Two stochastic model predictive control algorithms, which are referred to as distributionally robust model predictive control algorithms, are proposed in this article for a class of discrete linear ...systems with unbounded noise. Participially, chance constraints are imposed on both of the state and the control, which makes the problem more challenging. Inspired by the ideas from distributionally robust optimization (DRO), two deterministic convex reformulations are proposed for tackling the chance constraints. Rigorous computational complexity analysis is carried out to compare the two proposed algorithms with the existing methods. Recursive feasibility and convergence are proven. Simulation results are provided to show the effectiveness of the proposed algorithms.
An output feedback stochastic model predictive control is proposed in this article for a class of stochastic linear discrete-time systems, in which the uncertainties from external disturbance, ...measurement noise, and initial state estimation error are all considered. Particularly, the support sets of the uncertainties are unbounded and the distributions are not exactly known. Based on distributionally robust optimization, a deterministic convex reformulation is derived for handling chance constraints. Recursive feasibility and convergence of the algorithm are proven. A numerical example is provided to demonstrate the effectiveness of the proposed method.
•Bhattacharyya distance is proposed as a novel UQ metric in stochastic model updating.•The proposed likelihood is a capable connection between UQ metrics and updating tool.•Both Bhattacharyya and ...Euclidian distances are utilized in the updating framework.•Bhattacharyya distance is more comprehensive than Euclidian distance as a UQ metric.•Calculation is significantly reduced thanks to the approximate Bayesian computation.
The Bhattacharyya distance is a stochastic measurement between two samples and taking into account their probability distributions. The objective of this work is to further generalize the application of the Bhattacharyya distance as a novel uncertainty quantification metric by developing an approximate Bayesian computation model updating framework, in which the Bhattacharyya distance is fully embedded. The Bhattacharyya distance between sample sets is evaluated via a binning algorithm. And then the approximate likelihood function built upon the concept of the distance is developed in a two-step Bayesian updating framework, where the Euclidian and Bhattacharyya distances are utilized in the first and second steps, respectively. The performance of the proposed procedure is demonstrated with two exemplary applications, a simulated mass-spring example and a quite challenging benchmark problem for uncertainty treatment. These examples demonstrate a gain in quality of the stochastic updating by utilizing the superior features of the Bhattacharyya distance, representing a convenient, efficient, and capable metric for stochastic model updating and uncertainty characterization.
This paper describes lane change motion planning with a combination of probabilistic and deterministic prediction for automated driving under complex driving circumstances. The autonomous lane change ...should arrive safely at the destination. The subject vehicle needs to perceive and predict the behaviors of other vehicles with sensors. From the information of other vehicles, a collision probability is defined using a reachable set of uncertainty propagation. In addition, the lane change risk is monitored using predicted time-to-collision and safety distance to guarantee safety in lane change behavior. A safe driving envelope is defined as constraints based on the combinatorial prediction (probabilistic and deterministic) of the behavior of surrounding vehicles. To obtain the desired steering angle and longitudinal acceleration to maintain the automated driving vehicle under constraints, a stochastic model-predictive control problem is formulated. The proposed model has been evaluated by performing lane change simulations in MATLAB/Simulink, while considering the effect of combination prediction. Also, the proposed algorithm has been implemented on a test vehicle. The simulation and test results show that the proposed algorithm can handle complicated lane change scenarios, while guaranteeing safety.
An unaware susceptible-aware susceptible-vaccinated-infected-recovered (SuSaV IR) epidemic disease model has been developed and extensively examined to better understand the intricate dynamics of the ...disease transmission with saturated recovery function. A non-linear, monotonically increasing awareness function has been incorporated and its application is contingent upon the number of infected individuals. The spreading threshold R0 and its sensitivity indices are computed to determine both the prevalence and the potential decline of the spread of disease. Contour plots have been generated to explain how alterations in key parameters affect the evolution of infected individuals. In deterministic model, the condition R0<1 ensures the global stability of a disease-free state while R0>1 indicates the presence of a globally stable prevailing state. A numerical approach has been employed to pinpoint the stability switches for R0 which indicates transcritical bifurcation. Subsequently, a corresponding stochastic model is developed to investigate the impact of random external factors represented as white noise. In addition, the global existence and uniqueness of solutions, and the asymptotic behavior of solutions in the vicinity of steady-states are exhibited in the stochastic model. In the stochastic model, the extinction threshold Res is consistently below R0 due to noise intensity, leading to quicker disease extinction. In order to elucidate the influence of parameters and noise intensities on persistence threshold Rps and extinction threshold Res, a comprehensive sensitivity analysis and the variation of each noise intensity have been performed. This study shows that treatment can be used as an effective tool for controlling the spread of disease by lowering R0 and Rps. It has been empirically observed that high environmental fluctuations can serve as a suppressive factor for disease spread in stochastic model with R0,Rps>1 and the higher noise intensities lead to a faster disappearance of the disease. It is noticed that randomness in susceptible and infected individuals can exert a more significant influence on disease mitigation. The spread of infection exhibits a noteworthy dependence on environmental fluctuations. Additionally, to combat and mitigate the spread of disease, we have executed stochastic optimal control measures. Consequently, the control strategy has emerged as a potent tools for effectively managing the propagation of disease.
•Nonlinear and non-decreasing awareness programs linked to infected individuals.•Behavior of trajectories in both systems for R0<1 and R0>1 and switch stability.•Stochastic model reveals the effect of noise intensities for disease extinction and persistence.•Stochastic optimal control for the management of disease spread.
With the increasing proportion of renewable power generations, the frequency control of microgrid becomes more challenging due to stochastic power generations and dynamic uncertainties. The energy ...storage system (ESS) is usually used in microgrid since it can provide flexible options to store or release power energy. In this paper, an intelligent control strategy completely based on the adaptive dynamic programming (ADP) is developed for the frequency stability, which is designed to adjust the power outputs of micro-turbine and ESS when photovoltaic (PV) power generation is connected into the microgrid. Further, considering the changes of PV power and load demand in a day, the full utilization of PV power and the recycling of energy storage are realized through the proposed regulation strategy. Numerical simulation results validate the energy-storage-based intelligent frequency control strategy for the microgird with stochastic model uncertainties, and comparative studies based on PID, LQR and fuzzy logic control illustrate the superiority of the proposed control strategy.
•A novel distribution-free stochastic model updating methodology is developed.•This framework requires no limiting hypotheses on the distribution families.•Parameters with hybrid uncertainties are ...characterized by staircase densities.•Bhattacharyya distance quantifies discrepancy between model outputs and observations.•A deterministic updating is utilized as preconditioner to avoid non-unique solutions.
This work proposes a novel methodology to fulfil the challenging expectation in stochastic model updating to calibrate the probabilistic distributions of parameters without any assumption about the distribution formats. To achieve this task, an approximate Bayesian computation model updating framework is developed by employing staircase random variables and the Bhattacharyya distance. In this framework, parameters with aleatory and epistemic uncertainties are described by staircase random variables. The discrepancy between model predictions and observations is then quantified by the Bhattacharyya distance-based approximate likelihood. In addition, a Bayesian updating using the Euclidian distance is performed as preconditioner to avoid non-unique solutions. The performance of the proposed procedure is demonstrated with two exemplary applications, a simulated shear building model example and a challenging benchmark problem for uncertainty treatment. These examples demonstrate feasibility of the combined application of staircase random variables and the Bhattacharyya distance in stochastic model updating and uncertainty characterization.
This article presents a predictive home energy management system (HEMS) for a residential building with integration of a plug-in electric vehicle (PEV), a photovoltaic array, and a heat pump. A ...stochastic model predictive control (MPC) strategy is applied in the HEMS in order to minimize the home's electricity cost and reduce the PEV battery degradation cost. Moreover, the MPC ensures that home load demand, PEV battery charging requirements, and household thermal comfort conditions are met. The MPC operates in real-time and thus minimizes the effects of gap between the forecasted and real data on the HEMS performance by updating its control decisions and the forecast data as the stochastic parameters are realized in each time step. The obtained simulation results demonstrate that the proposed control strategy reaches 96% to 97% of ideal performance achieved by off-line optimization counterpart with perfect data.
Streamflow forecasts are essential for water resources management. Although there are many methods for forecasting streamflow, real-time forecasts remain challenging. This study evaluates streamflow ...forecasts using a process-based model (Soil and Water Assessment Tool-Variable Source Area model-SWAT-VSA), a stochastic model (Artificial Neural Network -ANN), an Auto-Regressive Moving-Average (ARMA) model, and a Bayesian ensemble model that utilizes the SWAT-VSA, ANN, and ARMA results. Streamflow is forecast from 1 to 8 d, forced with Quantitative Precipitation Forecasts from the US National Weather Service. Of the individual models, SWAT-VSA and the ANN provide better predictions of total streamflow (NSE 0.60–0.70) and peak flow, but underpredicted low flows. During the forecast period the ANN had the highest predictive power (NSE 0.44–0.64), however all three models underpredicted peak flow. The Bayesian ensemble forecast streamflow with the most skill for all forecast lead times (NSE 0.49–0.67) and provided a quantification of prediction uncertainty.
•Several modeling techniques are developed and forced with Quantitative Precipitation Forecasts to predict streamflow.•Both stochastic and process-based models are capable of providing valuable streamflow forecast information.•An ensemble model forecast streamflow with the greatest predictive power and quantified uncertainty in predictions.
This paper proposes a non-stationary three-dimensional (3D) irregular-shaped geometry-based stochastic model (IS-GBSM) for fifth generation (5G) and beyond massive multiple-input multiple-output ...(MIMO) millimeter wave (mmWave) unmanned aerial vehicle (UAV) channels. This is the first sixth generation (6G) massive MIMO mmWave UAV IS-GBSM that can model the UAV channel space-time non-stationarity, and can describe the impact of some unique UAV-related parameters, e.g., the UAV's moving direction, height, and speed, on channel statistical properties. To better represent the space-time non-stationarity in UAV scenarios, a novel UAV-related space-time cluster evolution algorithm is developed. The developed algorithm considers the characteristics of UAV communications on the modeling of space-time non-stationarity. Based on the proposed model, some channel statistical properties are derived and thoroughly investigated, including the space-time-frequency correlation function, Doppler power spectral density, envelope level crossing rate, and average fade duration. Some numerical results and interesting observations are given, and the impact of UAV-related parameters on channel statistical properties is explored, which can provide assistance for the design of 6G massive MIMO mmWave UAV communication systems. Finally, the applicability of the proposed model is verified by the close agreement between simulation results and measurement.
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