Nonlinear Parameter Perturbations Research Articles

Application of the Observation‐Oriented CNOP‐P Sensitivity Analysis Method in Evapotranspiration Simulation and Prediction Over the Tibetan Plateau

AbstractTo improve the ability to accurately simulate and predict evapotranspiration (ET) over the Tibetan Plateau (TP), an observation‐oriented sensitivity analysis (SA) method based on a conditional nonlinear optimal parameter perturbation (CNOP‐P) method is employed. With the observation‐oriented CNOP‐P SA method, a sensitive parameter subset among all parameters is first determined through comparison with observations of ET across the TP. Then, the sensitive parameter combination is optimized to evaluate the ET simulation ability and prediction skill over the TP. A traditional one‐at‐a‐time (OAT) method is also employed, and the results are compared with the numerical results obtained with the observation‐oriented CNOP‐P SA method. The results show that the identified parameter combination using the observation‐oriented CNOP‐P SA method is more sensitive than that using the OAT method for the estimation of ET at 13 sites on the TP. The above results demonstrate that it is important to determine the sensitive parameter combination using the observation‐oriented SA method to improve the ET simulation ability and prediction skill over the TP.

Applications of CNOP-P Method to Predictability Studies of Terrestrial Ecosystems

In this paper, recent research on terrestrial ecosystem predictability using the conditional nonlinear optimal parameter perturbation (CNOP-P) method is summarized. The main findings include the impacts of uncertainties in climate change on uncertainties in simulated terrestrial ecosystems, the identification of key physical parameters that lead to large uncertainties in terrestrial ecosystem modeling and prediction, and the evaluation of the simulation ability and prediction skill of terrestrial ecosystems by reducing key physical parameter errors. The study areas included the Inner Mongolia region, north–south transect of eastern China, and Qinghai–Tibet Plateau region. The periods of the studies were from 1961 to 1970 for the impacts of uncertainties in climate change on uncertainties in simulated terrestrial ecosystems, and from 1951 to 2000 for the identification of the most sensitive combinations of physical parameters. Climatic Research Unit (CRU) data were employed. The numerical results indicate the important role of nonlinear changes in climate variability due to the occurrences of extreme events characterized by CNOP-P in the abrupt grassland ecosystem equilibrium state and formation of carbon sinks in China. Second, the most sensitive combinations of physical parameters to the uncertainties in simulations and predictions of terrestrial ecosystems identified by the CNOP-P method were more sensitive than those obtained by traditional methods (e.g., one-at-a-time (OAT) and stochastic methods). Furthermore, the improvement extent of the simulation ability and prediction skill of terrestrial ecosystems by reducing the errors of the sensitive physical parameter combinations identified by the CNOP-P method was higher than that by the traditional methods.

Application of the CNOP‐P Ensemble Prediction (CNOP‐PEP) Method in Evapotranspiration Forecasting Over the Tibetan Plateau to Model Parameter Uncertainties

AbstractModel parameter errors are one of the sources of uncertainty when simulating or predicting evapotranspiration (ET) over the Tibetan Plateau (TP). To enhance the ET simulation ability and prediction skill over the TP, the conditional nonlinear optimal parameter perturbation (CNOP‐P) method is used to establish an ensemble prediction method (called the CNOP‐PEP method) to represent uncertainties arising due to the model parameters to implement ensemble prediction experiments. The one‐at‐a‐time (OAT) method and the traditional stochastically perturbed parametrization (SPP) scheme are also employed to implement ensemble prediction experiments for comparison with the CNOP‐PEP method. The numerical results show that all ensemble prediction experiments conducted with the three methods exhibit improved prediction skills compared to the reference ET over the TP. Furthermore, the prediction skill by employing the CNOP‐PEP method is more excellent than those of the OAT and SPP methods when predicting ET over the TP. The physical mechanism analysis shows that the improved evaporation characterization obtained with the ensemble prediction experiments plays a key role in reducing uncertainties when simulating and predicting ET over the TP. The above results indicate that ensemble prediction methods are a helpful tool to improve the simulation ability and prediction skill of the ET over the TP for analyzing model parameters. In addition, the CNOP‐PEP method can supply prime ensemble members to represent uncertainties in model parameters.

New delay-range-dependent exponential stability criterion and $ H_\infty $ performance for neutral-type nonlinear system with mixed time-varying delays

<abstract><p>For a neutral system with mixed discrete, neutral and distributed interval time-varying delays and nonlinear uncertainties, the problem of exponential stability is investigated in this paper based on the $ H_\infty $ performance condition. The uncertainties are nonlinear time-varying parameter perturbations. By introducing a decomposition matrix technique, using Jensen's integral inequality, Peng-Park's integral inequality, Leibniz-Newton formula and Wirtinger-based integral inequality, utilization of a zero equation and the appropriate Lyapunov-Krasovskii functional, new delay-range-dependent sufficient conditions for the $ H_\infty $ performance with exponential stability of the system are presented in terms of linear matrix inequalities. Moreover, we present numerical examples that demonstrate exponential stability of the neutral system with mixed time-varying delays, and nonlinear uncertainties to show the advantages of our method.</p></abstract>

Attitude control of on-orbit capture spacecraft with angular velocity constraint

Aiming at the attitude control problem of spacecraft in the capturing non-cooperative target process, a dual tracking robust adaptive attitude controller is designed. Firstly, a bounded virtual angular velocity is designed for the kinematics equations to guarantee that the attitude converges to zero quickly. Secondly, a new attitude controller is constructed based on the barrier Lyapunov function to ensure that the tracking error between virtual angular velocity and real angular velocity is bounded. The physical constraint of the angular velocity is satisfied. Applying Lyapunov's stability theory, the global asymptotic stability of the closed-loop system is analyzed. To overcome the nonlinear parameter perturbation with unknown upper bound in the process of capturing non-cooperative target, an adaptive updating law based on linear regression operator is constructed to estimate the rotational inertia on-line. Finally, the process of capturing the trajectory tracking of non-cooperative targets through numerical simulation. The simulation results demonstrate that the algorithm designed is effective and robust under the constraint of the bounded angular velocity or internal parameter perturbation with unknown upper bound.

A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach

This paper deals with the new formulated problem of designing a robust delay-dependent guaranteed optimal cost proportional-integral-derivative (PID) multivariable output feedback controller for linear uncertain time delay systems with nonlinear parameter perturbations using a linear matrix inequalities (LMI) approach. Several less conservative delay-dependent stability conditions are formulated for the time-delay system under consideration in terms of LMIs. Based on an augmented form of Lyapunov-Krasovskii functionals, the free weighting matrices and Wirtinger inequality techniques are employed to obtain improved performance. An optimal guaranteed cost PID controller which minimizes the upper bound of cost function is provided. The main advantage of the proposed approach is to decouple the input and the output gain matrices allowing to synthesize the controller gain matrices through a strict LMI technique. The synthesis conditions are thus formulated in LMI form which avoids the use of any iterative approach to resolve the feasibility problem. Two numerical examples selected from the literature are presented to illustrate the effectiveness of the developed methodology. The numerical results indicate that the proposed method performs efficiently in comparison to the approaches from the existing literature.

An improved whale optimization algorithm for locating critical slip surface of slopes

Locating a critical slip surface or calculating the minimum safety factor of a slope is important in geotechnical engineering, and also involves a complex optimization problem. A novel mathematical model considering linear and nonlinear failure criteria is developed to locate the critical slip surface. And an improved whale optimization algorithm (IWOA), which employs a nonlinear adjustment parameter and Gaussian perturbation operator in whale optimization algorithm (WOA), is proposed to examine this model. The parameter of IWOA is determined by numerical experiments. The performance of IWOA, WOA, salp swarm algorithm (SSA), and cuckoo search algorithm (CS) is investigated. Statistical analyses of twelve benchmark functions show that the four algorithms with high to low performances are IWOA, WOA, SSA and CS. Two multimodal functions for analyzing slope stability show that IWOA outperforms ant colony optimization algorithm (ACO), and imperialistic competitive algorithm (ICA). The time computational complexity of IWOA is same as WOA. Case studies of homogeneous and multilayer soil slopes indicate that the failure criterion has a significant effect on the minimum safety factor and the critical slip surface, and that IWOA can show better performance than WOA, SSA and CS. This study develops an efficient method to locate critical slip surfaces of soil slopes for engineers.

Uncertainty range of projected soil carbon responses to climate warming in China

AbstractSoil carbon is becoming increasingly difficult to predict due to uncertainties in climate warming. The main objective of this research is to estimate the scope of uncertainties in soil carbon, which is the difference between maximal and minimal estimations of soil carbon, caused by uncertainties in climate change in China, by applying the Lund–Potsdam–Jena (LPJ) model and an improved optimization method. Based on an original optimization method (conditional nonlinear optimal parameter perturbation, CNOP‐P), a cost function is revised to evaluate the scope of uncertainties in predicting soil carbon sequestration, avoiding the overestimation of uncertainties. Two types of climate change projections are obtained from 10 global circulation models (GCMs) under the Representative Concentration Pathway (RCP) 4.5 scenario using two methods. For the first type of climate change projection, the upper and lower limits of estimated future soil carbon sequestration are 102.7 and 65.5 Gt, respectively, whereas the reference soil carbon sequestration driven by an ensemble of 10 GCMs is 79.6 Gt. The estimated future soil carbon sequestration ranges from 79.4 to 91.6 Gt for the second type of climate change. The numerical results imply that these two types of climate change, constrained by the projection of 10 GCMs, are the main factors affecting the uncertainty range of estimated soil carbon.

Delay-Dependent Robust H∞ Performance for Uncertain Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

This paper deals with the problems of delay-dependent stability and H∞ performance for uncertain neutral systems with time-varying delays, and nonlinear perturbations. The time-varying delays are neutral, discrete, and distributed time-varying delays that the upper bounds for the delays are available. The restrictions on the derivatives of the discrete and distributed time-varying delays are removed, which mean that a fast discrete time-varying delay is allowed. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Firstly, by applying a novel Lyapunov-Krasovskii functional approach, Wirtinger-based integral inequality, Peng-Park’s integral inequality, decomposition technique of constant matrix, descriptor model transformation, Leibniz Newton formula and utilization of zero equation, and improved delay-dependent bounded real lemmas (BRL) for systems are established in terms of linear matrix inequalities (LMIs). Then, based on the obtained BRL, some less conservative delay-dependent stability criteria of uncertain neutral systems with mixed time-varying delays and nonlinear perturbations are obtained and improved H∞ performance criterion with the framework of LMIs is introduced. Finally, some numerical examples are given to illustrate that the presented method is effective.

Robust fuzzy adaptive integral sliding mode controller for offshore steel jacket platform

In this paper, a new fuzzy adaptive integral sliding mode controller is designed for suppressing the oscillation amplitudes of offshore platform subject to nonlinear wave-excited forces and parameter perturbation. First, an uncertain dynamic model of the offshore platform is considered. To overcome the constraint of the knowledge of offshore platform model, a new fuzzy adaptive integral sliding mode controller is proposed that is a combination of sliding mode as a robust controller, fuzzy mechanism as a universal approximator and an adaptive control law. In comparison with some existing controllers, the proposed control scheme requires much less control force and the vibration amplitudes are reduced significantly. This controller is designed based on solving a set of linear matrix inequalities. Finally, the simulation results show the effectiveness of the proposed control scheme.

Robust attitude controller design for miniature quadrotors

SummaryThis paper addresses the robust attitude control problem of miniature quadrotors. A simplified linear dynamical model is obtained for each attitude angle, whereas nonlinear dynamics, interaxis coupling, parameter perturbations, and external disturbances are considered as uncertainties. For each channel, a linear time‐invariant and decoupled robust controller are proposed based on a linear reduced‐order observer and a robust compensator. The observer is applied to estimate the angular velocities, and the robust compensator is introduced for reducing the effects of uncertainties. It is proven that the estimation errors of angular velocities and angular tracking errors can converge to the given neighborhood of the origin in a finite time. Experimental results on the miniature quadrotor are presented to verify the effectiveness of the proposed control approach. Copyright © 2015 John Wiley & Sons, Ltd.

Nonlinear Ensemble Parameter Perturbation for Climate Models

Abstract Model parameters can introduce significant uncertainties in climate simulations. Sensitivity analysis provides a way to quantify such uncertainties. Existing sensitivity analysis methods, however, cannot estimate the maximum sensitivity of the simulated climate to perturbations in multiple parameters. This study proposes the concept of nonlinear ensemble parameter perturbation (NEPP), which is independent of model initial conditions, to estimate the maximum effect of parameter perturbations on simulating Earth’s climate. The NEPP is obtained by solving a maximization problem, whose cost function is defined by the maximum deviation of a unique ensemble of short-term predictions with large enough members caused by parameter perturbations and whose optimal solution is obtained by an ensemble-based gradient approach. This method is used to investigate the effects of NEPP on the climate of the Lorenz-63 model and a complex climate model, the Grid-Point Atmospheric Model of IAP LASG, version 2 (GAMIL2). It is found that the NEPP is capable of estimating the maximum change in climate simulation caused by perturbations in multiple parameters when the Lorenz-63 model is used. With a low computational cost, the NEPP can cause remarkable changes in the climatology of GAMIL2. The results also illustrate that the effects of parameter perturbations on short-term weather predictions and those on long-term climate simulations are correlated.

L2–L∞ filtering for stochastic Markovian jump delay systems with nonlinear perturbations

This paper is concerned with the L2–L∞ filtering problem for Itô stochastic delayed Markovian jump systems subject to nonlinear parameter and sensor perturbations. The nonlinear perturbations in both state and measurement equations considered in the existing literature are generalizeed by including the cross information among the current state, the delayed state and the nonlinear perturbations. Based on a stochastic integral inequality and the convex analysis property, an L2–L∞ performance condition is presented to guarantee the mean-square exponential stability of the resulting filtering error system with prescribed L2–L∞ disturbance attenuation level. By utilizing the information of the time-varying delay, the delay is not estimated by the worst-case enlargement such that the conservatism is reduced. Then with the obtained performance analysis result, a stochastic L2–L∞ filter for the system under consideration is designed. Illustrative examples are given to demonstrate the usefulness of the developed approach.

Robust adaptive sliding mode control based on wavelet kernel principal component for offshore steel jacket platforms subject to nonlinear wave-induced force

This paper is concerned with adaptive integral sliding mode control (AISMC) based on a wavelet kernel support vector machine for offshore steel jacket platform subject to nonlinear wave-excited force and parameter perturbations. The sliding mode control technique is combined with adaptive control algorithm and wavelet support vector machine to achieve the desired attenuation on the wave-induced vibration and to limit the displacement of offshore platforms. In this method, wavelet kernel support vector machine is used to establish the adaptive controller and an on-line learning rule for the weighting vector and bias is derived. The most important feature of the proposed control strategy is its inherent robustness and its ability to handle the nonlinear behavior of the offshore platform. By means of this control scheme the performance of the AISMC has been improved. The performance of the proposed control strategy is compared with some existing control schemes. It is demonstrated that the proposed control scheme in this paper is more effective in improving the control performance of the offshore platform. This controller is designed based on solving a set of linear matrix inequalities. It has been illustrated through simulation results that the proposed control scheme is effective in improving the control performance of offshore platforms.

Robust [formula omitted] attitude control of a laboratory helicopter

This paper deals with the attitude tracking control problem for a three degree-of-freedom laboratory helicopter, which aims to improve tracking control performances of elevation and pitch channels. The model of each channel is considered as a linear system with equivalent disturbances which contain nonlinear uncertainties, coupling effects, parameter perturbations, and external disturbances. A state-feedback H∞ controller is applied to the linear model and a robust compensator is introduced to restrain the effects of equivalent disturbances. The robust properties of the closed-loop control system with the proposed controller are shown better than the standard H∞ controller. Experimental results demonstrate the improved performances of the proposed control strategy.

Real-Time Implementation of Decoupled Controllers for Multirotor Aircrafts

In this paper, a practical controller design method is presented to control six degrees of freedom multirotor aircrafts---quadrotors. The quadrotor system is divided into four subsystems; that is, the longitudinal, lateral, yaw, and height subsystems. Then, a linear and decoupled nominal model is obtained for each subsystem, whereas coupling and nonlinear dynamics, parametric perturbations, and external disturbances are considered as uncertainties. For each subsystem, a decoupled robust controller is then proposed. Although there exist coupling between each channel, the output tracking errors of the four subsystems are proven to ultimately converge into a-priori set neighborhood of the origin. Finally, real-time implementation results of the decoupled controller are given to demonstrate its viability and applicability.

Robust attitude tracking control of small-scale unmanned helicopter

Robust attitude control problem for small-scale unmanned helicopters is investigated to improve attitude control performances of roll and pitch channels under both small and large amplitude manoeuvre flight conditions. The model of the roll or pitch angular dynamics is regarded as a nominal single-input single-output linear system with equivalent disturbances which contain nonlinear uncertainties, coupling-effects, parameter perturbations, and external disturbances. Based on the signal compensation method, a robust controller is designed with two parts: a proportional-derivative controller and a robust compensator. The designed controller is linear and time-invariant, so it can be easily realised. The robust properties of the closed-loop system are proven. According to the ADS-33E-PRF military rotorcraft standard, the controller can achieve top control performances. Experimental results demonstrate the effectiveness of the proposed control strategy.

외란관측기를 이용한 모션 스테이지의 위치제어

For commercialized servo drives of the motion stage to include embedded controller, external terminal is provided for tracking command and encoder output, but internal terminal is not for control input. Thus, it is difficult to combine out signal of embedded controller with that of external compensator such as disturbance observer. In this study, for precise tracking control of motion stage without hardware change of the servo drive, tacking control system is composed of an inner loop of servo drive and an outer loop of disturbance observer. Then, the control system is designed so that the output response of actual plant corresponds with nominal model's in transient state as well as in steady state. Finally, the experiment results show that the designed control system is effective to reconcile actual plant behavior with nominal model under nonlinear friction and parameter perturbation.

Extended application of the conditional nonlinear optimal parameter perturbation method in the common land model

An extension of the conditional nonlinear optimal parameter perturbation (CNOP-P) method is applied to the parameter optimization of the Common Land Model (CoLM) for the North China Plain with the differential evolution (DE) method. Using National Meteorological Center (NMC) Reanalysis 6-hourly surface flux data and National Center for Environmental Prediction/Department of Energy (NCEP/DOE) Atmospheric Model Intercomparison Project II (AMIP-II) 6-hourly Reanalysis Gaussian Grid data, two experiments (I and II) were designed to investigate the impact of the percentages of sand and clay in the shallow soil in CoLM on its ability to simulate shallow soil moisture. A third experiment (III) was designed to study the shallow soil moisture and latent heat flux simultaneously. In all the three experiments, after the optimization stage, the percentages of sand and clay of the shallow soil were used to predict the shallow soil moisture in the following month. The results show that the optimal parameters can enable CoLM to better simulate shallow soil moisture, with the simulation results of CoLM after the double-parameter optimal experiment being better than the single-parameter optimal experiment in the optimization slot. Furthermore, the optimal parameters were able to significantly improve the prediction results of CoLM at the prediction stage. In addition, whether or not the atmospheric forcing and observational data are accurate can seriously affect the results of optimization, and the more accurate the data are, the more significant the results of optimization may be.

Robust Delay-Dependent Stability Criteria for Dynamic Systems with Nonlinear Perturbations and Leakage Delay

This paper studies the global asymptotic stability for uncertain systems with mixed delays. The mixed delays include constant delay in the leakage term (i.e., leakage delay) and time-varying delays. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. Based on a appropriate Lyapunov–Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a novel delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). Finally, three numerical examples are included to show the superiority of the proposed method.