Optimal operation of hydrothermal systems with Hydrological Scenario Generation through Bootstrap and Periodic Autoregressive Models

In electrical power systems with strong hydro generation, the use of adequate techniques to generate synthetic hydrological scenarios is extremely important for the evaluation of the ways the system behaves in order to meet the forecast energy demand. This paper proposes a new model to generate natural inflow energy scenarios in the long-term operation planning of large-sized hydrothermal systems. This model is based on the Periodic Autoregressive Model, PAR (p), where the identification of the p orders is based on the significance of the Partial Autocorrelation Function (PACF) estimated via Bootstrap, an intensive computational technique. The scenarios generated through this new technique were applied to the operation planning of the Brazilian Electrical System (BES), using the previously developed methodology of Stochastic Dynamic Programming based on Convex Hull algorithm (SDP-CHull). The results show that identification via Bootstrap is considerably more parsimonious, leading to the identification of lower orders models in most cases which retains the statistical characteristics of the original series. Additionally it presents a closer total mean operation cost when compared to the cost obtained via historic series.     

Uncertainty Quantification of Stochastic Simulation for Black-box Computer Experiments

Stochastic simulations applied to black-box computer experiments are becoming more widely used to evaluate the reliability of systems. Yet, the reliability evaluation or computer experiments involving many replications of simulations can take significant computational resources as simulators become more realistic. To speed up, importance sampling coupled with near-optimal sampling allocation for these experiments is recently proposed to efficiently estimate the probability associated with the stochastic system output. In this study, we establish the central limit theorem for the probability estimator from such procedure and construct an asymptotically valid confidence interval to quantify estimation uncertainty. We apply the proposed approach to a numerical example and present a case study for evaluating the structural reliability of a wind turbine.     

An upper bound on the cycle time of a stochastic marked graph using incomplete information on the transition firing time distributions

Stochastic marked graphs, a special class of stochastic timed Petri nets, are used for modelling and analyzing decision-free dynamic systems with uncertainties in timing. The model allows evaluating the performance of such systems under a cyclic process. Given the probabilistic characteristics of the transition times, the cycle time of the system can be determined from the initial marking. In this contribution, we compute an upper bound on the cycle time of a stochastic marked graph in case the probabilistic characteristics of the transition times are not fully specified.     

A Novel Simulation Method for Binary Discrete Exponential Families,With Application to Social Networks

Stochastic models for finite binary vectors are widely used in sociology, with examples ranging from social influence models on dichotomous behaviors or attitudes to models for random graphs. Exact sampling for such models is difficult in the presence of dependence, leading to the use of Markov chain Monte Carlo (MCMC) as an approximation technique. While often effective, MCMC methods have variable execution time, and the quality of the resulting draws can be difficult to assess. Here, we present a novel alternative method for approximate sampling from binary discrete exponential families having fixed execution time and well-defined quality guarantees. We demonstrate the use of this sampling procedure in the context of random graph generation, with an application to the simulation of a large-scale social network using both geographical covariates and dyadic dependence mechanisms.     

Sampling efficiency in Monte Carlo analyses

Stochastic processes that are sampled in Monte Carlo analyses can be so complex that sampling efficiency is difficult to attain. To handle these difficulties we introduce a model of the elements of a stochastic process which are relevant to the problem of sampling efficiency. From this model we derive a multistage estimating procedure which automatically adjusts the parameters of an efficient sampling design.     

Artificial neural network for discrete model order reduction with substructure preservation

This paper presents a new technique for model order reduction (MOR) that is based on an artificial neural network (ANN) prediction. The ANN-based MOR can be applied for different scale systems with substructure preservation. In the proposed technique, the ANN is implemented for predicting the unknown elements of the reduced order model. Prediction of the ANN architecture is based on minimizing the cost function obtained by the difference between the actual and desired system behaviour. The ANN prediction process is pursued while maintaining the full order substructure in the reduced model. The proposed ANN-based model order reduction method is compared to recently published work on MOR techniques. Simulation results verify the validity of the new MOR technique.     

Efficient simulation of general stochastic hybrid systems

General Stochastic Hybrid System (SHS) are characterised by Stochastic Differential Equations (SDEs) with discontinuities and Poisson jump processes. SHS are useful in model based design of Cyber-Physical System (CPS) controllers under uncertainty. Industry standard model based design tools such as Simulink/Stateflow® are inefficient when simulating, testing, and validating SHS, because of dependence on fixed-step Euler–Maruyama (EM) integration and discontinuity detection. We present a novel efficient adaptive step-size simulation/integration technique for general SHSs modelled as a network of Stochastic Hybrid Automatons (SHAs). We propose a simulation algorithm where each SHA in the network executes synchronously with the other, at an integration step-size computed using adaptive step-size integration. Ito’ multi-dimensional lemma and the inverse sampling theorem are leveraged to compute the integration step-size by making the SDEs and Poisson jump rate integration dependent upon discontinuities. Existence and convergence analysis along with experimental results show that the proposed technique is substantially faster than Simulink/Stateflow®when simulating general SHSs.     

Research on mean square exponential stability of networked control systems with multi-step delay

A new control mode is proposed for networked control systems whose network-induced delay is longer than a sampling period. The proposed control mode can make full use of control information and improve the performance of the system. Under the control mode, the mathematical model of networked control systems is obtained. Markov characteristic of the transfer delay is discussed. Based on Markov chain theory, the infinite horizon controller is designed, which is shown to render corresponding networked control systems mean square exponentially stable. Simulation results show the validity of the proposed theory.     

Enriched workflow modelling and Stochastic Branch-and-Bound

Workflow systems provide means and techniques for modelling, designing, performing and controlling repetitive (business) processes. The quality of commercial workflow systems is usually determined to a large extent by their versatility and multi-purpose application. One of the current trends in improving workflow systems lies in enriching modelling methods and techniques in order to enlarge design alternatives.The need for such advanced methods is particularly apparent in those fields in which the process duration can be determined only vaguely, but whose completion schedules are at the same time strictly enforced by a highly competitive market by means of fines and penalties. The risk of an overrun has to be weighed against the expected costs and benefits of certain measures reducing turn-around time and their combinations. Because they can help to avoid such penalties—or, at least, keep any potential losses low by identifying critical subprocesses and evaluate appropriate measures—modelling and evaluation techniques are becoming essential features of workflow systems.Methodologically, we use Stochastic Branch-and-Bound as a technique for finding “optimal” bundles of measures. A numerical study shows the benefits of this meta-approach by means of five stepwise-developed decision scenarios requiring rich modelling. Petri nets as a modelling tool and Stochastic Branch-and-Bound as an optimization technique determine for multi-mode resource constrained workflows of varying complexity an optimal workforce strategy with respect to the number of workers and their qualification.     

Nonlinear MPC: the Impact of Sampling on Closed Loop Stability

In this paper we consider model predictive control (MPC) schemes without stabilizing terminal constraints and/or costs for continuous time systems. While the estimates on the required prediction horizon length such that asymptotic stability of the MPC closed loop is guaranteed yield, in general, satisfactory results their applicability is limited due to the fact that the respective proofs assume that the input function can be switched arbitrarily often on compact time intervals. We present a technique which allows to determine a suitable discretization accuracy such that the obtained performance bound is preserved while the control signal is only switched at the sampling instants of the corresponding sampled data system. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solving stochastic chemical kinetics by Metropolis-Hastings sampling

This study considers using Metropolis-Hastings algorithm for stochastic simulation of chemical reactions. The proposed method uses SSA (Stochastic Simulation Algorithm) distribution which is a standard method for solving well-stirred chemically reacting systems as a desired distribution. A new numerical solvers based on exponential form of exact and approximate solutions of CME (Chemical Master Equation) is employed for obtaining target and proposal distributions in Metropolis-Hastings algorithm to accelerate the accuracy of the tau-leap method. Samples generated by this technique have the same distribution as SSA and the histogram of samples show it''s convergence to SSA     

Robustly complete synthesis of sampled-data control for continuous-time nonlinear systems with reach-and-stay objectives

Formal methods are becoming favorable for control and verification of safety-critical systems because of the rigorous model-based computation. Relying on an over-approximated model of the original system behaviors, formal control synthesis algorithms are not often complete, which means that a controller cannot necessarily be synthesized even if there exists one. The main result of this paper shows that, for continuous-time nonlinear systems, a sample-and-hold control strategy for a reach-and-stay specification can be synthesized whenever such a strategy exists for the same system with its dynamics perturbed by small disturbances. Control synthesis is carried out by a fixed-point algorithm that adaptively partitions the system state space into a finite number of cells. In each iteration, the reachable set from each cell after one sampling time is over-approximated within a precision determined by the bound of the disturbances. To meet such a requirement, we integrate validated high-order Taylor expansion of the system solution over one sampling period into every fixed-point iteration and provide a criterion for choosing the Taylor order and the partition precision. Two nonlinear system examples are given to illustrate the effectiveness of the proposed method.     

Digital idle speed control of automotive engines: A safety problem for hybrid systems

We address the idle speed control problem in automotive electronics using hybrid methods to derive a digital control law with guaranteed properties. Associating a switching system with the hybrid system that describes the engine operation is crucial to developing a computationally feasible approach. For switching systems with minimum and maximum dwell times and controlled resets, we are able to derive digital control strategies with guaranteed properties that ensure safety. The proposed methodology, while motivated by the idle control problem, is of general interest for hybrid systems for which minimum and maximum dwell times can be established. In our modeling approach, we do not assume synchronization between sampling time and switching time. This is an important technical aspect in general, and in particular for our application, where there is no reason why sampling and switching should be synchronized. Some simulation results are included to demonstrate the effectiveness of the approach.     

Sampled-data control of uncertain switched neutral nonlinear systems under asynchronous switching

The robust exponential stabilization for a class of the uncertain switched neutral nonlinear systems with time-varying delays based on the sampled-data control is investigated in this paper. The closed-loop system with sampled-data control is modeled as a continuous time system with a time-varying piecewise continuous control input delay. Considering the relationship between the sampling period and the dwell time of two switching instants, sampling interval with no switching and sampling interval with one switching are discussed, respectively. By Wirtinger-based inequality, Wirtinger-based double integral inequality, and free-weighting matrix technique, some delay-dependent sufficient conditions are given to guarantee the exponential stability of uncertain switched neutral nonlinear systems under asynchronous switching. In addition, sampled-data controllers can also be designed by special operations of matrices. Finally, two numerical examples are used to show the effectiveness of the approach proposed in this paper.     

Global fixed-time stabilization for a class of switched nonlinear systems with general powers and its application

This paper investigates the problem of global fixed-time stabilization for a class of uncertain switched nonlinear systems with the general powers, namely, the powers of the considered systems can be different odd rational numbers, even rational numbers or both odd and even rational numbers. By skillfully using the common Lyapunov function method and the adding a power integrator technique, a common state feedback control strategy is developed. It is proved that the proposed controller can guarantee that the state of the resulting closed-loop system converges to zero for any given fixed time under arbitrary switchings. Simulation results of the liquid-level system are provided to show the effectiveness of the proposed method.     

The cost of weather in a floating oil production system

New oil fields are being developed in deeper water where conventional production systems are impractical. One alternative is the floating production, storage and offloading system: oil is extracted and stored on a moored, floating tanker while a shuttle tanker transports the oil between the field and the refinery port. However, when the weather is too rough, mooring and offloading has to be suspended. If there is inadequate storage capacity, oil production also stops, resulting in a costly interruption to the revenue flow. Simulation experiments with different design configurations can identify the economic optimum that minimises the financial impact of the weather on the operation. However, not all of the uncertainties can be captured completely in a quantitative manner and sensitivity analyses suggest that a more robust configuration is a better option than the simple optimum.     

混合动力公交车能量控制策略的优化模型

针对混合动力公交车在循环工况内功率需求的特点,建立了未来功率需求贝叶斯预测模型;利用2-阶段随机动态规划模型将大规模的随机动态规划问题简化为多个小规模的随机动态规划问题和一个确定型动态规划问题;对于随机动态规划模型的求解,给出了稀疏表示的降维方法,将复杂的泛函极值问题转化为常规的随机动态优化问题,并采用分布估计算法和计算资源最优配置算法的计算机仿真优化算法对随机动态优化问题进行求解;给出了基于查表的在线控制策略,为模型的实际应用进行了有益的探索。     

A generalized stochastic goal programming model

In this paper we show how one can get stochastic solutions of Stochastic Multi-objective Problem (SMOP) using goal programming models. In literature it is well known that one can reduce a SMOP to deterministic equivalent problems and reduce the analysis of a stochastic problem to a collection of deterministic problems. The first sections of this paper will be devoted to the introduction of deterministic equivalent problems when the feasible set is a random set and we show how to solve them using goal programming technique. In the second part we try to go more in depth on notion of SMOP solution and we suppose that it has to be a random variable. We will present stochastic goal programming model for finding stochastic solutions of SMOP. Our approach requires more computational time than the one based on deterministic equivalent problems due to the fact that several optimization programs (which depend on the number of experiments to be run) needed to be solved. On the other hand, since in our approach we suppose that a SMOP solution is a random variable, according to the Central Limit Theorem the larger will be the sample size and the more precise will be the estimation of the statistical moments of a SMOP solution. The developed model will be illustrated through numerical examples.     

A model for strategic planning under uncertainty

Summary In this paper the multi-period strategic planning problem for a consumer sumer product manufacturing chain is considered. Our discussion is focused on investment decisions which, are economically optimal over the whole planning horizonT, while meeting customer demands and conforming to technological requirements. In strategic planning, time and uncertainty play important roles. The uncertainties in the model are due to different levels of forecast demands, cost estimates and equipment behaviour. The main aim of this paper is to develop and analyse a multiperiod stochastic model representing the entire manufacturing chain, from the acquisitions of raw material to the delivering of final products. The resulting optimization problem is computationally intractable because of the enormous, and sometimes unrealistic, number of scenarios that must be considered in order to identify the optimal planning strategy. We propose two different solution approaches; firstly, we apply a scenario risk analysis giving the related results of experiments on a particular real data set. We then describe and investigate an Integer Stochastic Programming formulation of the problem and propose, as a solution technique, a variation of Benders decomposition method, namely theL-shaped method.     

A flexible and generic approach to dynamic modelling of supply chains

In this paper, we present a new modelling approach for realistic supply chain simulation. The model provides an experimental environment for informed comparison between different supply chain policies. A basic simulation model for a generic node, from which a supply chain network can be built, has been developed using an object-oriented approach. This generic model allows the incorporation of the information and physical systems and decision-making policies used by each node. The object-oriented approach gives the flexibility in specifying the supply chain configuration and operation decisions, and policies. Stochastic simulations are achieved by applying Latin Supercube Sampling to the uncertain variables in descending order of importance, which reduces the number of simulations required. We also present a case study to show that the model is applicable to a real-life situation for dynamic stochastic studies.