning are called fuzzy systems in general[2―4]. The research on fuzzy systems has attracted broad attention[5―7]. For instance, universal ap- proximation proper…     

The application of Kolmogorov–Rényi statistics to problems of parameter uncertainty in systems design†

This paper presents a method for dealing with parameter uncertainty in system design which is based on the study of the statistical properties of an ensemble of systems defined by a given structure and by a priori parameter distributions rather than point parameter estimates. It is assumed that the model of the actual system is a random member of the ensemble. The object of the analysis is to design or modify the properties of the ensemble to ensure a high probability of adequate performance of the actual system. The primary statistical function employed is the sample distribution function. This function is used to estimate the true population distribution of a scalar variable chosen to measure the system property of interest. The sample distribution function is constructed from random samples of this figure of merit generated by a suitable digital computer programme. The accuracy of the estimation of the population distribution by the sample distribution is determined by application of statistical results of Kolmogorov and Rényi.     

A new conditional posterior Cramér-Rao lower bound for a class of nonlinear systems

In this paper, a new conditional posterior Cramér-Rao lower bound (CPCRLB) is proposed for a class of nonlinear systems, in which current measurement is dependent on current state as well as one step previous state. In order to compute the proposed CPCRLB recursively, a new particle filter for such class of nonlinear systems is designed, based on which a general formulation of the proposed CPCRLB can be derived. To facilitate practical engineering applications, CPCRLBs for special cases of such class of nonlinear systems, including nonlinear systems with coloured measurement noises and nonlinear systems with correlated noises at one epoch apart, are developed, respectively. Simulation results show the efficiency and superiority of the proposed CPCRLB as compared with existing CPCRLB.     

Modelling of the thermodynamic properties of the ABr–CeBr3 (A=Li–Cs ) systems

The thermodynamic properties of the ABr–CeBr₃ (A=Li–Cs) systems were assessed by the CALPHAD method. The liquid phase in the systems was described by the non-stoichiometric associate model. The entropies of mixing in the liquid ABr–CeBr₃ (A=Li,Na) systems are evaluated from experimental data. The entropies of mixing in the liquid ABr–CeBr₃ (A=K,Rb,Cs) systems, and the Gibbs energies of formation of pseudobinary compounds: A₃CeBr₆(s), A₂CeCl₅(s), ACe₂Cl₇(s) (A=K,Rb,Cs) were estimated due to the lack of experimental data. The presence of solid solution near NaBr was predicted from calculations. The nature of the liquid phase and precision of calculations were discussed.     

Observability of constant states of linear systems†

This paper tackles, in essence, two problems. In the first a method of analysis by freezing in intervals of slowly time-varying systems is developed. Under this method the parameters of a time-varying system are frozen in consecutive intervals to their value at the beginning of the interval. Thus in each interval the system becomes time-invariant, or a constant coefficient one, and analytic methods can be applied. Such a mode of solution enables the use of steps which are considerably larger than those common in classical numerical methods. Error estimates are given for the various cases.

In the second part the freezing in intervals method is applied to systems with a time-averaged non-linearity. A non-linear system with time-averaging can be regarded as one composed of a time-varying system with a variable parameter. A nonlinear operation, such as squaring, is performed on the signal of the system and followed by low-pass filtering. This filtered signal controls, in turn, the variable parameter. Detailed examples with error analyses are given. Digital simulation by the above and a slower, commonly used, method are included.