Uncertainties In System Dynamics Research Articles

FPGA-realization of an RBF-NN tuning PI controller for sensorless PMSM drives

The estimation and control of the rotor position for sensorless permanent magnet synchronous motor (PMSM) drives based on extended Kalman filter (EKF) and artificial neural network (ANN) is presented in this paper. The EKF is a rotor position estimator which is a full-order stochastic observer for the recursive optimum state estimation of a nonlinear dynamic system in real time by using signals that are in the noisy environment. An ANN constructed by radial basis function neural network (RBFNN) and a parameter adjustable mechanism is applied to speed control loop of the PMSM drives to cope with the effect of the system dynamic uncertainty and external load. In this paper, firstly, a mathematical model for PMSM is derived, and a sensorless FOC is built up. Secondly, the rotor position and rotor speed which are estimated by using EKF is described. These estimated values are feed-backed to the current loop for FOC and to the speed loop for RBFNN-based self-tuning PI control. Thirdly, a very high-speed IC hardware description language (VHDL) is presented to describe the behavior of the adopted control and estimation algorithm. Fourthly, to verify the correctness of the designed VHDL code of the control and the estimation algorithm, based on electronic design automation (EDA) simulator link, a co-simulation work is constructed by Simulink and ModelSim. And some simulation results verify the correctness and effectiveness. Finally, an experimental system with a PMSM, a motor driver circuit, and a field programmable gate array (FPGA) board are set up to implement the proposed rotor position estimation and speed control algorithm.

Numerical Methods for First Order Uncertain Stochastic Differential Equations

Uncertain stochastic calculus is a relatively new sub discipline of mathematics. This branch of mathematical sciences seeks to develop models that capture aleatory and epistemic features of generic uncertainty in dynamical systems. The growth of uncertain stochastic theory has given birth to a novel class of differential equations called uncertain stochastic differential equations (USDEs). Exact and analytic solutions to this family of differential equations are not always available. In such cases, numerical analysis provides a gateway to approximate solutions. This paper examines a Runge-Kutta method for solving USDEs. Before examining and applying the Runge-Kutta method, the paper states and proves the existence and uniqueness theorem. The Runge-Kutta method is then applied to solve an American call option pricing problem. This numerical algorithm proves to be effective and efficient because it produces almost the same results as compared to Chen's analytic formula and the classical Black-Scholes model.

Transformation of Uncertain Linear Fractional Order Differential Equations Into a Cooperative Form

Occurring uncertainties in dynamical systems can be difficult to handle. A solution can be found in exploiting cooperativity, which avoids the so-called wrapping effect and, hence, simplifies tasks such as the computation of guaranteed state enclosures, the design of interval observers, forecasting worst-case bounds and the identification of unknown parameters. Since not all dynamical systems are originally cooperative, a transformation of the state-space representation has been shown to be effective for ordinary differential equations. However, general approaches are not suitable for fractional order differential equations as they come with different stability regions. This paper shows a control approach for fractional order differential equations and then provides two different methods to transform the derived controlled system models into a cooperative form. The first method is applicable to systems with purely real eigenvalues while the other works for partially conjugate complex ones. Both methods are then validated on a battery system to compare the results and discuss their respective applicability.

The Data‐Limited Methods Toolkit (DLMtool): An R package for informing management of data‐limited populations

Abstract A simulation‐based approach known as management strategy evaluation (MSE) is increasingly used by resource managers to identify management procedures that are robust to uncertainties in system dynamics. The majority of global fish populations are data limited and there is large uncertainty over their population and exploitation dynamics. The Data‐Limited Methods Toolkit (DLMtool) is an R package that allows for rapid and flexible MSE specification. The package consolidates a large number of existing data‐limited management procedures and allows for rapid MSE testing of new approaches. The DLMtool package has supported transparent and rigorous decision‐making for a number of data‐limited populations, identifying robust management procedures and revealing performance trade‐offs.

Resilient Autonomous Control of Distributed Multiagent Systems in Contested Environments.

An autonomous and resilient controller is proposed for leader-follower multiagent systems under uncertainties and cyber-physical attacks. The leader is assumed nonautonomous with a nonzero control input, which allows changing the team behavior or mission in response to the environmental changes. A resilient learning-based control protocol is presented to find optimal solutions to the synchronization problem in the presence of attacks and system dynamic uncertainties. An observer-based distributed H∞ controller is first designed to prevent propagating the effects of attacks on sensors and actuators throughout the network, as well as to attenuate the effect of these attacks on the compromised agent itself. Nonhomogeneous game algebraic Riccati equations are derived to solve the H∞ optimal synchronization problem and off-policy reinforcement learning (RL) is utilized to learn their solution without requiring any knowledge of the agent's dynamics. A trust-confidence-based distributed control protocol is then proposed to mitigate attacks that hijack the entire node and attacks on communication links. A confidence value is defined for each agent based solely on its local evidence. The proposed resilient RL algorithm employs the confidence value of each agent to indicate the trustworthiness of its own information and broadcast it to its neighbors to put weights on the data they receive from it during and after learning. If the confidence value of an agent is low, it employs a trust mechanism to identify compromised agents and remove the data it receives from them from the learning process. The simulation results are provided to show the effectiveness of the proposed approach.

Fuzzy Differential Equations as a Tool for Teaching Uncertainty in Engineering and Science

This paper presents fuzzy differential equations in the context of teaching uncertainty in engineering and science. Moreover, the Cauchy problem is discussed as case of study to understand the importance of fuzzy differential equations as a natural way to model uncertainty in dynamical systems. The specific case of study reported in this paper is the Malthusian population dynamic model, which is solved by students both via analytical as well as computation al approaches as a result of applying problem-based learning teaching principles, and allowing to introduce the importance of uncertainty.

Capturing multi-stage fuzzy uncertainties in hybrid system dynamics and agent-based models for enhancing policy implementation in health systems research.

BackgroundIn practical research, it was found that most people made health-related decisions not based on numerical data but on perceptions. Examples include the perceptions and their corresponding linguistic values of health risks such as, smoking, syringe sharing, eating energy-dense food, drinking sugar-sweetened beverages etc. For the sake of understanding the mechanisms that affect the implementations of health-related interventions, we employ fuzzy variables to quantify linguistic variable in healthcare modeling where we employ an integrated system dynamics and agent-based model.MethodologyIn a nonlinear causal-driven simulation environment driven by feedback loops, we mathematically demonstrate how interventions at an aggregate level affect the dynamics of linguistic variables that are captured by fuzzy agents and how interactions among fuzzy agents, at the same time, affect the formation of different clusters(groups) that are targeted by specific interventions.ResultsIn this paper, we provide an innovative framework to capture multi-stage fuzzy uncertainties manifested among interacting heterogeneous agents (individuals) and intervention decisions that affect homogeneous agents (groups of individuals) in a hybrid model that combines an agent-based simulation model (ABM) and a system dynamics models (SDM). Having built the platform to incorporate high-dimension data in a hybrid ABM/SDM model, this paper demonstrates how one can obtain the state variable behaviors in the SDM and the corresponding values of linguistic variables in the ABM.ConclusionsThis research provides a way to incorporate high-dimension data in a hybrid ABM/SDM model. This research not only enriches the application of fuzzy set theory by capturing the dynamics of variables associated with interacting fuzzy agents that lead to aggregate behaviors but also informs implementation research by enabling the incorporation of linguistic variables at both individual and institutional levels, which makes unstructured linguistic data meaningful and quantifiable in a simulation environment. This research can help practitioners and decision makers to gain better understanding on the dynamics and complexities of precision intervention in healthcare. It can aid the improvement of the optimal allocation of resources for targeted group (s) and the achievement of maximum utility. As this technology becomes more mature, one can design policy flight simulators by which policy/intervention designers can test a variety of assumptions when they evaluate different alternatives interventions.

Online identification of large-scale chaotic system

The ensemble prediction system (EPS) is an approach employed in meteorology to estimate forecast uncertainty of dynamical systems. In EPS, an ensemble of auxiliary simulations is launched along with the main prediction. Recently, an application with the EPS framework was proposed as a method that enables algorithmic tuning of parameters of large-scale models, in cases where high-CPU demands make usual iterative optimization impractical. The approach was aimed and tested for operational numerical weather prediction models, with a relatively small number of parameters and well-tuned initial values. Here, we present a new version of the approach as a general-purpose parameter estimation method for situations where effective parallel computing is available, but high-CPU requirements exclude the use of standard sequential approaches. We treat the problem as a stochastic optimization task and employ an evolutionary approach, the differential evolution as the optimizer. We demonstrate improved convergence properties, especially for strongly biased initial values or higher number of parameters. For parametric uncertainty quantification, the approach can be considered as a heuristic sampler of the parameter distributions.

Pitch Channel Control of a REMUS AUV with Input Saturation and Coupling Disturbances

The motion of an underwater vehicle is prone to be affected by time-varying model parameters and the actuator limitation in control practice. Adaptive control is an effective method to deal with the general system dynamic uncertainties and disturbances. However, the effect of disturbances control on transient dynamics is not prominent. In this paper, we redesign the L 1 adaptive control architecture (L1AC) with anti-windup (AW) compensator to guarantee robust and fast adaption of the underwater vehicle with input saturation and coupling disturbances. To reduce the fluctuation of vehicle states, the Riccati-based AW compensator is utilized to compensate the output signal from L1AC controller via taking proper modification. The proposed method is applied to the pitch channel of REMUS vehicle’s six Degrees Of Freedom (DOF) model with strong nonlinearities and compared with L1AC baseline controller. Simulations show the effectiveness of the proposed control strategy compared to the original L1AC. Besides, the fluctuation in roll channel coupled with pitch channel is suppressed according to the performances of control tests.

Identifying target reference points for harvesting assessment-limited wildlife populations: a case study.

Identifying appropriate strategies for sustainable harvest is a challenge for many terrestrial vertebrate species because of uncertain system dynamics, limited data to inform population models, and potentially conflicting objectives that seek to harvest and maintain populations at desirable levels. The absence of monitoring and assessment infrastructure needed to regularly estimate abundance accentuates this challenge for many species, and limits application of rigorous state-dependent frameworks for decision making that are commonly advocated in natural resource management. Reference points, which define management targets or triggers for changing management, are often used to guide decision-making, but suffer from ambiguity when developed without explicit consideration of uncertainty or trade-offs among competing objectives. We describe an approach for developing unambiguous target reference points for assessment-limited species using structured decision making, and demonstrate the approach to develop target harvest rates for management of fall Wild Turkey (Meleagris gallopavo) harvests in the face of uncertain population and harvest dynamics. We use simulation and decision analyses to identify harvest rates that are optimal for accomplishing explicit management objectives in the face of uncertainty, and harvest rates with robust performance over broad regions of the demographic and harvest model parameter space. We demonstrate that population and harvest parameters commonly uncertain to wildlife managers interact to determine appropriate target harvest rates for Wild Turkeys, and that formally acknowledging a range of plausible values for structurally uncertain parameters results in more conservative target reference points than suggested by previously published studies. The structured decision making framework described here provides a natural conceptual and quantitative framework for extending our approach to develop unambiguous harvest targets for other assessment-limited wildlife populations while formally acknowledging structural uncertainty in system dynamics.

Neural Network-Based Passivity Control of Teleoperation System Under Time-Varying Delays.

In this paper, a novel neural network (NN)-based four-channel wave-based time domain passivity approach (TDPA) is proposed for a teleoperation system with time-varying delays. The designed wave-based TDPA aims to robustly guarantee the channels passivity and provide higher transparency than the previous power-based TDPA. The applied NN is used to estimate and eliminate the system's dynamic uncertainties. The system stability with linearity assumption on human and environment has been analyzed using Lyapunov method. The proposed algorithm is validated through experimental work based on a 3-DOF bilateral teleoperation platform in the presence of different time delays.

An Interval Estimator for Chlorine Monitoring in Drinking Water Distribution Systems Under Uncertain System Dynamics, Inputs and Chlorine Concentration Measurement Errors

Abstract The design of an interval observer for estimation of unmeasured state variables with application to drinking water distribution systems is described. In particular, the design process of such an observer is considered for estimation of the water quality described by the concentration of free chlorine. The interval observer is derived to produce the robust interval bounds on the estimated water quality state variables. The stability and robustness of the interval observer are investigated under uncertainty in system dynamics, inputs, initial conditions and measurement errors. The bounds on the estimated variables are generated by solving two systems of first-order ordinary differential equations. For that reason, despite a large scale of the systems, the numerical efficiency is sufficient for the on-line monitoring of the water quality. Finally, in order to validate the performance of the observer, it is applied to the model of a real water distribution network.

Uncertainty transformation via Hopf bifurcation in fast-slow systems.

Propagation of uncertainty in dynamical systems is a significant challenge. Here we focus on random multiscale ordinary differential equation models. In particular, we study Hopf bifurcation in the fast subsystem for random initial conditions. We show that a random initial condition distribution can be transformed during the passage near a delayed/dynamic Hopf bifurcation: (i) to certain classes of symmetric copies, (ii) to an almost deterministic output, (iii) to a mixture distribution with differing moments and (iv) to a very restricted class of general distributions. We prove under which conditions the cases (i)-(iv) occur in certain classes vector fields.

Fault Diagnosis of HVAC Air-Handling Systems Considering Fault Propagation Impacts Among Components

In a heating, ventilation, and air conditioning system, an air-handling system is a key module. Its components (e.g., air handling unit, air-mixing box, and fans), linked through airflows, condition air to a desired temperature and/or humidity based on comfort or controlled environment requirements. Identifying failure modes and estimating their severities allow maintenance crews to know which faults have occurred, how critical they are, and be guided in the repair process to improve the system availability. The problem of fault detection and diagnosis in air-handling systems is complex because of fault propagation across components, and high false alarm rates caused by uncertainties in system and measurement dynamics. In this paper, to capture fault propagation impacts in an efficient manner, dynamic hidden Markov models are developed to identify failure modes, since they contain state transition matrices depending on other components and do not generate joint states. To filter out false alarms, “coupled statistical process control” techniques are developed by using state transitions matrices representing coupling among components. Experimental results show that the method can effectively diagnose faults with high-diagnosis accuracy.

Neuro-Fuzzy Network Based Adaptive Tracking Controller for a Nonlinear System

In this paper, a neuro-fuzzy network-based adaptivetracking controller is suggested for controlling a type ofnonlinear system. Where two neuro-fuzzy networks have beenused to learn the system dynamics uncertainty bounds by usingLyapunov method. Then the output of these two networks isused to build a sliding mode controller. The stability of thecontrol system is proved and stable neuro-fuzzy controllerparameters adjustment laws are selected using Lyapunovtheory. The simulation case study shows that the controlled systemtracking the reference model effectively with smooth controleffort and robust performance has been achieved.

Output tracking for a class of nonlinear systems with mismatched uncertainties by active disturbance rejection control

In this paper, we apply active disturbance rejection control, an emerging control technology, to achieve practical output tracking for a class of nonlinear systems in the presence of vast matched and mismatched uncertainties including unknown internal system dynamic uncertainty, external disturbance, and uncertainty caused by the deviation of control parameter from its nominal value. The total disturbance influencing the performance of controlled output is refined first and then estimated by an extended state observer (ESO). Under the assumption that the inverse dynamics of the uncertain systems are bounded-input-bounded-state stable, a constant high gain ESO based output feedback is constructed to guarantee that the state is bounded and the output tracks practically a given reference signal. A time-varying gain ESO is also discussed to reduce the peaking value near the initial stages of ESO caused by constant high gain. Numerical simulations are presented to demonstrate the effectiveness of the proposed output-feedback control scheme.

Fractional order sliding mode control for tethered satellite deployment with disturbances

This paper proposes a fractional order sliding mode control for the deployment of tethered space systems with the consideration of uncertainty of external disturbances and unmodeled system dynamics. The proposed fractional order sliding mode control consists of two sub-sliding manifolds that are defined separately for the actuated and unactuated states. This, in turn, generates a control scheme to make all states move toward to the desired states. The stability analysis of the proposed control law indicates not only all states converge to the desired states at equilibrium but also disturbances caused by the uncertainty can be suppressed satisfactorily. Parametric studies are conducted to investigate the influences of fractional order and sub-sliding manifold of unactuated states on the performance of the proposed control law. The performance is compared with the sliding mode, PD and fractional order PD control laws for a baseline scenario of tether deployment. The proposed control law performs better than others in the settling time and the maximum pitch angle control in the presence of unwanted disturbances. Effectiveness and robustness of the proposed control law are demonstrated by computer simulations.

Transient stability enhancement control of power systems with time‐varying constraints

Transient control performance of power systems is extremely important, especially during the recovery stage from a system temporary fault. A large power angle error or generator relative speed could result in unrecoverable failure or system damage. In this study, a class of novel excitation controllers is proposed for power systems to place user-defined time-varying constraints on the system errors. First, the direct feedback linearisation technique is employed to transfer the original non-linear system to a linear one. An error transformation method is introduced to generate a new non-linear system, whose stability ensures that the time-varying constraints on the original system are satisfied. Thus, a backstepping-based excitation control methodology is designed for ideal case by assuming all system parameters are known. Thereafter, the uncertainties of system dynamics are also considered and compensated by designing an adaptive excitation controller. By utilising the standard Lyapunov synthesis, the closed-loop system is proved to be asymptotically stable, and all the other signals are bounded for the two control schemes. Furthermore, the system transient performance can be shaped arbitrarily with predefined trajectories, in the sense that the system errors never cross certain boundaries during transient phase. Eventually, extensive simulation studies demonstrate the feasibility of the theoretical results.

Robust distributed MPC for load frequency control of uncertain power systems

Reliable Load frequency control (LFC) is crucial to the operation and design of modern electric power systems. However, the power systems are always subject to uncertainties and external disturbances. Considering the LFC problem of a multi-area interconnected power system, this paper presents a robust distributed model predictive control (RDMPC) based on linear matrix inequalities. The proposed algorithm solves a series of local convex optimization problems to minimize an attractive range for a robust performance objective by using a time-varying state-feedback controller for each control area. The scheme incorporates the two critical nonlinear constraints, e.g., the generation rate constraint (GRC) and the valve limit, into convex optimization problems. Furthermore, the algorithm explores the use of an expanded group of adjustable parameters in LMI to transform an upper bound into an attractive range for reducing conservativeness. Good performance and robustness are obtained in the presence of power system dynamic uncertainties.

Basin entropy: a new tool to analyze uncertainty in dynamical systems.

In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in neuroscience, economy, astronomy, ecology and many other disciplines. Depending on the nature of the basins, prediction can be difficult even in systems that evolve under deterministic rules. From this respect, a proper classification of this unpredictability is clearly required. To address this issue, we introduce the basin entropy, a measure to quantify this uncertainty. Its application is illustrated with several paradigmatic examples that allow us to identify the ingredients that hinder the prediction of the final state. The basin entropy provides an efficient method to probe the behavior of a system when different parameters are varied. Additionally, we provide a sufficient condition for the existence of fractal basin boundaries: when the basin entropy of the boundaries is larger than log2, the basin is fractal.