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.
We perform a stochastic model reduction of the Kuramoto–Sakaguchi model for finitely many coupled phase oscillators with phase frustration. Whereas in the thermodynamic limit coupled oscillators ...exhibit stationary states and a constant order parameter, finite-size networks exhibit persistent temporal fluctuations of the order parameter. These fluctuations are caused by the interaction of the synchronised oscillators with the non-entrained oscillators. We present numerical results suggesting that the collective effect of the non-entrained oscillators on the synchronised cluster can be approximated by a Gaussian process. This allows for an effective closed evolution equation for the synchronised oscillators driven by a Gaussian process which we approximate by a two-dimensional Ornstein–Uhlenbeck process. Our reduction reproduces the stochastic fluctuations of the order parameter and leads to a simple stochastic differential equation for the order parameter.
•We reduce the deterministic dynamics of coupled oscillators to a self-consistent stochastic model for the synchronised oscillators.•The effect of the non-entrained rogue oscillators is modelled by an effective Gaussian process.•Fluctuations of the order parameter are described by coloured noise rather than Brownian motion.
In the late stages of an epidemic, infections are often sporadic and geographically distributed. Spatially structured stochastic models can capture these important features of disease dynamics, ...thereby allowing a broader exploration of interventions. Here we develop a stochastic model of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission among an interconnected group of population centers representing counties, municipalities, and districts (collectively, “counties”). The model is parameterized with demographic, epidemiological, testing, and travel data from Ontario, Canada. We explore the effects of different control strategies after the epidemic curve has been flattened. We compare a local strategy of reopening (and reclosing, as needed) schools and workplaces county by county, according to triggers for county-specific infection prevalence, to a global strategy of province-wide reopening and reclosing, according to triggers for province-wide infection prevalence. For trigger levels that result in the same number of COVID-19 cases between the two strategies, the local strategy causes significantly fewer person-days of closure, even under high intercounty travel scenarios. However, both cases and person-days lost to closure rise when county triggers are not coordinated and when testing rates vary among counties. Finally, we show that local strategies can also do better in the early epidemic stage, but only if testing rates are high and the trigger prevalence is low. Our results suggest that pandemic planning for the far side of the COVID-19 epidemic curve should consider local strategies for reopening and reclosing.
•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.