Problem Of Parameter Uncertainty Research Articles

A Varying-Parameter Adaptive Multi-Layer Neural Dynamic Method for Designing Controllers and Application to Unmanned Aerial Vehicles

As an increasing number of unmanned aerial vehicles (UAVs) have been widely applied in many aspects, controllers with higher performance are preferred. In this paper, a new varying-parameter adaptive multi-layer neural dynamic based controller (termed as VP-AMND controller) design method is proposed and applied to controllers of multi-rotor UAVs. First, a varying-parameter convergent neural dynamic (VP-CND) based controller is proposed and its convergence and robustness are theoretically proven. Second, by incorporating the adaptive control method into the VP-CND controller, the VP-AMND controller design method is proposed, of which the global stability, fast convergence speed and strong robustness can be guaranteed. Different from traditional triple zeroing dynamic (TZD) and VP-CND controllers, the proposed VP-AMND controller with self-tuning rates can estimate the unknown disturbances and enhance the stability of the system in the face of uncertainty. Third, computer simulation results verify that the multi-rotor UAVs with VP-AMND controllers can track time-varying trajectories quickly and solve the parameter uncertainty and disturbances problems effectively.

Event-triggered formation control of AUVs with fixed-time RBF disturbance observer

Aiming at the problem of model parameter uncertainty, unknown current disturbance and actuator input saturation of multi-AUVs formation control, an event-triggered formation strategy based on fixed-time Radial Basis Function(RBF) neural network adaptive disturbance observer is proposed, which can ensure formation control converge in fixed time. First of all, fixed time RBF disturbance observer (FRBFDO) is put forward to estimate lumped disturbance accurately. Based on the FRBFDO, with the combination of command filter and the back-stepping method, which is used to eliminate repeated derivation calculation explosion problem; Secondly, in order to save the energy consumption of network transmission resources, the event trigger mechanism is introduced into the multi-AUVs formation control. The fixed-time distributed formation controller is designed to realize the fixed-time stability of formation system, and the system convergence time is independent of the initial state. Finally, the effectiveness and rationality of the proposed algorithm are proved by the multi-AUVs formation simulation experiment.

Hybrid Process Models in Electrochemical Syntheses under Deep Uncertainty

Chemical process engineering and machine learning are merging rapidly, and hybrid process models have shown promising results in process analysis and process design. However, uncertainties in first-principles process models have an adverse effect on extrapolations and inferences based on hybrid process models. Parameter sensitivities are an essential tool to understand better the underlying uncertainty propagation and hybrid system identification challenges. Still, standard parameter sensitivity concepts may fail to address comprehensive parameter uncertainty problems, i.e., deep uncertainty with aleatoric and epistemic contributions. This work shows a highly effective and reproducible sampling strategy to calculate simulation uncertainties and global parameter sensitivities for hybrid process models under deep uncertainty. We demonstrate the workflow with two electrochemical synthesis simulation studies, including the synthesis of furfuryl alcohol and 4-aminophenol. Compared with Monte Carlo reference simulations, the CPU-time was significantly reduced. The general findings of the hybrid model sensitivity studies under deep uncertainty are twofold. First, epistemic uncertainty has a significant effect on uncertainty analysis. Second, the predicted parameter sensitivities of the hybrid process models add value to the interpretation and analysis of the hybrid models themselves but are not suitable for predicting the real process/full first-principles process model’s sensitivities.

A test on the location of the tangency portfolio on the set of feasible portfolios

Due to the problem of parameter uncertainty, specifying the location of the tangency portfolio (TP) on the set of feasible portfolios becomes a challenging task. The set of feasible portfolios is a parabola in the mean-variance space with optimal portfolios lying on its upper part. Using statistical test theory, we want to decide if the tangency portfolio is mean-variance efficient, i.e. if it belongs to the upper limb of the efficient frontier. In the opposite case, the investor would prefer to invest into the risk-free asset or into the global minimum variance portfolio which lies in the vertex of the set of feasible portfolios. Assuming that the portfolio asset returns are independent and multivariate normally distributed, we suggest a test on the location of the tangency portfolio on the set of feasible portfolios. The distribution of the test statistic is derived under both hypotheses, which we use to assess the power of the test and construct a confidence interval. Moreover, out-of-sample performance of the test is evaluated based on real data. The robustness to the assumption of normality is investigated via an extensive simulation study where we show that the new test is robust to the violation of the normality assumption and can also be used for heavy-tailed stochastic models. Moreover, in an empirical study we apply the developed theory to real data. We find that when the sample size is relatively large and a stable period is present on the market, then the mean-variance efficiency of the tangency portfolio can be statistically justified.

Reliability analysis of a load sharing k-out-of-n:F degradation system with dependent competing failures

This paper studies a load sharing k-out-of-n:F system such that its components degrade over time. Degradation of components causes dependent competing failures including soft and hard failures. After each failure, the extra workload redistributes on the surviving components and makes the change in distribution of degradation and hazard rate function of components. Furthermore, it makes a dependency property between the failure time of the components at consecutive stages of load sharing. Conditional distribution of the soft and hard failures as well as reliability function of the system are investigated. The maximum likelihood estimators of the unknown parameters and reliability function are also derived numerically. Moreover, a comprehensive example is presented to illustrate the proposed procedure in the paper. Finally, a simulation study is done and the parameter uncertainty problem is studied.

Nonlinear guaranteed cost attitude control via dynamic gain design

This paper investigates the guaranteed cost attitude control problem of a rigid-body subject to parameter uncertainty problem. The traditional LQR and guaranteed cost control (GCC) methods rest on linear systems and then entail model linearization in the application of attitude control by assuming small-angle rotations, since rigid-body attitude systems are highly nonlinear. In contrast, the proposed method effectively accounts for the nonlinearities inherent in the attitude dynamics of the rigid-body and ensures the attitude system with asymptotic stability and a guaranteed cost index. A linear state-feedback controller of the classical proportional/derivative (PD) structure is provided, which is off-line designed by some linear matrix inequality (LMI) conditions. Moreover, by virtue of the dynamic gain technology, the conditions are of simple structure, which thereby are easy to solve and eligible to turn into some optimization problems for optimizing the cost index and/or controller gains. The optimization problems are tractable to handle computationally and thus the optimal solution can be ensured. The developed theoretical results are illustrated by simulations.

Impulsive control and stability analysis of biped robot based on virtual constraint and adaptive optimization

This article is concerned with the problem of asymptotically stable periodic walking for a five‐link underactuated biped robot. Because of instantaneous change of two legs and complex dynamics during the walking process, the robot can be regarded as a nonlinear impulsive system. In order to make impulsive control of the robotic system, it is modeled as a rigid kinematic chain with Lagrange equations, which is strong coupling and hybrid. A novel state feedback controller is proposed to generate a closed‐loop periodic walking gait and track the desired trajectory of each joint. This controller is designed based on virtual constraint and hybrid zero dynamics. When the holonomic constraint of each actuator is zeroed by the controller, it can be regarded as an output. By using this method, the computation of the standard 5 degree of freedom (DOF) robot model can be reduced to 1 DOF. In addition, an adaptive optimization scheme is further investigated, which solves the problem of model parameter uncertainty. Finally, simulations are presented to illustrate the effectiveness of the proposed method.

Improving portfolio performance of renewable energy stocks using robust portfolio approach: Evidence from China

As the largest coal and the second largest crude oil consumer in the world, China has urgent task to develop its renewable energy industry quickly. By now, there are over 80 renewable energy companies listed in China’s stock exchanges. Thus to manage the market risk and achieve better investment returns of renewable energy stocks in China is of great value for policy makers and investors. The aim of this paper is to introduce an innovative portfolio allocation approach, robust portfolio, to improve portfolio performance of renewable energy stocks in China by considering the parameter uncertainty in the process of portfolio optimization. Furthermore, to make the conclusions more robust, we classify the stock market into three commonly recognized statuses: bull market, bear market and steady market, respectively, and compare the performances of robust portfolio method with traditional Markowitz approach. The empirical results indicate that the robust portfolio method can produce better performance of the renewable energy stock portfolio than Markowitz approach in various market statuses with much more flexibility in handling the problem of parameter uncertainty. This paper provides an alternative but very effective strategy other than Markowitz method for the portfolio allocation of renewable energy stocks in China.

Adaptive Fuzzy Sliding Mode Control Based on Pi-sigma Fuzzy Neutral Network for Hydraulic Hybrid Control System Using New Hydraulic Transformer

Control issue is the key for applying hydraulic hybrid system, especially for common pressure rail (CPR) system which has the huge potential to enhance efficiency. In the paper, the mathematical model of hydraulic cylinder speed control system using new hydraulic transformer is established. Then an adaptive fuzzy sliding mode controller based on Pi-sigma fuzzy neutral network is designed to solve the problem of parameter uncertainty and nonlinearity without establishing the precise model. Furthermore, compared to PID and conventional adaptive fuzzy system, the controller proposed can achieve good control performance and strong robustness in the presence of time-varying uncertainty.

Control Technologies of Deformable Air-Land Amphibious Vehicle Flight System

A deformable air-land amphibious vehicle suitable for complex urban terrain was designed, and its flight control method of area transfer was researched. The flight system structural model and dynamic model of the vehicle are established. Aiming at the problem of system parameter uncertainty caused by the deformation and trajectory tracking with the landing point change, the model reference adaptive compensator based on LQR attitude controller and PID height controller is added to solve it. Finally, the Matlab&Adams co-simulation is used to obtain the limit value of the deformation angle for area transformation. The efficiency of the control method is verified and the vehicle can track the desired trajectory.

Moment-Based Tests under Parameter Uncertainty

Abstract This paper considers moment-based tests applied to estimated quantities. We propose a general class of transforms of moments to handle the parameter uncertainty problem. The construction requires only a linear correction that can be implemented in sample and remains valid for some extended families of nonsmooth moments. We reemphasize the attractiveness of working with robust moments, which lead to testing procedures that do not depend on the estimator. Furthermore, no correction is needed when considering the implied test statistic in the out-of-sample case. We apply our methodology to various examples with an emphasis on the backtesting of value-at-risk forecasts.

Flatness-based adaptive nonlinear control for torque tracking of electro-hydraulic friction load simulator with uncertainties

Electro-hydraulic friction load simulator is able to simulate load for detecting and estimating the actuator system, which requires an ability to track accurately a given signal with high frequency. In this article, a flatness-based adaptive nonlinear controller is proposed for electro-hydraulic friction load simulator with parameter uncertainties to improve torque-tracking performance. The proposed control consists of state feedback, desired input feedforward and adaptive law to yield a stable closed-loop control system. State feedback is designed to stabilize the electro-hydraulic friction load simulator and achieve robustness against disturbances. Desired input feedforward is designed based on flatness property. And, it can enhance bandwidth by model compensation. Furthermore, in order to solve the problem of parameter uncertainty, adaptive law is adopted in this controller. The proposed controller theoretically guarantees asymptotic tracking performance in the absence of parameter uncertainties. High-accuracy tracking performance of the proposed control strategy is verified by experiments.

Salt and Pepper Noise Removal for Image Using Adaptive Pulse-Coupled Neural Network Optimized by Grey Wolf Optimization and Bidimensional Empirical Mode Decomposition

Aimed at the problem of poor noise reduction effect and parameter uncertainty of pulse-coupled neural network (PCNN), a hybrid image denoising method, using an adaptive PCNN that has been optimized by grey wolf optimization (GWO) and bidimensional empirical mode decomposition (BEMD), is presented. The BEMD is used to decompose the original image into multilayer image components. After a GWO is run to complete PCNN parameter optimization, an adaptive PCNN filter method is used to remediate the polluted noise points that correspond to the different image components, from which a reconstruction of the denoised image components can then be obtained. From an analysis of the image denoising results, the main advantages of the proposed method are as follows: (i) the method effectively solves the deficiencies that arise from the critical PCNN parameter determination issue; (ii) the method effectively overcomes the problem of high-intensity noise effects by providing a more targeted and efficient noise reduction process; (iii) when using this method, the noise points are isolated, and the original pixel points are restored well, which can lead to preservation of image detail information. When compared with traditional image denoising process algorithms, the proposed method can yield a better noise suppression effect, based on indicators including analysis of mutual information (MI), structural similarity (SSIM), the peak signal-to-noise ratio (PSNR) and the standard deviation (STD). The feasibility and applicability of the proposed denoising algorithm are also demonstrated experimentally.

Nonlinear fuzzy fault-tolerant control of hypersonic flight vehicle with parametric uncertainty and actuator fault

This study presents a nonlinear fuzzy fault-tolerant control (FTC) and a fault observer for longitudinal dynamics of hypersonic flight vehicle (HFV) with parameter uncertainty and actuator gain loss fault via sliding-mode and backstepping theory. An affine nonlinear dynamic model of HFV with parameter uncertainty and actuator fault is established based on feedback linearization technology. A nominal sliding-mode control is developed to track the command of altitude and velocity. Unknown nonlinear functions in the controller are approximated by fuzzy logic system through updating the weight parameters online. In view of the occurrence of actuator fault, a backstepping sliding-mode observer is constructed to estimate the fault. A nonlinear fuzzy FTC is then designed with the estimate fault obtained from the observer to address the problem of actuator fault and parameter uncertainty. The stability of the controller is analyzed utilizing Lyapunov theory. Numerical simulation results demonstrate the validity and robustness of the proposed controller and observer.

Model-based verification method for solving the parameter uncertainty in the train control system

This paper presents a parameter analysis method to solve the parameter uncertainty problem for hybrid system and explore the correlation of key parameters for distributed control system. For improving the reusability of control model, the proposed approach provides the support for obtaining the constraint sets of all uncertain parameters in the abstract linear hybrid automata (LHA) model when satisfying the safety requirements of the train control system. Then, in order to solve the state space explosion problem, the online verification method is proposed to monitor the operating status of high-speed trains online because of the real-time property of the train control system. Furthermore, we construct the LHA formal models of train tracking model and movement authority (MA) generation process as cases to illustrate the effectiveness and efficiency of the proposed method. In the first case, we obtain the constraint sets of uncertain parameters to avoid collision between trains. In the second case, the correlation of position report cycle and MA generation cycle is analyzed under both the normal and the abnormal condition influenced by packet-loss factor. Finally, considering stochastic characterization of time distributions and real-time feature of moving block control system, the transient probabilities of wireless communication process are obtained by stochastic time petri nets.

A novel input shaping method based on system output

This paper proposes a novel input shaping method for under-damped systems. The most important advantage of this method is that only the signals of system outputs are required for the filter design. As the model information on the target system is not needed, the problem of parameter uncertainty is avoided. The designed filter can minimize the difference between the outputs of the actual system and the reference model. Simulation and experimental results showed that the resulting filters were not only able to effectively eliminate the vibrations in the system outputs, but also achieve the desired system response time. The robustness of the resulting filters against the parameters variation was also verified by simulation and experimental results.

Global Sensitivity Analysis of the Optimal Capacity of Intersections

While the problem of optimizing traffic light phases dates back to the fifties, in the daily practice the optimal solutions are often still determined by means of deterministic approaches that assume to know exactly the incoming traffic flows and the other intersection parameters. In this framework, the problem of parameter uncertainty is normally neglected, and the flow variability is only taken into account by the responsive traffic light plans. In this paper, a hybrid model of traffic light dynamics, and a global sensitivity analysis approach are proposed with the aim of providing a methodology for evaluating the performance robustness of different traffic light optimization approaches with respect to parameters uncertainty and variability. To this end, two well known solution approaches are compared and discussed by means of a real world case study.

Robust nonlinear HVAC systems control with evolutionary optimisation

Purpose – The purpose of this research is to design a robust high-performance nonlinear multi-input multi-output heating, ventilation and air conditioning (HVAC) system controller for temperature and relative humidity regulation. Buildings are complex systems which are subjected to many unknown disturbances. Further complicating the control problem is the fact that, in practice, buildings and their systems have static nonlinearities such as power saturation that make stability difficult to guarantee. Therefore, in order to overcome these issues, a control system must be designed to be robust (performance insensitive) against uncertainties, static nonlinearities and effectively respond to unknown heat load and moisture disturbances. Design/methodology/approach – A state of the art nonlinear inverse dynamics (NID) technique is combined with a genetic algorithm (GA) optimisation scheme in order to improve robustness against uncertainty in the system's modelling assumptions. The parameter uncertainty problem is addressed by optimising the control system parameters over a specified range of uncertainty. The NID control structure provides further robustness with effective disturbance handling and a stability criteria that holds in the presence of actuator saturation. Findings – The proposed method delivers significantly more energy efficient performance whilst achieving improved thermal comfort when compared with a current industry standard HVAC controller design such as proportional-integral-derivative. The expected excellent response to disturbances is also demonstrated. Research limitations/implications – This method can easily be extended to account for other parameters with a specified uncertainty range. Practical implications – This research presents a method of optimised NID controller design which can be easily implemented in real HVAC controllers of building energy management systems with a high degree of confidence to provide high levels of thermal comfort whilst significantly reducing energy usage. Originality/value – A novel HVAC optimised NID control strategy using the robust inverse dynamics estimation feedback control topology with GA optimisation for improved robustness and tuning over a range of parameter uncertainty is described, designed and its performance benefits shown through simulation studies.

On the equivalence of quadratic optimization problems commonly used in portfolio theory

In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e., the Markowitz mean–variance problem as well as the problems based on the mean–variance utility function and the quadratic utility. Conditions are derived under which the solutions of these three optimization procedures coincide and are lying on the efficient frontier, the set of mean–variance optimal portfolios. It is shown that the solutions of the Markowitz optimization problem and the quadratic utility problem are not always mean–variance efficient.The conditions for the mean–variance efficiency of the solutions depend on the unknown parameters of the asset returns. We deal with the problem of parameter uncertainty in detail and derive the probabilities that the estimated solutions of the Markowitz problem and the quadratic utility problem are mean–variance efficient. Because these probabilities deviate from one the above mentioned quadratic optimization problems are not stochastically equivalent. The obtained results are illustrated by an empirical study.

The Unified Design for Inter-Area Stability Control Based on Backstepping

This paper proposes a unified method for inter-area power oscillations which is the key to solve coordination problems caused by different mathematical models and control theories. Firstly, the unified model, breaking the constraints of the network topology, component and the precise extents in the process, is established based on global signals. Secondly, making use of the structural feature of the unified system model, it combines advanced control theory to resolve the problem of parameter uncertainty and model error. Finally, the control law is effectively derived with backstepping method. The simulation results in Matlab show the validity of the proposed method.