Stable adaptive control for a plant with randomly varying parameters

Adaptive control is considered for a two-dimensional linear discrete-time plant with randomly drifting parameters. The certainty equivalent minimum variance control law along with the projection-like identification algorithm are used. The stability of the parameter estimates and exponential stability of the closed-loop system are proved in the absence of any persistent excitation assumption.     

Stability problem of a periodically varying system

In this paper we investigate the problem of stability for periodically time-varying systems. This study is needed, for instance, to determine robustness and stability of repetitive learning systems used in the control of complex systems such as robotic manipulators. We use classical and new results for the stability of linear time-varying systems to re-establish an upper bound on the rate of parameter variations of the periodically time-varying systems, We then examine in detail the effects of these variations on the asymptotic and exponential stability of a special class of systems.     

Stability and performance analysis of randomly deployed wireless networks

A growing demand for mobile services is taking the deployment of wireless local area networks away from the notion of carefully planned and carefully managed settings into randomly deployed and independently managed (if at all) network settings. This results in contentious networks that serve highly mobile nodes. In fact, research reveals that in most metropolitan cities in Europe and the US the size of closely located and contentious access points is overwhelmingly high (in the order of thousands). Subsequently, the performance of these networks is often unstable and unpredictable. This paper aims to investigate the extent of performance fluctuations in randomly deployed networks. It also aims to investigate the contribution of various adaptation strategies at different abstraction layers to deal with these fluctuations. We present the outcome of an exhaustive simulation for different applications, including VoIP, HTTP, and FTP. We will demonstrate that collision due to hidden-terminals is a minor influence on the performance and stability of these networks, whereas dynamic channel allocation greatly affects them. Moreover, HTTP applications are less affected by both inter- and intra-channel interferences compared with FTP and VoIP applications.     

Neural and adaptive controllers for a non-minimum phase varying time-delay system

In this paper we study a non-minimum phase discrete time system with varying time-delay. We first propose several open loop control architectures based on non-linear neural networks and study their ability to handle the different difficulties of the control problem. All the methods are tested and compared to a baseline linear controller, on a simulated river system. This plant is submitted to perturbations corresponding to water withdrawals and lateral inflows. The above architectures are not able to cope with such perturbations. We then propose a model combining a feed-forward neural network based learning controller and a feedback adaptive controller. The performances of this model are compared to a similar architecture containing linear feed-forward and feedback controllers.     

Tracking randomly varying parameters: Analysis of a standard algorithm

In linear stochastic system identification, when the unknown parameters are randomly time varying and can be represented by a Markov model, a natural estimation algorithm to use is the Kalman filter. In seeking an understanding of the properties of this algorithm, existing Kalman-filter theory yields useful results only for the case where the noises are gaussian with covariances precisely known. In other cases, the stochastic and unbounded nature of the regression vector (which is regarded as the output gain matrix in state-space terminology) precludes application of standard theory. Here we develop asymptotic properties of the algorithm. In particular, we establish the tracking error bounds for the unknown randomly varying parameters, and some results on sample path deviations of the estimates.     

OCR applied to an electronic voting system

This paper describes a new electronic secure voting system based on automatic paper ballot reading. It presents how the system is organized, it also describes our OCR system and how it is implemented to read paper ballots, and it ends showing some experimental results. The first step of the OCR system consists in extracting from each character several simple features, which help us to perform distortion processing. These simple features are used to define a key which possibly allows us to identify the character. If this is not the matter and there are several candidates for the obtained key, we need to extract more complex features. This second process is based on the use of floating masks, which are specific for each feature, and on the following of its trajectory through the character stroke. The text was submitted by the authors in English. J.K. Espinosa received MS and PhD degrees in Electrical Engineering from the University of the Basque Country, Spain, in 1989 and 2002, respectively. Since 1989, he has been an assistant professor in Telematic Engineering at the Electronics and Telecommunications Department of the University of the Basque Country. He teaches courses in computer programming, data communication, and computer networks and services. His research interests include digital image processing software, optical character recognition, electronic voting systems, video transmission over the Internet, and telematic applications. I. Goirizelaia is professor in the Electronics and Telecommunication Department at the School of Engineering, University of the Basque Country. He received his electrical engineering degree in 1981 and his PhD in electrical engineering in 1987, both from the University of the Basque Country. He worked for Stanford Research Institute (1983–1985) as an international fellow and for LABEIN research laboratory (1986), and in 1987 he started his own company dedicated to industrial applications of image processing techniques. He was vice president for university enterprise relations of the University of the Basque Country from 1998 to 2000. He was a visiting scientist at the MIT Media Lab for six months in 2004. His research interest is the development of advanced information technology, focusing on teleeducation, web based learning environments, and electronic voting technology. He is also interested in security schemes based on image processing algorithms applied to watermarking of digital images. Currently, he is vice president of the University of the Basque Country. J.J. Igarza received his MS degree in 1986 from the Physics Faculty and his MS degree in software engineering in 1997 from the Engineering School of the University of the Basque Country. From 1986 to 1996, he worked as a researcher for a machine vision company, and since 1997, he has been a lecturer at the Engineering School of Bilbao. His research interests include multimodal biometric databases, on-line and offline signature verification, and human-machine interactions.     

Properties of a combined adaptive/second-order sliding mode controlalgorithm for some classes of uncertain nonlinear systems

In this paper, a combined adaptive/variable structure control approach is presented that exploits the good properties of the backstepping procedure and of a second-order sliding-mode control algorithm. This algorithm enables one to attain the conditions S=0, S˙=0 (second-order sliding mode) in a finite time, S=0 being a predefined sliding manifold. The combined approach retains the stability and convergence features of the original adaptive strategy. In addition, it allows one to deal with systems with uncertainties of more general types, ensuring robustness, as well as a reduction in the computational load     

state estimation with fading measurements,randomly varying nonlinearities and probabilistic distributed delays

In this paper, the state estimation problem is investigated for a class of discrete‐time stochastic systems in simultaneous presence of three network‐induced phenomena, namely, fading measurements, randomly varying nonlinearities and probabilistic distributed delays. The channel fading is characterized by the ?th‐order Rice fading model whose coefficients are mutually independent random variables with given probability density functions. Two sequences of random variables obeying the Bernoulli distribution are utilized to govern the randomly varying nonlinearities and probabilistic distributed delays. The purpose of the problem addressed is to design an state estimator such that the dynamics of the estimation errors is stochastically stable and the prespecified disturbance rejection attenuation level is guaranteed. Through intensive stochastic analysis, sufficient conditions are established under which the addressed state estimation problem is recast as a convex optimization one that can be solved via the semi‐definite program method. Finally, a simulation example is provided to show the usefulness of the proposed state estimation scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Nonlinear adaptive controller applied to an Antilock Braking System with parameters variations

The control of an Antilock Braking System is a difficult problem, due to its nonlinear dynamics and to the uncertainties in its characteristics and parameters. To overcome these issues, in this work an adaptive controller is proposed. The controller is designed under the assumption that the friction coefficient is unknown, and further perturbing frictions act on the system. Finally, the convergence to an ε-ball of the origin is proved when these perturbing parameters vary. The performance of the nonlinear dynamic controllers is evaluated by some experimental tests on a mechatronic system representing a quarter-car model. The results show how the controller ensures the tracking of the desired reference and identifies the unknown parameters.     

Stability analysis of constrained MPC applied to discrete-time nonlinear with CLF system

The model predictive control （MPC） strategy with a control Lyapunov function （CLF） as terminal cost is commonly used for its guaranteed stability. In most of the cases, CLF is locally designed, and the region of attraction is limited, especially when under control constraints. In this article, the stability and the region of attraction of constrained MPC that is applied to the discrete-time nonlinear system are explicitly analyzed. The region of feasibility is proposed to substitute the region of attraction, which greatly reduces the calculation burden of terminal constraints inequalities and guarantees the stability of the MPC algorithm. Also, the timevariant terminal weighted factor is proposed to improve the dynamic performance of the close-loop system. Explicit experiments verify the effectiveness and feasibility of the relative conclusions, which provide practically feasible ways to stabilize the unstable and/or fast-dynamic systems.     

Stability analysis of constrained MPC with CLF applied to discrete-time nonlinear system

The problem of counting the number of spanning trees is an old topic in graph theory with important applications to reliable network design. Usually, it is desirable to put forward a formula of the number of spanning trees for various graphs, which is not only interesting in its own right but also in practice. Since some large graphs can be composed of some existing smaller graphs by using the product of graphs, the number of spanning trees of such large graph is also closely related to that of the corresponding smaller ones. In this article, we establish a formula for the number of spanning trees in the lexicographic product of two graphs, in which one graph is an arbitrary graph G and the other is a complete multipartite graph. The results extend some of the previous work, which is closely related to the number of vertices and Lapalacian eigenvalues of smaller graphs only.     

Gain scheduling adaptive control applied to a particular mixer-settler equipment

The mixer-settler based on phase inversion (MSBPI) is a system used for treatment of wastewaters in order to reduce the content of oils and greases from wastewaters produced in oil industry. Its operation principle combines mixing, extraction and separation by decantation in a unique process. In particular, for control purpose, the level of the interface between organic solvent and water, in the separation section, is a critical variable to guarantee performance and security during operation of the MSBPI. In this work, an image-based detector to monitor the organic solvent–water interface level is proposed and a feedback control loop for the process is presented. Initially, a conventional controller (PID) was implemented and, subsequently, a strategy of gain scheduling adaptive control was developed in order to improve the process response in closed-loop. The experimental results showed that the adaptive control presented an efficient performance, even when disturbances of significant magnitude were applied to the process.     

Poor convergence in applying an optimal integral regulator to a system with a RHS zero

Necessary and sufficient conditions of the optimal regulator incorporating integral feedback were given by Porter Ill and Smith and Davison [2]. This note presents a problem of poor convergence in an iterative solution of the discrete Riccati equations when an optimal regulator incorporatingr = mintegral feedback is applied to a system which has a zero on the RHS ofs-plane, whererandmare the input and output dimensions, respectively. The problem of poor convergence was clarified by simulation studies and analytically examined based on certain assumptions. The poor convergence is due to poor choice of an initial guess in the above special situation. However, this problem is very important from a practical point of view because the initial guess is difficult in the first stage of regulator design.     

Stability and convergence of F iterative scheme with an application to the fractional differential equation

In this paper, we prove that F iterative scheme is almost stable for weak contractions. Further, we prove convergence results for weak contractions as well as for generalized non-expansive mappings due to Hardy and Rogers via F iterative scheme. We also prove that F iterative scheme converges faster than the some known iterative schemes for weak contractions. An illuminative numerical example is formulated to support our assertion. Finally, utilizing our main result the solution of nonlinear fractional differential equation is approximated.

     

Parameter convergence of a new class of adaptive controllers

A new class of adaptive control schemes for minimum-phase linear time invariant (LTI) systems has recently been developed using nonlinear design techniques which guarantee improved transient performance in addition to closed-loop stability and asymptotic tracking. In this paper we establish the parameter convergence properties of this new class of schemes in the presence of persistently exciting signals and compare them with the properties of the traditional adaptive controllers. We show that the new class of adaptive controllers has stronger parameter convergence properties in the presence of overparameterization     

An adaptive region segmentation combining surrogate model applied to correlate design variables and performance parameters in a transonic axial compressor

Surrogate models have been widely applied to correlate design variables and performance parameters in turbomachinery optimization applications. With more design variables and uncertain factors taken into account in an optimization design problem, the mathematical relations between the design variables and the performance parameters might present linear, low-order nonlinear or even high-order nonlinear characteristics, and are usually analytically unknown. Therefore, it is required that surrogate models have high adaptability and prediction accuracy for both the linear and nonlinear characteristics. The paper mainly investigates the effectiveness of an adaptive region segmentation combining surrogate model based on support vector regression and kriging model applied to a transonic axial compressor to approximate the complicated relationships between geometrical variables and objective performance outputs with different sampling methods and sizes. The purpose is to explore the prediction accuracy and computational efficiency of this adaptive surrogate model in real turbomachinery applications. Three different sampling techniques are studied: (1) uniform design; (2) Latin hypercube sampling method; (3) Sobol quasi-random design. For the low dimensional case with five variables, the adaptive region segmentation combining surrogate model performs better (not worse) than the single component surrogate in terms of prediction accuracy and computational efficiency. In the meanwhile, it is also noted that the uniform design applied to the adaptive surrogate model has more advantages over the Latin hypercube sampling method especially for the small sample size cases, both performing better than the Sobol quasi-random design. Moreover, a high dimensional case with 12 variables is also utilized to further validate the prediction advantage of the adaptive region segmentation combining surrogate model over the single component surrogate, and the computational results favor it. Overall, the adaptive region segmentation combining surrogate model has produced acceptable to high prediction accuracy in presenting complex relationships between the geometrical variables and the objective performance outputs and performed robustly for a transonic axial compressor problem.

     

Parameter convergence and minimal internal model with an adaptive output regulation problem

The parameter convergence of nonlinear adaptive control systems is an important yet not well addressed issue. In this paper, using the global robust output regulation problem of output feedback systems with unknown exosystems as a platform, we will show that the well known persistency of excitation (PE) condition still guarantees the convergence of the estimated parameter vector to the true parameter vector. Moreover, the PE condition will be satisfied if the internal model is minimal in certain sense.