- Détails du magazine
- Format
- Magazine
- eISSN
- 2083-8492
- Première publication
- 05 Apr 2007
- Période de publication
- 4 fois par an
- Langues
- Anglais

#### Chercher

- Accès libre

Fundamental Limitations of the Decay of Generalized Energy in Controlled (Discrete–Time) Nonlinear Systems Subject to State and Input Constraints

Pages: 629 - 639

#### Résumé

This paper is devoted to the analysis of fundamental limitations regarding closed-loop control performance of discrete-time nonlinear systems subject to hard constraints (which are nonlinear in state and manipulated input variables). The control performance for the problem of interest is quantified by the decline (decay) of the generalized energy of the controlled system. The paper develops (upper and lower) barriers bounding the decay of the system’s generalized energy, which can be achieved over a set of asymptotically stabilizing feedback laws. The corresponding problem is treated without the loss of generality, resulting in a theoretical framework that provides a solid basis for practical implementations. To enhance understanding, the main results are illustrated in a simple example.

#### Mots clés

- decay rate maximization
- Lyapunov function
- nonlinear control systems

- Accès libre

Multiquery Motion Planning in Uncertain Spaces: Incremental Adaptive Randomized Roadmaps

Pages: 641 - 654

#### Résumé

Sampling-based motion planning is a powerful tool in solving the motion planning problem for a variety of different robotic platforms. As its application domains grow, more complicated planning problems arise that challenge the functionality of these planners. One of the main challenges in the implementation of a sampling-based planner is its weak performance when reacting to uncertainty in robot motion, obstacles motion, and sensing noise. In this paper, a multi-query sampling-based planner is presented based on the optimal probabilistic roadmaps algorithm that employs a hybrid sample classification and graph adjustment strategy to handle diverse types of planning uncertainty such as sensing noise, unknown static and dynamic obstacles and an inaccurate environment map in a discrete-time system. The proposed method starts by storing the collision-free generated samples in a matrix-grid structure. Using the resulting grid structure makes it computationally cheap to search and find samples in a specific region. As soon as the robot senses an obstacle during the execution of the initial plan, the occupied grid cells are detected, relevant samples are selected, and in-collision vertices are removed within the vision range of the robot. Furthermore, a second layer of nodes connected to the current direct neighbors are checked against collision, which gives the planner more time to react to uncertainty before getting too close to an obstacle. The simulation results for problems with various sources of uncertainty show a significant improvement compared with similar algorithms in terms of the failure rate, the processing time and the minimum distance from obstacles. The planner is also successfully implemented and tested on a TurtleBot in four different scenarios with uncertainty.

#### Mots clés

- motion planning
- uncertainty
- roadmaps
- sampling
- obstacle avoidance

- Accès libre

PI Observer Design for a Class of Nondifferentially Flat Systems

Pages: 655 - 665

#### Résumé

This paper presents a methodology and design of a model-free-based proportional-integral reduced-order observer for a class of nondifferentially flat systems. The problem is tackled from a differential algebra point of view, that is, the state observer for nondifferentially flat systems is based on algebraic differential polynomials of the output. The observation problem is treated together with that of a synchronization between a chaotic system and the designed observer. Some basic notions of differential algebra and concepts related to chaotic synchronization are introduced. The PI observer design methodology is given and it is proven that the estimation error is uniformly ultimately bounded. To exemplify the effectiveness of the PI observer, some cases and their respective numerical simulation results are presented.

#### Mots clés

- model-free-base PI reduced-order observer
- synchronization
- nondifferentially flat system
- algebraic observability condition
- uniform ultimate boundedness

- Accès libre

A Spectral Method of the Analysis of Linear Control Systems

Pages: 667 - 679

#### Résumé

A spectral method of the analysis of linear control systems is considered. Within the framework of this approach the

#### Mots clés

- anisotropy-based control theory
- anisotropic norm
- ℋ-norm
- ℋ-norm

- Accès libre

Stability and Transparency of Delayed Bilateral Teleoperation with Haptic Feedback

Pages: 681 - 692

#### Résumé

Haptic guidance can improve control accuracy in bilateral teleoperation. With haptic sensing, the human operator feels that he grabs the robot on the remote side. There are results on the stability and transparency analysis of teleoperation without haptic guidance, and the analysis of teleoperation with haptic feedback is only for linear and zero time-delay systems. In this paper, we consider more general cases: the bilateral teleoperation systems have time-varying communication delays, the whole systems are nonlinear, and they have force feedback. By using the admittance human operator model, we propose a new control scheme with the interaction passivity of the teleoperator. The stability and transparency of the master-slave system are proven with the Lyapunov–Krasovskii method. Numerical simulations illustrate the efficiency of the proposed control methods.

#### Mots clés

- teleoperation
- force control
- stability
- transparency

- Accès libre

A Trajectory Planning Based Controller to Regulate an Uncertain 3D Overhead Crane System

Pages: 693 - 702

#### Résumé

We introduce a control strategy to solve the regulation control problem, from the perspective of trajectory planning, for an uncertain 3D overhead crane. The proposed solution was developed based on an adaptive control approach that takes advantage of the passivity properties found in this kind of systems. We use a trajectory planning approach to preserve the accelerations and velocities inside of realistic ranges, to maintaining the payload movements as close as possible to the origin. To this end, we carefully chose a suitable S-curve based on the Bezier spline, which allows us to efficiently handle the load translation problem, considerably reducing the load oscillations. To perform the convergence analysis, we applied the traditional Lyapunov theory, together with Barbalat’s lemma. We assess the effectiveness of our control strategy with convincing numerical simulations.

#### Mots clés

- overhead crane
- adaptive control
- passivity
- trajectory planning
- Barbalat’s lemma

- Accès libre

Robust Extremum Seeking for a Second Order Uncertain Plant Using a Sliding Mode Controller

Pages: 703 - 712

#### Résumé

This paper suggests a novel continuous-time robust extremum seeking algorithm for an unknown convex function constrained by a dynamical plant with uncertainties. The main idea of the proposed method is to develop a robust closed-loop controller based on sliding modes where the sliding surface takes the trajectory around a zone of the optimal point. We assume that the output of the plant is given by the states and a measure of the function. We show the stability and zone-convergence of the proposed algorithm. In order to validate the proposed method, we present a numerical example.

#### Mots clés

- convex optimization
- extremum seeking
- continuous-time gradient algorithm
- dynamical constrained optimization
- unknown functions

- Accès libre

A Conservative Scheme with Optimal Error Estimates for a Multidimensional Space–Fractional Gross–Pitaevskii Equation

Pages: 713 - 723

#### Résumé

The present work departs from an extended form of the classical multi-dimensional Gross–Pitaevskii equation, which considers fractional derivatives of the Riesz type in space, a generalized potential function and angular momentum rotation. It is well known that the classical system possesses functionals which are preserved throughout time. It is easy to check that the generalized fractional model considered in this work also possesses conserved quantities, whence the development of conservative and efficient numerical schemes is pragmatically justified. Motivated by these facts, we propose a finite-difference method based on weighted-shifted Grünwald differences to approximate the solutions of the generalized Gross–Pitaevskii system. We provide here a discrete extension of the uniform Sobolev inequality to multiple dimensions, and show that the proposed method is capable of preserving discrete forms of the mass and the energy of the model. Moreover, we establish thoroughly the stability and the convergence of the technique, and provide some illustrative simulations to show that the method is capable of preserving the total mass and the total energy of the generalized system.

#### Mots clés

- generalized Gross–Pitaevskii system
- Riesz fractional diffusion
- discrete uniform Sobolev inequality
- conservative method
- optimal error bounds

- Accès libre

An Lmi–Based Heuristic Algorithm for Vertex Reduction in LPV Systems

Pages: 725 - 737

#### Résumé

The linear parameter varying (LPV) approach has proved to be suitable for controlling many non-linear systems. However, for those which are highly non-linear and complex, the number of scheduling variables increases rapidly. This fact makes the LPV controller implementation not feasible for many real systems due to memory constraints and computational burden. This paper considers the problem of reducing the total number of LPV controller gains by determining a heuristic methodology that combines two vertices of a polytopic LPV model such that the same gain can be used in both vertices. The proposed algorithm, based on the use of the Gershgorin circles, provides a combinability ranking for the different vertex pairs, which helps in solving the reduction problem in fewer attempts. Simulation examples are provided in order to illustrate the main characteristics of the proposed approach.

#### Mots clés

- linear parameter varying (LPV) paradigm
- linear matrix inequality (LMI)
- Gershgorin circles
- gain scheduling
- controller design

- Accès libre

An Adaptive Identification Method Based on the Modulating Functions Technique and Exact State Observers for Modeling and Simulation of a Nonlinear Miso Glass Melting Process

Pages: 739 - 757

#### Résumé

The paper presents new concepts of the identification method based on modulating functions and exact state observers with its application for identification of a real continuous-time industrial process. The method enables transformation of a system of differential equations into an algebraic one with the same parameters. Then, these parameters can be estimated using the least-squares approach. The main problem is the nonlinearity of the MISO process and its noticeable transport delays. It requires specific modifications to be introduced into the basic identification algorithm. The main goal of the method is to obtain on-line a temporary linear model of the process around the selected operating point, because fast methods for tuning PID controller parameters for such a model are well known. Hence, a special adaptive identification approach with a moving window is proposed, which involves using on-line registered input and output process data. An optimal identification method for a MISO model assuming decomposition to many inner SISO systems is presented. Additionally, a special version of the modulating functions method, in which both model parameters and unknown delays are identified, is tested on real data sets collected from a glass melting installation.

#### Mots clés

- continuous systems
- modulating functions
- system identification
- exact state observer
- glass forehearths

- Accès libre

An Automatic Collision Avoidance Algorithm for Multiple Marine Surface Vehicles

Pages: 759 - 768

#### Résumé

In recent years, unmanned surface vehicles have been widely used in various applications from military to civil domains. Seaports are crowded and ship accidents have increased. Thus, collision accidents occur frequently mainly due to human errors even though international regulations for preventing collisions at seas (COLREGs) have been established. In this paper, we propose a real-time obstacle avoidance algorithm for multiple autonomous surface vehicles based on constrained convex optimization. The proposed method is simple and fast in its implementation, and the solution converges to the optimal decision. The algorithm is combined with the PD-feedback linearization controller to track the generated path and to reach the target safely. Forces and azimuth angles are efficiently distributed using a control allocation technique. To show the effectiveness of the proposed collision-free path-planning algorithm, numerical simulations are performed.

#### Mots clés

- unmanned surface vehicles
- obstacle avoidance
- control allocation
- constrained convex optimization

- Accès libre

Using Information on Class Interrelations to Improve Classification of Multiclass Imbalanced Data: A New Resampling Algorithm

Pages: 769 - 781

#### Résumé

The relations between multiple imbalanced classes can be handled with a specialized approach which evaluates types of examples’ difficulty based on an analysis of the class distribution in the examples’ neighborhood, additionally exploiting information about the similarity of neighboring classes. In this paper, we demonstrate that such an approach can be implemented as a data preprocessing technique and that it can improve the performance of various classifiers on multiclass imbalanced datasets. It has led us to the introduction of a new resampling algorithm, called Similarity Oversampling and Undersampling Preprocessing (SOUP), which resamples examples according to their difficulty. Its experimental evaluation on real and artificial datasets has shown that it is competitive with the most popular decomposition ensembles and better than specialized preprocessing techniques for multi-imbalanced problems.

#### Mots clés

- imbalanced data
- multi-class learning
- re-sampling
- data difficulty factors
- similarity degrees

- Accès libre

Revisiting the Optimal Probability Estimator from Small Samples for Data Mining

Pages: 783 - 796

#### Résumé

Estimation of probabilities from empirical data samples has drawn close attention in the scientific community and has been identified as a crucial phase in many machine learning and knowledge discovery research projects and applications. In addition to trivial and straightforward estimation with relative frequency, more elaborated probability estimation methods from small samples were proposed and applied in practice (e.g., Laplace’s rule, the _{h}√2 that is optimal according to the mean absolute error of the estimation result. In this paper we show that, even though the articulation of Piegat’s formula seems different, it is in fact a special case of the _{a} =1_{.} In the context of an experimental framework, we present an in-depth analysis of several probability estimation methods with respect to their mean absolute errors and demonstrate their potential advantages and disadvantages. We extend the analysis from single instance samples to samples with a moderate number of instances. We define small samples for the purpose of estimating probabilities as samples containing either less than four successes or less than four failures and justify the definition by analysing probability estimation errors on various sample sizes.

#### Mots clés

- probability estimation
- small samples
- minimal error
- -estimate

- Accès libre

Password–Authenticated Group Key Establishment from Smooth Projective Hash Functions

Pages: 797 - 815

#### Résumé

Password-authenticated key exchange (PAKE) protocols allow users sharing a password to agree upon a high entropy secret. Thus, they can be implemented without complex infrastructures that typically involve public keys and certificates. In this paper, a provably secure password-authenticated protocol for group key establishment in the common reference string (CRS) model is presented. While prior constructions of the group (PAKE) can be found in the literature, most of them rely on idealized assumptions, which we do not make here. Furthermore, our protocol is quite efficient, as regardless of the number of involved participants it can be implemented with only three communication rounds. We use a (by now classical) trick of Burmester and Desmedt for deriving group key exchange protocols using a two-party construction as the main building block. In our case, the two-party PAKE used as a base is a one-round protocol by Katz and Vaikuntanathan, which in turn builds upon a special kind of smooth projective hash functions (KV-SPHFs). Smooth projective hash functions (SPHFs) were first introduced by Cramer and Shoup (2002) as a valuable cryptographic primitive for deriving provable secure encryption schemes. These functions and their variants proved useful in many other scenarios. We use here as a main tool a very strong type of SPHF, introduced by Katz and Vaikuntanathan for building a one-round password based two party key exchange protocol. As evidenced by Ben Hamouda

#### Mots clés

- group key exchange
- password authentication
- smooth projective hashing

- Accès libre

Improved Reference Image Encryption Methods Based on 2^{K} Correction in the Integer Wavelet Domain

^{K}

Pages: 817 - 829

#### Résumé

Many visually meaningful image encryption (VMIE) methods have been proposed in the literature using reference encryption. However, the most important problems of these methods are low visual quality and blindness. Owing to the low visual quality, the pre-encrypted image can be analyzed simply from the reference image and, in order to decrypt nonblind methods, users should use original reference images. In this paper, two novel reference image encryption methods based on the integer DWT (discrete wavelet transform) using 2^{k}^{k}^{k}

#### Mots clés

- visually meaningful image encryption
- 2 correction
- discrete wavelet transform
- least significant bits embedding