E-type Systems Research Articles

Repetitive Control for Lur’e-Type Systems: Application to Mechanical Ventilation

Repetitive control (RC) has shown to achieve superior rejection of periodic disturbances. Many nonlinear systems are subject to repeating disturbances. The aim of this article is to develop a continuous-time RC design with stability guarantees for nonlinear Lur’e-type systems. Approximate output tracking is achieved by combining an internal model, consisting of a finite number of linear oscillators with frequencies at the reference frequency and at its multiples, with a stabilizer that guarantees a convergence property of the closed-loop system. The developed RC approach is applied to a nonlinear mechanical ventilation system for intensive care units (ICUs), which can be modeled as a Lur’e-type system. The experimental study confirms that the RC scheme is able to successfully follow the desired target pressure profile to properly support the ventilation needs of an adult patient.

Refined frequency estimates for stability domains of synchronization systems

n this paper we examine stability of Lur’e-type systems arising as a feedback superpositions of infinite-dimensional linear blocks, described by integrodifferential Volterra equations, and periodic nonlinearities. Such systems have multiple equilibria, so traditional methods of stability investigation, defined for systems with single equilibrium are no good here. In the paper traditional Popov method of a priori integral indices is combined with two special techniques: Leonov’s nonlocal reduction method and the Bakaev-Guzh procedure. As a result new frequency–algebraic stability criteria are established, yielding tightened estimates of stability domains in the space of the system’s parameters.

Computationally efficient identification of continuous-time Lur’e-type systems with stability guarantees

In this paper, we propose a parametric system identification approach for a class of continuous-time Lur’e-type systems. Using the Mixed-Time-Frequency (MTF) algorithm, we show that the steady-state model response and the gradient of the model response with respect to its parameters can be computed in a numerically fast and efficient way, allowing efficient use of global and local optimization methods to solve the identification problem. Furthermore, by enforcing the identified model to be inside the set of convergent models, we certify a stability property of the identified model, which allows for reliable generalized usage of the model also for other excitation signals than those used to identify the model. The effectiveness and benefits of the proposed approach are demonstrated in a simulation case study. Furthermore, we have experimentally shown that the proposed approach provides fast identification of both medical equipment and patient parameters in mechanical ventilation and, thereby, enables improved patient treatment.

Synchronization of Lur’e-type nonlinear systems in linear dynamical networks having fast convergence rate and large DC gain

This paper studies the problem of synchronization in a dynamical network, where we identify the nodes of the undirected graph as identical Lur’e-type nonlinear systems and the edges as heterogeneous and asymptotically stable linear systems, i.e., both of the nodes and edges are dynamical systems. It is shown that sufficiently fast convergence rate of each edge guarantees the dynamic edges degenerate into their associated static maps, equivalent to assigning the constant weights to the edges (as in the usual synchronization problems). Thus, in effect, the dynamical network becomes the static one characterized by the Laplacian matrix of the graph with the weights being the gains of the static maps. Then, the large DC gains of the edges, i.e., the large weights, are shown to yield the synchronization of the state variables of the Lur’e-type systems in the static network. The synchronization in the dynamical network is at last guaranteed by the combination of these two results. The results in this paper are applicable to the synchronization of the terminal voltages of the Lur’e-type circuits that are interconnected with each other via the lines having their associated line admittances.

Fast Identification of Continuous-Time Lur’e-type Systems with Stability Certification

In this paper, we propose an approach for parametric system identification for a class of continuous-time Lur’e-type systems using only steady-state input and output data. Employing a quasi-Newton optimization scheme, we minimize an output error criterion constrained to the set of convergent models, which enforces a stability certificate on the identified model. To compute the steady-state model response efficiently, we adopt the Mixed-Time-Frequency (MTF) algorithm. Furthermore, using the MTF algorithm, we present a method to efficiently compute the gradient of the objective function with any user-defined accuracy. Starting with an initial convergent model estimate, the developed identification algorithm optimizes parameter estimates. The effectiveness of the proposed approach is illustrated in a simulation example.

Synchronization Analysis of Piecewise-Linear Lur’e Systems under Sampled-Data Control

Abstract This article addresses the master-slave synchronization problem of chaotic Lur’e-type systems under sampled-data control. In particular, the system nonlinearity is assumed to be described by a piecewise-linear function. Based on a Lur’e-type Lyapunov function and a looped-functional approach, LMI-based conditions are formulated to ensure that the difference between master and slave states converges asymptotically to zero provided that the time interval between two consecutive samples respects some bounds. An optimization problem is then proposed to determine the maximum allowable time between two successive samples in order to guarantee the synchronization. A Chua’s circuit example illustrates the result.

A robust congestion control scheme for cluster wireless multimedia sensor networks with propagation delay and external interference

Congestion control in cluster wireless multimedia sensor networks is capable of delivering and gathering multimedia information, while propagation delay and external interference may cause it unable to achieve the maximal network throughput without congestion control. To solve the problem, based on the additive-increase multiplicative-decrease adjustment strategy, a robust congestion control model is proposed with a scheduling scheme in cluster wireless multimedia sensor networks considering the neighbor feedback. The robust congestion control model is a Lur’e-type system. The cluster wireless multimedia sensor network is capable of achieving the desired cluster synchronization with network parameters provided by Lyapunov–Krasovskii functionals. Sufficient conditions of the robust congestion control are formulated by linear matrix inequalities. Numerical results show the effectiveness of the proposed scheme.

Stability Investigation of an Idle Speed Control Loop for a Hybrid Electric Vehicle

In this brief, we investigate the stability of an idle speed control (ISC) loop for a hybrid electric vehicle (HEV). The actuators in an HEV powertrain are subject to delays, which can cause instability. Furthermore, in a parallel hybrid setup, these actuators are coupled via a dual mass flywheel, introducing nonlinear behavior through a mechanical dead-zone. The resulting control loop is a Lur’e-type nonlinear system with delays. To investigate its stability, a simple Lyapunov–Krasovskii functional is constructed, taking into account the delays and nonlinear feedback part simultaneously. By means of a quadratic program formulation, conservatism regarding the nonlinearity is reduced. A powertrain model is presented from which an idle speed controller has been designed and successfully implemented on an electronic control unit. Finally, it can be shown that stability for the ISC loop is guaranteed, based on the controller design model of the HEV powertrain.

Frequency domain based real-time performance optimization of Lur'e systems

Nonlinear effects can lead to performance degradation in (controlled) dynamical systems. This paper provides a practical method to optimally compensate performance degrading nonlinear effects in Lur'e-type systems in an automated way. Using novel frequency domain based techniques, a well defined performance measure is derived and real-time performance optimization is achieved by application of extremum seeking algorithm. This yields a new method for real-time compensation of performance degrading nonlinear effects, which is successfully demonstrated in both simulation and experiment.

CHAOS SYNCHRONIZATION IN THE PRESENCE OF NOISE

In this paper, we first develop a systematic procedure of state feedback control, based on a Lur'e-type system, to analyze the synchronization of two chaotic systems in the presence of random white noise. With the aid of the modified independent component analysis (ICA), the real chaotic signal can be extracted from a noisy source where the chaotic signal has been contaminated by random white noise. Hence, a new scheme has been proposed in this paper to combine the modified ICA design and the state feedback control method for achieving chaos synchronization. The synchronization time can be arbitrarily designed to guarantee stability, even if the system's output is corrupted by measuring noise. A Duffing system example is provided to show the effectiveness of the proposed scheme. The new scheme is first used for control systems with measurement noise which can replace the conventional Kalman filter.

Robust control of uncertain LTI plant with input saturation constraint: H ∞ loop-shaping approach

This article addresses a robust controller design technique for an uncertain linear time invariant plant with input saturation constraint. The uncertainty of the plant is presented in a normalised coprime factorisation framework, which is a general description of the unstructured uncertainty of the system. For controller synthesis, the H ∞ loop-shaping method adopted is new to the actuator saturation control problem. In the presence of input saturation, the H ∞ loop-shaping framework has been transformed into an equivalent Lur'e-type system, and then Popov absolute stability criteria are applied to ensure closed-loop stability against unstructured uncertainty and saturation nonlinearity of the system. For the synthesising controller, a sequence of design steps has been addressed by formulating the design constraints in a bilinear matrix inequality framework. To show the effectiveness of the proposed method, a numerical example has been demonstrated.

Effects on the chaotic system of fractional order PI α controller

When a Lur’e-type system which cannot exhibit chaotic behavior and whose linear part is of a second order, is tried to be controlled by an integer order controller, chaotic behaviors can occur depending on the controller parameters. In this article, in the case when a fractional order PIα is chosen, provided that the controller parameters remain unchanged, the effect of the integral order α for the interval 0<α<1 has been investigated. It has been shown through two examples that depending on the integral order α, the fractional order PIα controller prevents the chaotic behavior by releasing the extra dynamics that was loaded onto the system by the integer order PI controller. To determine at which α parameter the system exhibits chaotic behavior, the frequency domain approach based chaos prediction method—Genesio–Tesi conjecture—has been used.

Anticipating synchronization of chaotic Lur’e systems

In this paper we consider the anticipating synchronization of chaotic time-delayed Lur'e-type systems in a master-slave setting. We introduce three scenarios for anticipating synchronization, and give sufficient conditions for the existence of anticipating synchronizing slave systems in terms of linear matrix inequalities. The results obtained are illustrated on a time-delayed Rossler system and a time-delayed Chua oscillator.

Explicit stability conditions for time-discrete vector Lur'e-type systems

Non-linear discrete-time Lur'e-type systems are considered. Explicit stability conditions are suggested. They are formulated in terms of the determinants of characteristic polynomials. Moreover, an estimate for the region of attraction of the zero solution is derived.

Software evolution—Background, theory, practice

This paper opens with a brief summary of some 30 years of study of the software evolution phenomenon. The results of those studies include the SPE program classification, a principle of software uncertainty and laws of E-type software evolution. The laws were termed so because they encapsulate phenomena largely independent of the people, the organisations and the domains involved in the evolution of the E-type systems studied. Recent studies have refined earlier conclusions, yielded practical guidelines for software evolution management and provide a basis for the formation of a theory of software evolution. Given the volume of published material and the extent of recent discussions on the topic (see, e.g., [Proc. ICSM, Montreal, 2002, p. 66]), this paper is restricted to an overview that exposes the significance of the evolution phenomenon and its study to the wider community, providing a basis for the future and, in particular, development of a theory of software evolution.

A limit cycle stability criterion for Lur'e-type non-linear Systems

A new limit cycle stability criterion for non-linear Lur'e-type systems is derived in this paper. The result is achieved via the approach of transient oscillations analysis and the main approximation of the method consists in the use of the describing function relative to the non-linear part of the system.

Weak stochastic stability for the Lur'e-type nonlinear system

Sufficient condition is derived for Lur'e-type nonlinear system to be weakly stochastically stable subject to random input.

Estimates of the transient response of Lur'e-type systems

The problem of estimating the extreme time constants associated with the transient response of a Lur&apos;e-type nonlinear system is considered. This problem has been discussed in the recent past by Vogt,1 who showed that bounds for these time constants can be obtained from a knowledge of the eigenvalues of the linear part of the system. The object of the present study has been to improve upon this result, by including the effects of the nonlinear part. The proposed method is believed to be quite simple and is illustrated with the help of numerical examples.