Estimation Of Uncertain Parameters Research Articles

An adaptive robust model predictive control for indoor climate optimization and uncertainties handling in buildings

Model predictive control (MPC) in building automation and control (BAC) applications is challenged by difficulties in constructing accurate building models and handling uncertain disturbances. An adaptive robust model predictive control (ARMPC) is proposed to refine building models and handle uncertainty of disturbances. A model adaptation function is incorporated to perform online estimation of uncertain parameters of the building model using online measured building operation data, as the MPC controller is in operation. An additive uncertainty model to represent uncertainties of disturbances is integrated with the building model for robust optimization. The control performance of the ARMPC is compared with MPC controllers without adaptive modelling and robust optimization, as well as a conventional thermostat through simulation constructed based on a test building. When an energy-saving-biased setting is applied, ARMPC achieves the best thermal comfort performance among the tested controllers. The energy savings achieved by the ARMPC vary from ≈20% to ≈15%, compared to the thermostat, as uncertainty level of internal load increases from 0% to 60%. MPC controllers without adaptive modelling and robust optimization maintain ≈20% energy savings as the uncertainty level increases but at the expense of compromising thermal comfort. When a thermal-comfort-biased setting is applied, the MPC controllers maintain the indoor predicted mean vote (PMV) within a narrow range around thermal neutrality while achieving energy savings of around 10%, compared to the thermostat. The adaptive modelling and robust optimization of the ARMPC prevent the indoor condition from violating the constrains due to model inaccuracy and uncertainties in measured disturbances.

Robust Process Design in Pharmaceutical Manufacturing under Batch-to-Batch Variation

Model-based concepts have been proven to be beneficial in pharmaceutical manufacturing, thus contributing to low costs and high quality standards. However, model parameters are derived from imperfect, noisy measurement data, which result in uncertain parameter estimates and sub-optimal process design concepts. In the last two decades, various methods have been proposed for dealing with parameter uncertainties in model-based process design. Most concepts for robustification, however, ignore the batch-to-batch variations that are common in pharmaceutical manufacturing processes. In this work, a probability-box robust process design concept is proposed. Batch-to-batch variations were considered to be imprecise parameter uncertainties, and modeled as probability-boxes accordingly. The point estimate method was combined with the back-off approach for efficient uncertainty propagation and robust process design. The novel robustification concept was applied to a freeze-drying process. Optimal shelf temperature and chamber pressure profiles are presented for the robust process design under batch-to-batch variation.

Event-Triggered Algorithms for Leader–Follower Consensus of Networked Euler–Lagrange Agents

This paper proposes three different distributed event-triggered control algorithms to achieve leader–follower consensus for a network of Euler–Lagrange agents. We first propose two model-independent algorithms for a subclass of Euler–Lagrange agents without the vector of gravitational potential forces. By model-independent, we mean that each agent can execute its algorithm with no knowledge of the agent self-dynamics. A variable-gain algorithm is employed when the sensing graph is undirected; algorithm parameters are selected in a fully distributed manner with much greater flexibility compared to all previous work studying event-triggered consensus problems. When the sensing graph is directed, a constant-gain algorithm is employed. The control gains must be centrally designed to exceed several lower bounding inequalities, which require limited knowledge of bounds on the matrices describing the agent dynamics, bounds on network topology information, and bounds on the initial conditions. When the Euler–Lagrange agents have dynamics that include the vector of gravitational potential forces, an adaptive algorithm is proposed. This requires more information about the agent dynamics but allows for the estimation of uncertain parameters associated with the agent self-dynamics. For each algorithm, a trigger function is proposed to govern the event update times. The controller is only updated at each event, which ensures that the control input is piecewise constant and thus saves energy resources. We analyze each controller and trigger function to exclude Zeno behavior.

Multistage NMPC with on-line generated scenario trees: Application to a semi-batch polymerization process

We present a multistage NMPC scheme with adaptive on-line scenario-tree generation. The scenario tree is assembled from predictions of worst-case uncertainty realizations that are identified based on a first-order approximation of the process model. The key property of the presented approach is that the size of the resultant optimal control problems does not scale directly with the number of uncertain model parameters. We demonstrate the applicability of the approach with an industrially relevant semi-batch polymerization process under parametric model uncertainty and noisy, incomplete state measurements. By allowing to account explicitly for estimation errors, the presented approach yields increased robustness when compared to nominal NMPC and a standard multistage NMPC scheme. Moreover, we investigate a combination of the presented approach with on-line estimation of uncertain model parameters alongside approximation of their confidence region to reduce the uncertainty range and consequently mitigate unnecessary conservatism. The results show that adaptation of model and uncertainty range yields considerable economic benefits without impairing the attained level of robustness for the considered process.

A hierarchical Lyapunov-based cascade adaptive control scheme for lower-limb exoskeleton

This paper proposes a hierarchical Lyapunov-based adaptive cascade control scheme for a lower-limb exoskeleton with control saturation. The proposed approach is composed by two control levels with cascade structure. At the higher layer of the structure, a Lyapunov-based back-stepping regulator including adaptive estimation of uncertain parameters and friction force is designed for the leg dynamics, to minimize the deviation of the joint position and its reference value. At the lower layer, a Lyapunov-based neural network adaptive controller is in charge of computing control action for the hydraulic servo system, to follow the force reference computed at the high level, also to compensate for model uncertainty, nonlinearity, and control saturation.The proposed approach shows to be capable in minimizing the interaction torque between machine and human, and suitable for possible imprecise models. The robustness of the closed-loop system is discussed under input constraint. Simulation experiments are reported, which shows that the proposed scheme is effective in imposing smaller interaction torque with respect to PD controller, and in control of models with uncertainty and nonlinearity.

Adaptive personalized multivariable artificial pancreas using plasma insulin estimates

An adaptive and personalized multivariable artificial pancreas (mAP) system using plasma insulin estimates is proposed to efficiently accommodate major disturbances to the blood glucose concentration, such as meal and physical activity. Accurate adaptive glycemic models are developed through a recursive subspace identification technique with wearable physiological measurements and estimates of unannounced meal effect and plasma insulin concentration (PIC) along with continuous glucose concentration signals to characterize the glucose concentration dynamics under various conditions such as food consumption and physical activity. The identified models with time-varying parameters are employed in the design of an adaptive model predictive control (MPC) system that is cognizant of the PIC. The adaptive controller parameters, dynamic PIC constraint, addition of physiological measurements from wearable devices, feature variables generated from the glucose measurements, and estimation of uncertain model parameters, including the meal effect, enable the mAP system to effectively compute the optimal insulin infusion over diverse diurnal variations without meal and exercise announcements. Simulation case studies using a multivariable simulator demonstrate the efficacy of the proposed mAP system.

Modeling Schistosoma japonicum Infection under Pure Specification Bias: Impact of Environmental Drivers of Infection.

Uncertainties in spatial modeling studies of schistosomiasis (SCH) are relevant for the reliable identification of at-risk populations. Ecological fallacy occurs when ecological or group-level analyses, such as spatial aggregations at a specific administrative level, are carried out for an individual-level inference. This could lead to the unreliable identification of at-risk populations, and consequently to fallacies in the drugs’ allocation strategies and their cost-effectiveness. A specific form of ecological fallacy is pure specification bias. The present research aims to quantify its effect on the parameter estimates of various environmental covariates used as drivers for SCH infection. This is done by (i) using a spatial convolution model that removes pure specification bias, (ii) estimating group and individual-level covariate regression parameters, and (iii) quantifying the difference between the parameter estimates and the predicted disease outcomes from the convolution and ecological models. We modeled the prevalence of Schistosoma japonicum using group-level health outcome data, and city-level environmental data as a proxy for individual-level exposure. We included environmental data such as water and vegetation indexes, distance to water bodies, day and night land surface temperature, and elevation. We estimated and compared the convolution and ecological model parameter estimates using Bayesian statistics. Covariate parameter estimates from the convolution and ecological models differed between 0.03 for the nearest distance to water bodies (NDWB), and 0.28 for the normalized difference water index (NDWI). The convolution model presented lower uncertainties in most of the parameter estimates, except for NDWB. High differences in uncertainty were found in night land surface temperature (0.23) and elevation (0.13). No significant differences were found between the predicted values and their uncertainties from both models. The proposed convolution model is able to correct for a pure specification bias by presenting less uncertain parameter estimates. It shows a good predictive performance for the mean prevalence values and for a positive number of infected people. Further research is needed to better understand the spatial extent and support of analysis to reliably explore the role of environmental variables.

Genetic parameters of rumination time and feed efficiency traits in primiparous Holstein cows under research and commercial conditions

Feed efficiency has the potential to be improved both through feeding, management, and breeding. Including feed efficiency in a selection index is limited by the fact that dry matter intake (DMI) recording is only feasible under research facilities, resulting in small data sets and, consequently, uncertain genetic parameter estimates. As a result, the need to record DMI indicator traits on a larger scale exists. Rumination time (RT), which is already recorded in commercial dairy herds by a sensor-based system, has been suggested as a potential DMI indicator. However, RT can only be a DMI indicator if it is heritable, correlates with DMI, and if the genetic parameters of RT in commercial herd settings are similar to those in research facilities. Therefore, the objective of our study was to estimate genetic parameters for RT and the related traits of DMI in primiparous Holstein cows, and to compare genetic parameters of rumination data between a research herd and 72 commercial herds. The estimated heritability values were all moderate for DMI (0.32-0.49), residual feed intake (0.23-0.36), energy-corrected milk (ECM) yield (0.49-0.70), and RT (0.14-0.44) found in the research herd. The estimated heritability values for ECM were lower for the commercial herds (0.08-0.35) than that for the research herd. The estimated heritability values for RT were similar for the 2 herd types (0.28-0.32). For the research herd, we found negative individual level correlations between RT and DMI (-0.24 to -0.09) and between RT and RFI (-0.34 to -0.03), and we found both positive and negative correlations between RT and ECM (-0.08 to 0.09). For the commercial herds, genetic correlations between RT and ECM were both positive and negative (-0.27 to 0.10). In conclusion, RT was not found to be a suitable indicator trait for feed intake and only a weak indicator of feed efficiency.

Improved robust adaptive backstepping control approach on STATCOM for non‐linear power systems

The problem of large disturbance attenuation in the single-machine infinite-bus system with a static synchronous compensator (STATCOM) is proposed to be alleviated by an improved robust backstepping algorithm, which utilises error compensation and sliding mode variable structure control methods to achieve stability. For STATCOM systems with internal and external disturbances, the adaptive backstepping method is used to construct the storage function, and a non-linear L 2 gain interference rejection controller and parameter substitution law are applied simultaneously. The improved method differs from the traditional adaptive backstepping design in terms of error-compensation design methodology, in order to ensure robustness and insensitivity to large disturbances of the STATCOM system, and furthermore, preserving useful non-linearities and the real-time estimation of uncertain parameters. Finally, a simulation demonstrates that the improved method is more efficient than traditional adaptive backstepping with respect to the speed of adaptation and the response of the STATCOM system. Hence, the effectiveness and practicality of the proposed control method is demonstrated by engineers in applications.

A formation and traction control design for multiple mobile robots

This paper presents a decentralized controller design for formation and traction control of multiple robots with collision avoidance. The proposed control design consists of two steps: formation control design with collision avoidance and traction control design for movement of robot formation along the desired trajectory. In the first step, a formation controller is designed based on the formation graph model of multiple robots and potential function approach. Then, the traction control input is derived in the second step by locating the virtual leader at the central position of robot formation which leads mobile robots to follow the assigned trajectory in formation. In this distributed control design, parameter uncertainty in kinematic system model is also accommodated by deriving an adaptive rule for estimation of uncertain system parameters. Together with the stability analysis of the proposed controller, simulation and experiment results verify the feasibility and effectiveness of the distributed controller for multi-robot coordination.

Bayesian Inference for Correlations in the Presence of Measurement Error and Estimation Uncertainty

Whenever parameter estimates are uncertain or observations are contaminated by measurement error, the Pearson correlation coefficient can severely underestimate the true strength of an association. Various approaches exist for inferring the correlation in the presence of estimation uncertainty and measurement error, but none are routinely applied in psychological research. Here we focus on a Bayesian hierarchical model proposed by Behseta, Berdyyeva, Olson, and Kass (2009) that allows researchers to infer the underlying correlation between error-contaminated observations. We show that this approach may be also applied to obtain the underlying correlation between uncertain parameter estimates as well as the correlation between uncertain parameter estimates and noisy observations. We illustrate the Bayesian modeling of correlations with two empirical data sets; in each data set, we first infer the posterior distribution of the underlying correlation and then compute Bayes factors to quantify the evidence that the data provide for the presence of an association.

Validation of uncertainty estimation in engine cold start

The engine cold start period produces the majority of harmful hydrocarbon emissions during engine operation, and, therefore, the reduction of such emissions is key to maintaining ultra low emission vehicle standards. Emissions reduction can be achieved by the design and implementation of controllers with effective tracking performance and estimation of uncertain parameters in the system. Effective tracking performance can be achieved by driving down error in the tracking of desired engine state trajectories. Estimation of uncertainty can be achieved through the use of an adaptive controller. In this work, an adaptive sliding controller is designed in order to achieve both goals, and implemented on an engine test cell. Experimental results show the reduction of the tracking error as well as estimation of model uncertainty in the engine test cell.

Validation of uncertainty estimation in engine cold start

The engine cold start period produces the majority of harmful hydrocarbon emissions during engine operation, and, therefore, the reduction of such emissions is key to maintaining ultra low emission vehicle standards. Emissions reduction can be achieved by the design and implementation of controllers with effective tracking performance and estimation of uncertain parameters in the system. Effective tracking performance can be achieved by driving down error in the tracking of desired engine state trajectories. Estimation of uncertainty can be achieved through the use of an adaptive controller. In this work, an adaptive sliding controller is designed in order to achieve both goals, and implemented on an engine test cell. Experimental results show the reduction of the tracking error as well as estimation of model uncertainty in the engine test cell.

What Really Happens at the End of the Rainbow? – Paying the Price for Reducing Uncertainty (Using Reverse Hydrology Models)

Modelling of environmental processes is subject to a high degree of uncertainty due to the incorporation of random errors and a lack of knowledge about how processes operate at the scale of interest. Use of uncertain data when identifying and calibrating a model can lead to disinformative data being included in the procedure, resulting in uncertain parameter estimation and ambiguity in the outcomes. Rainfall-runoff modelling where a single rain-gauge is often assumed to be representative of the potentially highly variable (in both space and time) rainfall field is a good example. The noisy pattern of rainfall inputs is transformed by the catchment into streamflow. The streamflow pattern is dependent on the spatio-temporal pattern of rainfall and of the dominant processes operating within the catchment. Inverse modelling of the catchment dynamics, that is, inferring catchment rainfall from streamflow, provides a possible means of improving the estimated rainfall input because all rain falling on the catchment becomes streamflow, and thus, providing improved forecasts of the streamflow output. A combination of inverse modelling, time series analysis, spatial analysis and spectral analysis may also help to provide an insight into the complex processes operating within the catchment system. This paper applies a novel method for inferring true catchment rainfall from streamflow highlighting that the streamflow is better estimated using inferred rainfall than observed rainfall (from a single gauge) because a single gauge only gives a partial description of the rainfall field. However reducing uncertainty in this way comes at a price, in this case, the reduction in time-resolution of the inferred rainfall series.

Adaptive output voltage tracking controller for uncertain DC/DC boost converter

ABSTRACTThis paper presents a cascade output voltage control strategy for an uncertain DC/DC boost converter adopting an adaptive current controller in its inner loop. Considering the non-linearity, load uncertainties and parameter uncertainties of the converter, the proposed controller is designed following the conventional cascade voltage controller design method. The proposed method makes the following three contributions. First, a coordinate transformation is introduced for the inner loop, enabling avoidance of the singularity problem caused by the estimates of uncertain parameters. Second, a slight modification to the adaptation law is performed to guarantee closed-loop stability in the presence of the time-varying component of the load current. Third, the outer-loop controller is devised such that its performance can be adjusted without any parameter information. The closed-loop performance is demonstrated through simulations and experiments using the DSP28335 with a 3 kW DC/DC boost converter.

A new method to improve estimation of uncertain parameters in the Ensemble Kalman filter by re-parameterization employing prior statistics correction

The Ensemble Kalman Filter (EnKF) is a Monte Carlo based method to assimilate the measurement data sequentially in time. Although, EnKF has some advantages over the other Kalman based methods to deal with non-linear and/or high dimensional reservoir models, it also suffers from deficiency in estimation of non-Gaussian parameters. In this work, we propose a re-parameterization method to handle non-Gaussian parameters via Ensemble Kalman Filter framework. For this purpose, concept of cumulative distribution function transformation has been used. In addition, the statistics of prior information have been aggregated in the state vector in order to capture the prior uncertainties of non-Gaussian parameters. To evaluate the performance of the new method, three estimation examples have been implemented. These examples are designed to evaluate the performance of the proposed method to estimate both local and global parameters. The performance of method in handling non-Gaussian prior as well as capturing the prior uncertainty has been assessed. The results revealed that, the proposed method handled both non-Gaussian prior and capturing of the prior uncertainties of the local and global parameters quite efficiently. Compared to previously conducted researches, new algorithm would considerably reduce the number of required ensemble members to converge to the appropriate solution. Standard ensemble Kalman filter and normal score transformation have been also implemented for each setup; the obtained results show that the new proposed method outperforms the other alternate methods.

A multispecies biomass dynamics model for investigating predator–prey interactions in the Bering Sea groundfish community

Concerns over long-term cumulative impacts of fishing on marine ecosystems and the status of many marine species have led to calls for ecosystem-based approaches to fishery management. Single-species population dynamics models traditionally used in fisheries stock assessments lack separate accounting of predation mortality and often underestimate natural mortality. Age-structured models used for stock assessments in the Alaska region are biologically realistic, but their applicability is limited to a relatively small number of commercially exploited species because they require accurate survey and fishery age composition data. The objective of this study was to develop relatively simple age-aggregated multispecies models that describe biomass dynamics of some commercially and ecologically important groundfish species in the eastern Bering Sea by accounting for their trophic interactions. We developed and contrasted two alternative model formulations: a multispecies biomass dynamics (MBD) model and a multispecies delay difference (MDD) model. Both MBD and MDD models were able to capture observed trends in survey biomass data over 1982–2009. Although the MDD model fit the survey biomass estimates better than the MBD model, the MDD model and its maximum likelihood parameters produced biologically unrealistic biomass projections at values of instantaneous fishing mortality (F)>0.14. Strong positive correlations among many of the predation parameters resulted in highly uncertain parameter estimates. Consistent with previous studies, both multispecies models predicted the multispecies B0, MSY, and FMSY to be lower than the sum of the estimates from single-species assessment models. Although the results of the current study should be taken with caution because of high estimation uncertainty, our multispecies models can be a useful addition to the current management process by providing estimates of natural mortality and tactical advice on the implications of single-species harvest strategies for the broader groundfish community in the eastern Bering Sea.

Uncertainty decomposition-based fault-tolerant adaptive control of flexible spacecraft

A fault-tolerant adaptive control scheme is developed for attitude tracking of flexible spacecraft with unknown inertia parameters, external disturbance, and actuator faults. The uncertainties of flexibility and dynamics are parameterized, and the control gain matrix uncertainty is handled using an uncertainty decomposition. The control scheme, with adaptive laws of the overall system uncertain parameter estimates, guarantees the system stability and asymptotic attitude tracking properties. Simulation results illustrate the effectiveness of the proposed control scheme.

Robust economic-statistical design of X-bar control chart

Control charts are developed to monitor the service and production processes. The fact that many processes have uncertain parameters is a barrier to obtain the best design of the control charts. In this paper, economic statistical design (ESD) of the X-bar control chart utilising robust optimisation approach that considers interval estimates of uncertain parameters is investigated. A heuristic algorithm is developed to obtain the robust scheme of the control chart. Robust design for an industrial problem is compared with traditional ESD, and heuristic design. Numerical analyses and simulation study show that the proposed X-bar control chart offers a better approach and more reliable solutions for practitioners.

Design of a Novel Nonlinear Observer to Estimate Sideslip Angle and Tire Forces for Distributed Electric Vehicle

For four-wheel independently driven (4WD) distributed electric vehicle (DEV), vehicle dynamics control systems such as direct yaw moment control (DYC) can be easily achieved. Accurate estimation of vehicle state variables and uncertain parameters can improve the robustness of vehicle dynamics control system. Various sensors are generally equipped to the acquisition of the vehicle dynamics. For both technical and economic reasons, some fundamental vehicle parameters, such as the sideslip angle and tire-road forces, can hardly be obtained through sensors directly. Therefore, this paper presented a state observer to estimate these variables based on Unscented Kalman Filter (UKF). To improve the accuracy of UKF, measurement noise covariance is also self-adaptive regulated. In addition, a nonlinear dynamics tire model is utilized to improve the accuracy of tire lateral force estimation. The simulation and experiment results show that the proposed observer can provide the precision values of the vehicle state.