Uncertain Part Research Articles

Recurrent Fuzzy Neural Network Control for Mimo Nonlinear Systems

Abstract This paper develops a design method of recurrent fuzzy neural network (RFNN) control system for multi-input multi-output (MIMO) nonlinear dynamic systerns. This control system consists of a state feedback controller and an RFNN controller. The state feedback controller is a basic stabilizing controller to stabilize the system, and the RFNN controller presents a robust controller to deal with uncertain parts of system dynamics and external disturbances. The adaptive laws of the RFNN parameters are derived based on the Lyapunov synthesis approach and a projection algorithm, so that the stability of the system and convergence of the parameters can be guaranteed. The simulation results for a robotic system and an ecological system confirm the effectiveness of the proposed design method.

3D geological mapping and potential field modelling of West Arnhem Land, Northern Territory

A regional scale 3D geological map of the upper crustal sequence in the West Arnhem Land region, Northern Territory, was compiled from surface mapping, limited drilling information, and liberal amounts of geological inference. Modelling of the gravity and magnetic field response of this map was proposed as a means of evaluating the viability of this geological hypothesis. A relatively large number of mass density and magnetic property measurements were available to constrain the transformation of 3D geological maps into property models in preparation for potential field modelling. The presence of numerous magnetic dykes, sills, and stratigraphic horizons provided many challenges for producing geologically-realistic magnetic property models at a regional scale. Modelling of the gravity field at this scale was far more straight forward and successful. After completing various forward modelling experiments, a stochastic procedure will be used to derive a large number of geological maps by making small changes to the highly uncertain interpretive parts of the original 3D geological map. It is expected that a subset of these derived geological maps will have associated mass density models that can adequately reproduce the gravity field observations. The common characteristics of the geological models in this subset will be isolated using statistical techniques and used to refine our representation of the regional scale 3D geological features.

관측기 기반 시스템에 대한 강인 디지털 재설계

본 논문은 관측기 기반 시스템에 대한 강인 디지털 재설계 방안을 제안한다. 디지털 재설계란, 기존의 안정화 된 연속시간 플랜트와 이산 시간에서 설계된 디지털 제어기와의 상태 접합 및 안정도 분석을 통해 전체 시스템을 재구성하는 것을 말한다. 그리고 전 역적 접근을 위한 방안으로서 문제를 볼록 최적화 관점으로 변환 후, 에러가 가질 수 있는 놈의 영역을 최소화하여 상태 접합을 이루고자 하였다. 본 논문에서는 관측기 기반 시스템에 대한 디지털 재설계를 목표로 하되, 추가적인 파라미터 불확실성을 고려한 강인 디지털 재설계를 구성하게 된다. 파라미터 불확실성은 이산화 과정에서 구조적 형태가 변화하기 때문에, 이를 고려하여 주어진 식을 선형 행렬 부등식 형태로 나타내게 된다. 이 조건들을 통해 디지털 재 설계의 상태 접합 및 안정도가 유도 가능하다는 것을 본 논문에서 증명하게 된다. In this paper, we presents robust digital redesign (DR) method for observer-based linear time-invariant (LTI) system. The term of DR involves converting an analog controller into an equivalent digital one by considering two condition: state-matching and stability. The design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between interpolated linear operators to be matched. Also, by using the bilinear and inverse bilinear approximation method, we analyzed the uncertain parts of given observer-based system more precisely, When a sampling period is sufficiently small, the conversion of a analog structured uncertain system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the state-matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs).

불확실성을 갖는 비선형 시스템의 강인한 지능형 디지털 재설계

본 논문은 불확실성을 포함한 비선형 시스템에 대한 제어를 위해 강인 지능형 디지털 재설계의 전 역적 접근 방안에 대해 제안하고자 한다. 이산화를 통한 제어기 설계에 있어서 불확실성이 포함된 실시간 비선형 시스템에 대해 보다 효율적이고 안정적인 접근을 위해 T-S 퍼지 모델이 사용되었다. 그리고 전역적 접근을 위한 방안으로서 문제를 볼록 최적화 관점으로 변환 후, 오차가 가질 수 있는 놈의 영역을 최소화 하여 상태 접합을 이루고자 하였다. 또한 쌍선형과 역 쌍선형 기법을 사용함으로써 불확실성이 포함된 비선형 시스템을 보다. 더 정확하게 분석하였다. 샘플링 기간이 충분히 작다면, 불확실 비선형 시스템의 실시간 시스템으로의 전환이 충분한 이유를 가지게 된다. 전 역적 접근을 통한 디지털로 제어된 시스템은 선형 행렬 부등식 형태로 바꾸어 시스템의 안정성을 보장하고자 하였다. 마지막으로 T-S 퍼지 모델로 분석된 혼돈 Lorenz system에 적용함으로써 제안된 방법의 안정성과 효율성을 확인한다. This paper presents intelligent digital redesign method for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent the complex system. And global approach design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between nonlinearly interpolated linear operators to be matched. Also, by using the bilinear and inverse bilinear approximation method, we analyzed nonlinear system's uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the global state-matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). Finally, a TS fuzzy model for the chaotic Lorentz system is used as an . example to guarantee the stability and effectiveness of the proposed method.

A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers

In this paper we propose a new arithmetic and a novel order relation for interval numbers. We shall show that this new interval arithmetic satisfies some operational properties and has the merit that it reduces uncertainties coming from classic ones. We shall also show that the order relation introduced in this paper is a linear or partial order (satisfying reflexivity, anti-symmetry and transitivity), and has the property of comparability. This is in contrast to the existing interval orders which do not have the property of comparability. Numerical examples on profit intervals and uncertain interval data will be presented to demonstrate the usefulness and applicability of these new arithmetic and order relations.

A novel approach in uncertain programming part II: a class of constrained nonlinear programming problems with interval objective functions

In this paper we present a novel approach to a class of constrained nonlinear programming problems with interval objective functions. In this approach we first introduce a new concept of optimal solutions to the nonlinear programming problem, based on a new linear order relation for interval numbers proposed in Part 1 of this series. We then propose two efficient methods for the solution of the nonlinear optimization problem with respect to the new interval order relation. Comparisons between our approach and some existing methods will be given using illustrative examples. The numerical results show the superiority of our method to the existing ones.

ROBUST H∞ FILTERING FOR DISCRETE-TIME NONLINEAR STOCHASTIC SYSTEMS

In this paper we establish an H∞ filtering theory for discrete-time stochastic systems with uncertainties of a stochastic nature. In particular, we model the uncertain part of the system as a white noise. The theory which is developed in this paper is based on the concept of stochastic dissipativity. It is shown in this paper that stochastic dissipation yields a stochastic Bounded Real Lemma (BRL) which is the basis for the filtering theory developed in this paper. A necessary and sufficient conditions for the existence of a solution to the filtering problem are established. The issue of feasible solutions is discussed and sufficient conditions for a feasible solution to the filtering problem are given in terms of matrix inequalities.

Powrer Series를 이용한 불확실성을 갖는 비선형 시스템의 지능형 디지털 재설계

This paper presents intelligent digital redesign method of global approach for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent tile complex system. And global approach design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between nonlinearly interpolated linear operators to be matched. Also, by using the power series, we analyzed nonlinear system`s uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the global state-matching of tile digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). Finally, a TS fuzzy model for the chaotic Lorentz system is used as an example to guarantee the stability and effectiveness of the proposed method.

Object recognition with uncertain geometry and uncertain part detection

This paper presents a method for object recognition once parts have been detected. The recognition task is formulated as a graph problem searching for the characteristic geographical arrangements of (possibly missing) parts. The objective function is Bayesian maximum a posteriori estimation, integrating the image likelihood as a posteriori probability of the part detectors. The variability in the arrangement of object parts is captured by a Gaussian distribution after translation normalization. By employing two special properties of a Gaussian distribution, we are able to deal with missing parts situation where the chosen origin is not detected. We use an A ∗ algorithm to find the optimal solution for the graph search problem. Experiments are performed on both synthetic and real data to demonstrate good results and fast performance of the recognition.

Probabilistic Argumentation Systems with Decision Variables

The general concept of probabilistic argumentation systems PAS is restricted to the two types of variables: assumptions, which model the uncertain part of the knowledge, and propositions, which model the rest of the information. Here, we introduce a third kind into PAS: so-called decision variables. This new kind allows to describe the decisions a user can make to react on some state of the system. Such a decision allows then possibly to reach a certain goal state of the system. Further, we present an algorithm, which exploits the special structure of PAS with decision variables. Some results related with this paper were published in (Anrig and Baziukaite, 2003a).

Accuracy of theoretical equations for diffusion currents at a disk electrode

The uncertainty of the most accurate and convenient theoretical equation for the diffusion current at a disk electrode now available, the Shoup–Szabo equation, was found experimentally. The diffusion coefficient and the concentration of the electroactive species were calculated from the two adjustable parameters of the equation that were obtained by curve fitting of the observed chronoamperogram to the equation. The value of the concentration obtained differed from the actually known value, and the difference between these two values changed according to the time region of the chronoamperogram analyzed. The maximum deviation from its known value of the concentration obtained was ±3%. The dummy data obtained from the results of the digital simulation of this problem gave similar results. The most uncertain part of the equation covered the time region of the usual chronoamperogram taken by a μm- or mm-sized disk electrode.

Sliding mode state observation for non-linear systems

In this paper a class of non-linear systems with uncertainty and a Lipschitz part is considered. The non-linear part satisfies the Lipschitz condition, whilst the uncertain part is a bounded function. A sliding mode observer is designed to yield feedforward compensation input to stabilize the error estimation system with and without a Lipschitz non-linearity. Sufficient conditions for stability of the Thau observer are also proposed. These conditions ensure the stability of the non-linear observer by selecting a suitable observer gain matrix. In general, when the system contains unmatched uncertainty, ultimate boundedness is obtained. The ultimate boundedness radius depends upon the defined ‘distance of the unmatched uncertainty’. Some sufficient conditions may ensure the stability of a non-linear observer for systems with uncertainties.

Comments upon Two Fragments of a Cryptographic Papyrus

This short notification tries to examine the two remained fragments of a Greek magical cryptographic papyrus (POsl III, 75, and PMich inv. 534) from new aspects. Regarding the characters of the cryptographic alphabet used in the text, it seems plausible that Greek music notation had a significant effect on the development of the cipher, as far as the transformation methods are concerned. The next section draws attention not only to the uncertain parts of the present transcription but also to the problematic points of Karl Preisendanz's interpretation of the whole magic spell. It also implies a new interpretation, which does not assume that the author “confused” the names of Typhon and Osiris but suggests that the spell is addressed to much more vicious powers than Isis.

Load characterization during transportation

The reliability of a product is a function of the product’s architecture, constituent parts and materials, as well as its life cycle environmental conditions. Of these, determination of the life cycle environment (which includes manufacturing, handling, transportation, and application conditions) is often the most uncertain part in the calculation of reliability. This paper presents a methodology to measure and characterize the dynamic nature of a transportation environment induced by a commercial carrier service on a packaged product. An example is given, and the measured environment is compared with standard industry data.

From manufacturing scheduling to supply chain coordination: The control of complexity and uncertainty

With time-based competition and rapid technology advancements, effective manufacturing scheduling and supply chain coordination are critical to quickly respond to changing market conditions. These problems, however, are difficult in view of inherent complexity and various uncertainties involved. Based on a series of results by the authors, decomposition and coordination by using Lagrangian relaxation is identified in this paper as an effective way to control complexity and uncertainty. A manufacturing scheduling problem is first formulated within the job shop context with uncertain order arrivals, processing times, due dates, and part priorities as a separable optimization problem. A solution methodology that combines Lagrangian relaxation, stochastic dynamic programming, and heuristics is developed. Method improvements to effectively solve large problems are also highlighted. To extend manufacturing scheduling within a factory to coordinate autonomic members across chains of suppliers, a decentralized supply chain model is established in the second half of this paper. By relaxing cross-member constraints, the model is decomposed into member-wise subproblems, and a nested optimization structure is developed based on the job shop scheduling results. Coordination is performed through the iterative updating of cross-member prices without accessing other members’ private information or intruding their decision-making authorities, either with or without a coordinator. Two examples are presented to demonstrate the effectiveness of the method. Future prospects to overcome problem inseparability and improve computing efficiency are then discussed.

Optimized Robust Filter for Uncertain Discrete Time System and Its Application to Flight Test

An optimized robust filtering algorithm for uncertain discrete-time systems is presented. To get a series of computational equations, the uncertain part generated by the uncertain systematic matrix in the expression of the error-covariance matrix of time update state estimation is optimized and the least upper bound of the uncertain part is given. By means of these results, the equivalent systematic matrix is obtained and a robust time update algorithm is built up. On the other hand, un-certain parts generated by the uncertain observation matrix in the expression of the error-covariance matrix of measurement update state estimation are optimized, and the largest lower bound of the un-certain part is given. Thus both the time update and measurement update algorithms are developed. By means of the matrix inversion formula, the expression structures of both time update and measurement update algorithms are all simplified. Moreover, the convergence condition of a robust filter is developed to make the results easy to application. The results of flight data processing show that the method presented in this paper is efficient.

Extending community ecology to landscapes

A goal of landscape ecology is to infer processes or constraints that generate spatial pattern in communities and ecosystems. The rich tradition of plant community ecology is now being extended to address spatial pattern in vegetation over large spatial extents. The challenge in this is that vegetation pattern on landscapes is fine-grained, which presents sampling problems for large study areas. Further, spatial autocorrelation in ecological data, coupled with strong patterns of correlation among environmental factors (such as the gradient complexes governed by elevation) make it difficult to make clear inferences about the agents patterning landscape-scale vegetation. Here we review the methods of plant community ecology as extended to landscapes and illustrate the challenges with a case study from Sequoia-Kings Canyon National Park in California’s southern Sierra Nevada. We outline an iterative approach to such studies, with three stages. The first stage is a pilot study to characterize the spatial scaling of environmental factors presumed to be important to vegetation; this stage can often be conducted virtually, using digital terrain data. The second stage is iterative and consists of building a preliminary explanatory model using a combination of ordination, classification, and Mantel tests: all analyses based on the same ecological distance or dissimilarity matrices. This preliminary model is then attacked to find its uncertain or sensitive parts, and these parametric conditions are mapped into geographic space to identify candidate sites for follow-up field studies in the third stage. This approach ensures that the most uncertain aspects of the preliminary model are refined in an efficient manner. As the approach proceeds toward a richer understanding of species-environment relationships and vegetation pattern, a need emerges for new kinds of field studies and novel extensions to existing statistical analyses. We discuss possible extensions of these as a natural consequence of this iterative process of model construction and revision.

Radical innovation: triggering initiation of opportunity recognition and evaluation

The gap between a firm’s reservoir of technical knowledge and the formation of a project to explore the commercial potential of a breakthrough technical insight or discovery is the first major discontinuity in the radical innovation lifecycle. The first step toward bridging that gap occurs when the researcher with the technical insight recognizes that it might have commercial potential and decides to alert a research manager. In our longitudinal study of eight radical innovation projects in six large, multi‐national, R&D‐intensive firms, the initiation of a radical innovation project was neither frequent nor routine. In fact the participants in the study indicated that the initiation of a project – in their terminology, the ‘fuzzy front end of innovation’– was the most challenging and uncertain part of the lifecycle. In this paper we explore the case data to illuminate the nature of the initiation gap. In addition we present an assessment framework that can help researchers decide whether or not to bring their technical idea to the attention of management. If the decision is positive, the assessment tool can help them prepare for the discussion with management and identify the strengths and weaknesses of the case to submitted for evaluation.

On the output feedback stability for non-linear uncertain control systems

In this paper, we will study the stability problem by output feedback of a class of uncertain control systems, whose nominal part is linear and whose uncertain part is norm-bounded by a known function. We propose an output controller that forces the state to the origin, in the global exponential stability sense.

Robust stability of uncertain systems with differentiable nonlinearity

Abstract The aim of this paper is to find the robust stability conditions of a closed-loop tune invariant systems, winch consist of the robust stable uncertain linear part and the differ entiable nonlinearity as feedback. The nonlinearity satisfies usual sector limitations and some additional weak conditions. When Lite linear part is certain all that was said is close to known Kalman-Aizerman problem. The solution of the robust absolute stability problem is obtained by means of special Lyapunov function.