Uncertain Hybrid Research Articles

A method for adaptive hybrid output regulation of linear systems

Abstract: In this paper we deal with the problem of adaptive output regulation for a class of uncertain hybrid linear systems whose state jumps periodically according to a known clock. The goal is to present a design methodology for internal model-based hybrid regulators in presence of hybrid exosystems that are unknown both in the flow dynamics and jump map, which are assumed to range in a finite set. The arguments used in this paper strongly rely on the ones recently presented in Cox et al. [2016] and, in particular, on the notion of visibility of the “hybrid steady-state generator”. The design methodology is then applied to the practical case of torque control of a DC-motor in presence of an uncontrolled rectifier.

Hybrid bond graph model based for robust fault detection and isolation

The article deals with the robust fault detection and isolation based on linear fractional transformation hybrid bond graph. The main objective is to improve the robustness of fault detection step in the presence of parametric uncertainties in hybrid models in order to minimize the false alarms. The scientific interest of the proposed method is the use of only one tool – the bond graph not only for dynamic modelling of uncertain hybrid system but also for generation of adaptive thresholds needed in residual evaluation step. For this task, hybrid bond graph uncertain model approach with controlled junctions in linear fractional transformation form (allowing to represent graphically the parametric uncertainties) is first proposed to represent all the modes of the hybrid system. Second, based on causal and structural properties of the hybrid bond graph, analytical redundancy relations (with nominal and uncertain part) valid for all the modes are then derived systematically from the diagnostic hybrid bond graph. An application to a hydraulic system is used to illustrate this method.

An approach to interval-valued intuitionistic uncertain linguistic multi-attribute group decision making

The purpose of this paper is to investigate interval-valued intuitionistic uncertain linguistic multi-attribute group decision making with incomplete weight information and interactive conditions. In order to obtain the comprehensive attribute values of alternatives, the induced generalized Shapley interval-valued intuitionistic uncertain linguistic hybrid Choquet averaging (IGS-IVIULHCA) operator is defined, which globally considers not only the importance of elements and the ordered positions but also their correlations. Based on gray relational analysis (GRA) method, models for the optimal fuzzy measures are constructed. Then, a new decision approach is developed, which considers the interactive characteristics between elements in a set. Finally, a numerical example is presented to illustrate the proposed approach and demonstrate its practicality and effectiveness.

An Approach to Uncertain Linguistic Multi-Attribute Group Decision Making Based on Interactive Index

In this paper, two uncertain linguistic Choquet aggregation operators called the induced uncertain linguistic hybrid generalized Shapley Choquet weighted averaging (IULHGSCWA) operator and the induced uncertain linguistic hybrid generalized Shapley Choquet geometric mean (IULHGSCGM) operator are defined. To reduce the complexity of solving a fuzzy measure, the induced uncertain linguistic hybrid 2-additive generalized Shapley Choquet weighted averaging (IULHAGSCWA) operator and the induced uncertain linguistic hybrid 2-additive generalized Shapley Choquet geometric mean (IULHAGSCGM) operator are presented. When the weight information is incompletely known, models for the optimal fuzzy measures on an expert set, on an attribute set and on their ordered sets are built, respectively. Furthermore, an approach to multi-attribute group decision making under uncertain linguistic environment is developed, which can cope with the interdependent or correlative characteristics between elements. Finally, a practical application is selected to illustrate the validity and practicability of the developed procedure.

A New Numerical Method for Optimal Control of a Class of Hybrid Systems

Optimal control of uncertain hybrid systems is a major concern in control engineering. For optimal control of hybrid systems, there are a variety of direct methods, including parametric control and state-based parametric control. A reason that indirect methods are less used for optimal control of hybrid systems is difficulty in working with it and its primary valuing. The present study develops a new numerical method for optimal control of hybrid systems which decreases special restrictions of optimal control functions of hybrid systems per provided solution by a Bellman inequality. The obtained results show that an optimal control problem can be easily solved by converting it to an optimization problem. In addition, the used method obtained more accurate numerical value of the performance index. The results showed that the proposed method leads to greater convergence of the algorithm used in optimal control problems. The efficiency and performance of the proposed method was tested by an application example. Keywords: Bellman Inequality, Hybrid Systems, Optimal Control, Optimization Problems

A New Numerical Method for Optimal Control of a Class of Hybrid Systems

Optimal control of uncertain hybrid systems is a major concern in control engineering. For optimal control of hybrid systems, there are a variety of direct methods, including parametric control and state-based parametric control. A reason that indirect methods are less used for optimal control of hybrid systems is difficulty in working with it and its primary valuing. The present study develops a new numerical method for optimal control of hybrid systems which decreases special restrictions of optimal control functions of hybrid systems per provided solution by a Bellman inequality. The obtained results show that an optimal control problem can be easily solved by converting it to an optimization problem. In addition, the used method obtained more accurate numerical value of the performance index. The results showed that the proposed method leads to greater convergence of the algorithm used in optimal control problems. The efficiency and performance of the proposed method was tested by an application example.

Robust semiclassical internal model based regulation for a class of hybrid linear systems

A new robust error-feedback regulator is proposed for a class of uncertain hybrid systems with periodic jumps, using a hybrid extension of the classical internal model principle. The plant need not be minimum phase, square nor SISO. The proposed regulator contains an internal model composed by two main units, a flow internal model providing the correct input to achieve regulation during flows, and a jump internal model resetting the state of the regulator at each period. Such a structure reminds internal model design for ripple-free regulation of sampled-data systems; an important difference is that here the jump internal model must contain more copies of the relevant dynamics of the exosystem with respect to the flow internal model.

Robust adaptive speed control of uncertain hybrid electric vehicle using electronic throttle control with varying road grade

The design objective of this paper is to apply various control techniques to control the speed of a hybrid electric vehicle (HEV) using an electronic throttle control system (ETCS). The DC servo motor is used for controlling the angular position of the throttle valve. A proportional-integral-derivative (PID), a self-tuning fuzzy PID (STF-PID) controller and a model reference adaptive system (MRAS) with a sliding mode (SM) adaptation mechanism are used for controlling the speed of the nonlinear vehicle. The integral error performance indices (IEPI) such as the integral of the absolute error (IAE), the integral of the square of error (ISE) and the time domain performance specifications such as overshoot (OS), settling time (ST) and rise time (RT) are taken into consideration for the performance analysis of HEV. The robust H∞ controller using mixed sensitivity approach is designed and implemented for the linearized HEV. The robust stability of uncertain HEV with H∞ controller using Kharitonov’s theorem is analyzed, and the stability margin of the linearized vehicle system is determined. These control techniques are developed to achieve the robust performance of the throttle controlled HEV with the target to achieve a wide range of speed, fuel economy, reduced pollution and improved efficiency.

SOME INDUCED UNCERTAIN GEOMETRIC AGGREGATION OPERATORS WITH PURE LINGUISTIC INFORMATION AND THEIR APPLICATION TO GROUP DECISION MAKING

In this paper, we develop some new aggregation operators with pure linguistic information including the uncertain pure linguistic weighted geometric mean (UPLWGM) operator, the induced uncertain pure linguistic ordered weighted geometric mean (IUPLOWGM) operator, and the induced uncertain pure linguistic hybrid geometric mean (IUPLHGM) operator. These developed aggregation operators are very suitable to deal with the situation where the input arguments are represented in uncertain pure linguistic variables. Also, as a more general type of aggregation operator, the IUPLHGM operator is based on the UPLWGM and IUPLOWGM operators, and it can reflect the importance degrees of both the given uncertain linguistic variables and their ordered positions. Moreover, in the situations where the information about all the attribute weights, the attribute values and the expert weights are expressed in the form of linguistic labels variables, we develop an approach based on the IUPLHGM operator for multiple attribute group decision making with pure linguistic information. Finally, an application of the developed approach to group decision making problem regarding the selection of investments is given. Also, we present a comparative analysis with other related decision making methods to demonstrate the effectiveness of the developed approach.

Trachemys grayi emolli(Testudines, Emydidae) in Honduras and its systematic relationships based on mitochondrial DNA

We report the discovery of a population of Trachemys grayi emolli in southern Honduras. Verification of the species was based on both morphological and molecular data (ND4, COI, ctyb). We discuss problems that arise from the use of sequences from non-vouchered pet trade and turtle farm samples for inferring phylogenetic relationships and confirming species identifications. We postulate that incongruence between mitochondrial and nuclear trees may relate to introgressive hybridisation amongst captive animals. This highlights the dangers of using pet trade specimens of uncertain origin and potential hybrid status in molecular phylogenetic studies. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Uncertain Linguistic Aggregation Distance Measures and Their Application to Group Decision Making

We introduce a method based on distance measures for group decision making under uncertain linguistic environment. We develop some uncertain linguistic aggregation distance measures called the uncertain linguistic weighted distance (ULWD) measure, the uncertain linguistic ordered weighted distance (ULOWD) measure, and the uncertain linguistic hybrid weighted distance (ULHWD) measure. We study some of their characteristic, and we prove that the ULWD and the ULOWD are special cases of the ULHWD measure. Finally, we develop an application of the ULHWD measure in a group decision making problem concerning the evaluation of university faculty for tenure and promotion with uncertain linguistic information.

Study on the hazardous materials' vehicle scheduling route based on uncertain operator

In order to select the best vehicle scheduling route for hazardous materials, a new method based on uncertain operator is proposed. On the foundation of establishing the indices of hazardous materials' vehicle scheduling routes, some basic theories of Uncertain Linguistic Hybrid Aggregation ULHA operator are used and the multi-attribute vehicle scheduling route decision-making method based on ULHA is set up. Finally, an example shows the method is feasible.

Guaranteed cost control for uncertain stochastic hybrid complex delayed networks

Guaranteed cost control for uncertain stochastic hybrid complex delayed networks

Research on Digital Reference Service in the Library in Uncertain Linguistic Environment

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems for evaluating the digital reference service in the library with uncertain linguistic information. We utilize the uncertain linguistic weighted averaging (ULWA) operator and uncertain linguistic hybrid aggregation (ULHA) operator to aggregate the uncertain linguistic information corresponding to each alternative and get the overall value of the digital reference service in the library, then rank the ecommerce websites and select the most desirable one(s) by using the formula of the degree of possibility for the comparison between two uncertain linguistic variables. Finally, an illustrative example for evaluating digital reference service in the library is given to verify the developed approach and to demonstrate its practicality and effectiveness.

An Approach to Potential Evaluation of Emerging Technology Commercialization with Uncertain Linguistic Information

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems for potential evaluation of emerging technology commercialization with uncertain linguistic information. Then, we have developed an uncertain linguistic hybrid harmonic mean (ULHHM) operator. We have proved both ULWHM and ULOWHM operators are the special case of the ULHHM operator. The ULHHM operator generalizes both the ULWHM and ULOWHM operators, and reflects the importance degrees of both the given arguments and their ordered positions. Based on the ULWHM and ULHHM operators, we have proposed an approach to MAGDM for potential evaluation of emerging technology commercialization under uncertain linguistic environment. Finally an illustrative example for potential evaluation of emerging technology commercialization with uncertain linguistic information has been given to show the developed approach and to demonstrate its feasibility and practicality.

Contingent Hybrid Systems

This work proposes the first steps for studying resilient control for uncertain hybrid systems. We take a rather radical approach and consider the situations of severe uncertainty. This requires the replacement of classical Kolmogorov probabilities with special concepts from the generalized measure theory. To achieve this goal, we need a rigorous and carefully developed mathematical framework, which constitutes the major contribution of this paper. Technically, the resilience framework of hybrid systems is defined in two steps. First, we introduce the contingent hybrid system that is a mathematical model where uncertainty is quantized using both probabilities and generalized measures. Then, the concept of lithe decision is introduced for this model. The new method combines decision theory with model predictive control and statistics for uncertainty measures.

Control of Uncertain Hybrid Nonlinear Systems Using Particle Filters

This paper proposes an optimization-based algorithm for the control of uncertain hybrid nonlinear systems. The considered system class combines the nondeterministic evolution of a discrete-time Markov process with the deterministic switching of continuous dynamics which itself contains uncertain elements. A weighted particle filter approach is used to approximate the uncertain evolution of the system by a set of deterministic runs. The desired control performance for a finite time horizon is encoded by a suitable cost function and a chance-constraint, which restricts the maximum probability for entering unsafe state sets. The optimization considers input and state constraints in addition. It is demonstrated that the resulting optimization problem can be solved by techniques of conventional mixed-integer nonlinear programming (MINLP). As an illustrative example, a path planning scenario of a ground vehicle with switching nonlinear dynamics is presented.

Fuzzy ordered distance measures

Xu and Chen (J Syst Sci Syst Eng 17:432---445, 2008) introduced a type of ordered weighted distance measures called ordered weighted distance (OWD) measures whose fundamental aspect is the reordering step, which can be used in many actual fields, including group decision making, medical diagnosis, data mining, and pattern recognition, etc. The OWD measures are very suitable to deal with situations where the input data are expressed in exact numerical values. In this paper, we consider situations with linguistic, interval or fuzzy preference information, and develop some fuzzy ordered distance measures, such as linguistic ordered weighted distance measure, uncertain ordered weighted distance measure, linguistic hybrid weighted distance measure, and uncertain hybrid weighted distance measure, etc. After that, based on hybrid weighted distance measures, we establish a consensus reaching process of group decision making with linguistic, interval, triangular or trapezoidal fuzzy preference information.

Bridges over Troubled Waters: Two Touring Tempest s, 2010-2011

Beginning with Sam Mendes' 2010 Tempest - part of the director's transatlantic "Bridge Project" - and expanding to include Declan Donnellan's 2011 Russian-language Tempest for Cheek by Jowl, this essay considers the place of run-of-the-mill, big-budget, Anglophone Shakespeare alongside more daring, offbeat or niche productions. Mendes' Tempest serves as a typical example of high-profile but mediocre classical theatre, being part of a global tour and helmed by an established director, yet strangely unspecific in its reading of the play. The Anglo-American production was an uncertain hybrid of familiar styles, alternately minimalist and elaborate, and relied on the crutches of overblown sentiment, tired interpretations and a clumsy multimedia component. Donnellan's Tempest is held up in contrast, indicating the richness to be found outside the sphere of ordinary Anglophone Shakespeare. Its confident aesthetic choices, nuanced interpretation of character, and clear post-Cold War geopolitical commentary gained the Russo-English Tempest a significantly more positive reception than its Anglo-American cousin. Donnellan's production articulated, with depth, material that mattered to a global audience. Contrast Mendes' reduction of Shakespeare to a safe, muddled kind of high-status boredom.

Robust finite‐time stability of impulsive dynamical linear systems subject to norm‐bounded uncertainties

AbstractRobust finite‐time stability (FTS) for a class of uncertain hybrid systems is tackled for the first time in this paper. In particular, uncertain impulsive dynamical linear systems (U‐IDLS) are considered. U‐IDLS exhibit jumps in the state trajectory that can be either time‐driven (time‐dependent IDLS) or driven by specific state values (state‐dependent IDLS). Furthermore, U‐IDLS may exhibit uncertainties both in the linear dynamic and in the jump equation. In this paper, sufficient conditions for FTS of IDLS are provided. These results require the solution of feasibility problems involving differential‐difference linear matrix inequalities (D/DLMIs), which can be numerically solved in an efficient way, as illustrated in the proposed examples. Copyright © 2010 John Wiley & Sons, Ltd.