Complex Uncertain Systems Research Articles

Least squares parameter estimation for uncertain fractional differential equations and application to stock model

In recent years, uncertain fractional differential equations was proposed for the description of complex uncertain dynamic systems with historical characteristics. For wider applications of uncertain fractional differential equations, researches on parameter estimation for uncertain fractional differential equations are of great importance. In this paper, based on the thought of least squares estimation and uncertain hypothesis test, an algorithm of parameter estimation for uncertain fractional differential equations is discussed. Finally, we consider the application of uncertain fractional differential equations based model to predict the forecasting stock price of three major indexes of U.S. stocks and make a comparison between uncertain fractional differential equations, uncertain differential equations and stochastic differential equations.

Conditional Sliding Mode Control-Based Fixed-Time Stabilization of Fuzzy Uncertain Complex System

Conditional Sliding Mode Control-Based Fixed-Time Stabilization of Fuzzy Uncertain Complex System

An Experimental Investigation for Detection, Localization, and Quantification of Compound Changes in Complex Uncertain Systems

An Experimental Investigation for Detection, Localization, and Quantification of Compound Changes in Complex Uncertain Systems

Reliability-constrained optimal attitude-vibration control for rigid-flexible coupling satellite using interval dimension-wise analysis

This study proposes an uncertain optimal attitude–vibration control method for rigid–flexible coupling satellites with reliability constraints based on the interval dimension-wise analysis. To model the complex uncertain control system, multi–source uncertainties in rigid–flexible coupling satellites are quantified to interval parameters. Based on the nominal rigid–flexible coupling satellite dynamic model, the interval attitude–vibration model is derived and the corresponding coupled state equation is established. Considering polynomial chaos expansions in the surrogate model, an interval dimension-wise analysis (IDWA) method is proposed to predict the uncertain state response of the uncertain attitude–vibration control system, which can help solve the overestimation problem of the conventional perturbation method. An interval linear quadratic regulator (LQR) is proposed by combining the IDWA method and deterministic LQR, to accurately optimize the uncertain control input and cost function. With regard to harsh deterministic state response constraints, this study proposes a non-probabilistic time-dependent reliability method, which allows for an effective evaluation by flexibly characterizing the relationship between the uncertain state response and threshold. The reliability-constrained multi–objective optimal attitude–vibration control problem can be solved by considering the nominal cost function and uncertain state response as two optimization objectives. The effectiveness of the proposed method is verified using a rigid–flexible coupling satellite.

Convex Temporal Convolutional Network-Based Distributed Cooperative Learning Control for Multiagent Systems.

Due to its great efficiency, scalability, and inclusivity, distributed cooperative learning control has gotten a lot of attention. For complex uncertain multiagent systems, it is challenging to model the uncertainties and exploit the cooperative learning ability of the systems. To address these issues, we proposed a novel convex temporal convolutional network-based distributed cooperative learning control for uncertain discrete-time nonlinear multiagent systems. A new concept of using a convex temporal convolutional network (CTCNet) is proposed for estimating the uncertain agent dynamics in a cooperative way. Unlike previous methods that require adjustment of network weights for different control tasks, the proposed CTCNet can map the high-dimensional input-output space into a deep space spanned by basis features that represent the inherent properties of the system, so it has good robustness for different tasks. Consequently, to improve the control performance, a CTCNet-based distributed cooperative learning control method that shares learned knowledge through the communication topology among adaptive laws of CTCNet is proposed. Furthermore, the asymptotic convergence of system tracking errors to an arbitrarily small neighborhood of the origin is strictly proved. Finally, the simulation results are given to illustrate that our suggested method has higher control accuracy, stronger robustness, and anti-interference ability than the existing methods.

A novel approach based on fault tree analysis and Bayesian network for multi-state reliability analysis of complex equipment systems

Due to the complex structure of multi-state complex systems and the lack of data, information, and knowledge, the uncertainty of the logical relationship between the failure states of systems and components and the uncertainty of related failure data become the key issues in the reliability analysis of multi-state complex systems. In this paper, combined with multi-state fault tree (MSFT), a multi-state reliability assessment framework for complex systems considering uncertainty based on multi-source information fusion and multi-state Bayesian network (MSBN) is proposed. The multi-source information fusion method combines historical data and experts’ opinions to solve the uncertainty problem of multi-state failure data in complex equipment systems effectively. Based on the multi-source information fusion method, the calculation method of multi-state prior probability and the construction method of conditional probability are given. By constructing the conditional probability table (CPT), the uncertain logic relationship between the multi-state nodes is effectively expressed, which effectively improves the efficiency of CPT acquisition for MSBN and reduces the workload of experts scoring. Finally, a mud circulating system is taken as an example to prove the proposed method, and the specific calculation process, evaluation results, and some discussions are given. The results show that the proposed method is an effective multi-state reliability analysis method for complex uncertain multi-state systems.

Neural message-passing for objective-based uncertainty quantification and optimal experimental design

Various real-world scientific applications involve the mathematical modeling of complex uncertain systems with numerous unknown parameters. Accurate parameter estimation is often practically infeasible in such systems, as the available training data may be insufficient and the cost of acquiring additional data may be high. In such cases, based on a Bayesian paradigm, we can design robust operators retaining the best overall performance across all possible models and design optimal experiments that can effectively reduce uncertainty to enhance the performance of such operators maximally. While objective-based uncertainty quantification (objective-UQ) based on MOCU (mean objective cost of uncertainty) provides an effective means for quantifying uncertainty in complex systems, the high computational cost of estimating MOCU has been a challenge in applying it to real-world scientific/engineering problems. In this work, we propose a novel scheme to reduce the computational cost for objective-UQ via MOCU based on a data-driven approach. We adopt a neural message-passing model for surrogate modeling, incorporating a novel axiomatic constraint loss that penalizes an increase in the estimated system uncertainty. As an illustrative example, we consider the optimal experimental design (OED) problem for uncertain Kuramoto models, where the goal is to predict the experiments that can most effectively enhance robust synchronization performance through uncertainty reduction. We show that our proposed approach can accelerate MOCU-based OED by four to five orders of magnitude, without any visible performance loss compared to the state-of-the-art. The proposed approach applies to general OED tasks, beyond the Kuramoto model.

Combining generalized modeling and specific modeling in the analysis of ecological networks.

The complexity of real food webs involves uncertainty in data and in underlying ecological processes, and modeling approaches deal with these challenges differently. Generalized modeling provides a linear stability analysis without narrow specification of all processes, and conventional dynamical systems models approximate functional forms to discuss trajectories in phase space. This study compares results and ecological interpretations from both methods in four-species ecological networks at steady state. We find that a specific (dynamical systems) model only provides a subset of stability data from the generalized model, which spans many plausible dynamic scenarios, allowing for conflicting results. Nevertheless, both approaches reveal that fixed points become stable when nutrient flows to predators are fettered and even more when the basal growth rate approaches a maximum. The specific model identifies a distinct ecosystem response to bottom-up forcing, the enrichment of lower trophic levels. Enrichment stabilizes a fixed point when basal species are in a resource-deprived environment but destabilizes it if resources become more abundant. The generalized model provides less specific information since infinitely many paths of enrichment are hypothetical. Nevertheless, generalized modeling of ecological systems is a powerful technique that enables a meta analysis of these uncertain complex systems.

A data‐driven scheduling approach for integrated electricity‐hydrogen system based on improved DDPG

AbstractThe involvement of hydrogen energy systems has been recognised as a promising way to mitigate climate problems. As a kind of efficient multi‐energy complementary system, the hydropower‐photovoltaic‐hydrogen (HPH) system could be an ideal approach to combining hydrogen with an installed renewable energy system to improve the flexibility of energy management and reduce power curtailment. However, the intra‐day scheduling of HPH system brings challenges due to the time‐related nonlinear hydropower generation process, the complex energy conversion process and the uncertain natural resource supply. Faced with these challenges, an improved deep deterministic policy gradient (DDPG)‐based data‐driven scheduling algorithm is proposed. In contrast to the prevalent DDPG, two sets of actor‐critic networks are properly designed based on prior knowledge‐based deep neural networks for the considered complex uncertain system to search for near‐optimal policies and approximate actor‐value functions. In addition, customized reward functions are proposed with the consideration of interactions among different energy supplies, which helps to improve convergence speed and stability. Finally, the case study results demonstrate that the proposed system model and the optimal energy management strategy based on the improved DDPG algorithm can guide the electricity‐hydrogen system to achieve rapid response and more reasonable energy management.

Uncertain Hypergraphs: A Conceptual Framework and Some Topological Characteristics Indexes

In practical applications of hypergraph theory, we are usually surrounded by the state of indeterminacy. This paper employs uncertainty theory to address indeterministic information. We initially put forward the idea of an uncertain hypergraph by combining hypergraph theory with uncertainty theory in order to provide a useful tool to deal with a variety of uncertain complex systems and to create a new interdisciplinary research field. The main focus of this paper is to propose a conceptual framework of uncertain hypergraphs and to study the operations of uncertain hypergraphs. Moreover, some topological indexes are proposed to describe the characteristics of the structures of uncertain hypergraph. Additionally, some further research directions are discussed.

Accelerating Optimal Experimental Design for Robust Synchronization of Uncertain Kuramoto Oscillator Model Using Machine Learning

The need for efficient computational screening of molecular candidates that possess desired properties frequently arises in various scientific and engineering problems, including drug discovery and materials design. However, the large size of the search space containing the candidates and the substantial computational cost of high-fidelity property prediction models makes screening practically challenging. In this work, we propose a general framework for constructing and optimizing a virtual screening (HTVS) pipeline that consists of multi-fidelity models. The central idea is to optimally allocate the computational resources to models with varying costs and accuracy to optimize the return-on-computational-investment (ROCI). Based on both simulated as well as real data, we demonstrate that the proposed optimal HTVS framework can significantly accelerate screening virtually without any degradation in terms of accuracy. Furthermore, it enables an adaptive operational strategy for HTVS, where one can trade accuracy for efficiency.

Quantifying the Multi-Objective Cost of Uncertainty

Various real-world applications involve modeling complex systems with immense uncertainty and optimizing multiple objectives based on the uncertain model. Quantifying the impact of the model uncertainty on the given operational objectives is critical for designing optimal experiments that can most effectively reduce the uncertainty that affect the objectives pertinent to the application at hand. In this paper, we propose the concept of mean multi-objective cost of uncertainty (multi-objective MOCU) that can be used for objective-based quantification of uncertainty for complex uncertain systems considering multiple operational objectives. We provide several illustrative examples that demonstrate the concept and strengths of the proposed multi-objective MOCU. Furthermore, we present a real-world example based on the mammalian cell cycle network to demonstrate how the multi-objective MOCU can be used for quantifying the operational impact of model uncertainty when there are multiple, possibly competing, objectives.

Observer-based robust control for flexible-joint robot manipulators: A state-dependent Riccati equation-based approach

In this paper, the robust control problem is tackled by employing the state-dependent Riccati equation (SDRE) for uncertain systems with unmeasurable states subject to mismatched time-varying disturbances. The proposed observer-based robust (OBR) controller is applied to two highly nonlinear, coupled and large robotic systems: namely a manipulator presenting joint flexibility due to deformation of the power transmission elements between the actuator and the robot known as flexible-joint robot (FJR) and also an FJR incorporating geared permanent magnet DC motor dynamics in its dynamic model called electrical flexible-joint robot (EFJR). A novel state-dependent coefficient (SDC) form is introduced for uncertain EFJRs. Rather than coping with the OBR control problem for such complex uncertain robotic systems, the main idea is to solve an equivalent nonlinear optimal control problem where the uncertainty and disturbance bounds are incorporated in the performance index. The stability proof is presented. Solving the complicated robust control problem for FJRs and EFJRs subject to uncertainty and disturbances via a simple and flexible nonlinear optimal approach and no need of state measurement are the main advantages of the proposed control method. Finally, simulation results are included to verify the efficiency and superiority of the control scheme.

Robust decentralized switched controller design for linear continuous-time systems

Abstract The paper is devoted to obtain original equivalent subsystem method to design of decentralized controller for linear large scale systems. On the theoretical example a new robust decentralized PID switched controller design procedure is obtained for linear time-varying (gain scheduled plant model) uncertain complex system with decentralized output and input structure. Controller design procedure to decentralized controller design performs on the subsystem level. The designed decentralized switched controller ensures the robust stability of closed-loop complex polytopic system with performance H 2 quadratic cost function (QSR). The proposed practical examples with ideal or non-ideal switch of switching parameters show the effectiveness of equivalent subsystem approach.

An Approach to Design Robust Tracking Controllers for Nonlinear Uncertain Systems

This paper provides an approach to design robust smooth controllers that allow a plant belonging to a broad class of nonlinear uncertain systems, with possible real actuators and subject to bounded or rate-bounded disturbances, to track a sufficiently smooth reference signal with an error norm smaller than a prescribed value. The proposed control laws are based on the concept of majorant systems and allow one to establish asymptotic bounds for the tracking error and its first and second derivatives. The proposed controller design is based on two parameters: the first is related to the minimum eigenvalue of an appropriate matrix, which the practical stability depends on, and the second is determined by the desired maximum norm of the tracking error and its convergence velocity. If the trajectories to be tracked are not sufficiently smooth, suitable filtering laws are proposed to facilitate implementation of the control laws and reduce the control magnitude, especially during the transient phase. The obtained theoretical results are validated in two case studies. The first one presents a tracking control design for an industrial robot, both in the joint space and workspace, with and without real actuators or velocity measurement noise. The second one deals with tracking control design for a complex uncertain nonlinear system.

Adaptive synchronization of Julia sets generated by Mittag-Leffler function

This paper investigates Julia sets for a class of complex uncertain discrete systems involving Mittag-Leffler functions. Julia sets of some classical maps are generalized, and the influence of parameter α on the characteristics of these fractal sets is discussed. An adaptive control strategy is proposed to synchronize Julia sets of two systems with different parameters and identify their unknown parameters. An example is presented to further verify the correctness and effectiveness of main theoretical results.

Reliability analysis method of the uncertain system based on fuzzy GO methodology and its application in electro-hydrostatic actuator

The Goal-Oriented (GO) methodology is a success-oriented method for system reliability analysis. However, it is not suitable to evaluate the reliability of uncertain system caused by the insufficient or fluctuated data, model uncertainty, new components, and other external factors. In our study, with the combination of fuzzy set theory and the GO model, the triangular fuzzy number and the extended principle are introduced to quantify the fuzzy uncertainties of input and output state probability respectively. Hence, a new reliability analysis method of fuzzy GO methodology for the uncertain system is proposed. It serves to obtain the membership function of the intuitionistic fuzzy state probability and the fuzzy confidence interval by using the parameter programming for system reliability analysis. As a typical small sample complex electromechanical system, the reliability analysis of electro-hydrostatic actuator (EHA) has the characteristic of fuzzy uncertainty. Using EHA as the research object, the reliability analysis is conducted by the GO methodology, the fuzzy FTA method, and the fuzzy GO methodology respectively. The comparison results of the three methodologies show that the fuzzy GO methodology is an effective and a promising method, which is a reasonable and meaningful extension of the GO methodology. It can be used as a new reliability analysis method for the complex uncertain multi-state systems.

Structured H-Infinity Controller for an Uncertain Deregulated Power System

A deregulated power system is considered to be a highly complex uncertain system due to the presence of multiple bilateral transactions. Load frequency control in such a system hence assumes significance because of the challenging nature of operation and therefore use of robust controllers is imperative. Conventional robust controller designs give higher order controllers and hence restricts its application in the industry. But the alternative is to use structured H-infinity controllers, which give sufficiently lower-order controllers and can be used in system with nonlinearities. In this paper, structured H-infinity controller has been designed for a deregulated power system considering the effect of nonlinearities like generation rate constraint, governor deadband, and time delay associated with communication network in the system from practical point of view. These physical constraints demand an electrical energy storage system. Hence, load frequency control is accomplished with a structured H-infinity controller supplemented with redox flow battery in each area of a two-area deregulated power system consisting of GENCOs of reheat thermal type.

Centralized Fault Detection of Complex Uncertain Hybrid Systems

This paper presents a centralized fault detection scheme for hybrid systems with nonlinear uncertain continuous dynamics and measurement noise. The scheme features a modular observer based on a modified hybrid automaton framework, that models each subsystem individually and the whole system as a composition of these models. The fault detection scheme employs a filtering approach, that attenuates the effect of measurement noise and allows tighter detection thresholds, and also an algorithm that handles autonomous mode transitions. As a result, the proposed approach can detect both discrete and parametric faults and guarantees no false alarms under all circumstances. Simulation results from a two-tank hybrid system example illustrate the effectiveness of the proposed scheme.

Hierarchy evaluation of water resources vulnerability under climate change in Beijing, China

Rapid population growth and increased economic activity impose an urgent challenge on the sustainability of water resources in Beijing. Water resources system is a complex uncertain system under climate change which is of vulnerability. But water resources system vulnerability research is relatively weak. In this study, we present a multifunctional hierarchy indicator system for the performance evaluation of water resources vulnerability (WRV) under climate change. We established an evaluation model, i.e., analytic hierarchy process combining set pair analysis (AHPSPA) model, for assessing WRV, in which weight is determined by the analytic hierarchy process (AHP) method and the evaluation degrees are determined by the set pair analysis (SPA) theory. According to the principle of scientificalness, representative, completeness and operability, the index systems and standard of water resources vulnerability evaluation are established based on the analysis of sensibility and adaptability which include five subsystems: climate change, water resources change, social and economic infrastructure, water use level and water security capability. The AHPSPA model is used to assess water resource vulnerability in Beijing with 26 indexes under eight kinds of future climate change scenarios. Certain and uncertain information quantity of the WRV is calculated by connection numbers in the AHPSPA model. Results show that the WRV of Beijing is in the middle vulnerability (3 or III) under above-mentioned different climate change scenarios. The uncertain information is between 37.77 and 39.99 % in the WRV evaluation system in Beijing. Compared with present situation, the WRV will become better under scenario I and III and will become worse under scenario II, scenario IV, scenario representative concentration pathways (RCP)2.6, scenario RCP4.5, scenario RCP6.0 and scenario RCP8.5. In addition, we find that water resources change and water use level factors play more important role in the evaluation system of water resource vulnerability in Beijing. Finally, we make some suggestions for water resources management of Beijing.