Direct identification of continuous-time linear switched state-space models

This paper presents an algorithm for direct continuous-time (CT) identification of linear switched state-space (LSS) models. The key idea for direct CT identification is based on an integral architecture consisting of an LSS model followed by an integral block. This architecture is used to approximate the continuous-time state map of a switched system. A properly constructed objective criterion is proposed based on the integral architecture in order to estimate the unknown parameters and signals of the LSS model. A coordinate descent algorithm is employed to optimize this objective, which alternates between computing the unknown model matrices, switching sequence and estimating the state variables. The effectiveness of the proposed algorithm is shown via a simulation case study.Comment: Preprint submitted to IFAC World Congress 202

Robust and stochastic approaches to network capacity design under demand uncertainty

This thesis considers the network capacity design problem with demand uncertainty using the stochastic, robust and distributionally robust stochastic optimization approaches (DRSO). Network modeling in itself has found wide areas of application in most fields of human endeavor. The network would normally consist of source (origin) and sink (destination) nodes connected by arcs that allow for flows of an entity from the origin to the destination nodes. In this thesis, a special type of the minimum cost flow problem is addressed, the multi-commodity network flow problem. Commodities are the flow types that are transported on a shared network. Offered demands are, for the most part, unknown or uncertain, hence a model that immune against this uncertainty becomes the focus as well as the practicability of such models in the industry. This problem falls under the two-stage optimization framework where a decision is delayed in time to adjust for the first decision earlier made. The first stage decision is called the "here and now", while the second stage traffic re-adjustment is the "wait and see" decision. In the literature, the decision-maker is often believed to know the shape of the uncertainty, hence we address this by considering a data-driven uncertainty set. The research also addressed the non-linearity of cost function despite the abundance of literature assuming linearity and models proposed for this. This thesis consist of four main chapters excluding the "Introduction" chapter and the "Approaches to Optimization under Uncertainty" chapter where the methodologies are reviewed. The first of these four, Chapter 3, proposes the two models for the Robust Network Capacity Expansion Problem (RNCEP) with cost non-linearity. These two are the RNCEP with fixed-charge cost and RNCEP with piecewise-linear cost. The next chapter, Chapter 4, compares the RNCEP models under two types of uncertainties in order to address the issue of usefulness in a real world setting. The resulting two robust models are also comapared with the stochastic optimization model with distribution mean. Chapter 5 re-examines the earlier problem using machine learning approaches to generate the two uncertainty sets while the last of these chapters, Chapter 6, investigates DRSO model to network capacity planning and proposes an efficient solution technique

Model based forecasting for demand response strategies

The incremental deployment of decentralized renewable energy sources in the distribution grid is triggering a paradigm change for the power sector. This shift from a centralized structure with big power plants to a decentralized scenario of distributed energy resources, such as solar and wind, calls for a more active management of the distribution grid. Conventional distribution grids were passive systems, in which the power was flowing unidirectionally from upstream to downstream. Nowadays, and increasingly in the future, the penetration of distributed generation (DG), with its stochastic nature and lack of controllability, represents a major challenge for the stability of the network, especially at the distribution level. In particular, the power flow reversals produced by DG cause voltage excursions, which must be compensated. This poses an obstacle to the energy transition towards a more sustainable energy mix, which can however be mitigated by using a more active approach towards the control of the distribution networks. Demand side management (DSM) offers a possible solution to the problem, allowing to actively control the balance between generation, consumption and storage, close to the point of generation. An active energy management implies not only the capability to react promptly in case of disturbances, but also to ability to anticipate future events and take control actions accordingly. This is usually achieved through model predictive control (MPC), which requires a prediction of the future disturbances acting on the system. This thesis treat challenges of distributed DSM, with a particular focus on the case of a high penetration of PV power plants. The first subject of the thesis is the evaluation of the performance of models for forecasting and control with low computational requirements, of distributed electrical batteries. The proposed methods are compared by means of closed loop deterministic and stochastic MPC performance. The second subject of the thesis is the development of model based forecasting for PV power plants, and methods to estimate these models without the use of dedicated sensors. The third subject of the thesis concerns strategies for increasing forecasting accuracy when dealing with multiple signals linked by hierarchical relations. Hierarchical forecasting methods are introduced and a distributed algorithm for reconciling base forecasters is presented. At the same time, a new methodology for generating aggregate consistent probabilistic forecasts is proposed. This method can be applied to distributed stochastic DSM, in the presence of high penetration of rooftop installed PV systems. In this case, the forecasts' errors become mutually dependent, raising difficulties in the control problem due to the nontrivial summation of dependent random variables. The benefits of considering dependent forecasting errors over considering them as independent and uncorrelated, are investigated. The last part of the thesis concerns models for distributed energy markets, relying on hierarchical aggregators. To be effective, DSM requires a considerable amount of flexible load and storage to be controllable. This generates the need to be able to pool and coordinate several units, in order to reach a critical mass. In a real case scenario, flexible units will have different owners, who will have different and possibly conflicting interests. In order to recruit as much flexibility as possible, it is therefore importan

Optimization with mixed-integer, complementarity and bilevel constraints with applications to energy and food markets

In this dissertation, we discuss three classes of nonconvex optimization problems, namely, mixed-integer programming, nonlinear complementarity problems, and mixed-integer bilevel programming. For mixed-integer programming, we identify a class of cutting planes, namely the class of cutting planes derived from lattice-free cross-polytopes, which are proven to provide good approximations to the problem while being efficient to compute. We show that the closure of these cuts gives an approximation that depends only on the ambient dimension and that the cuts can be computed efficiently by explicitly providing an algorithm to compute the cut coefficients in $O(n2^n)$ time, as opposed to solving a nearest lattice-vector problem, which could be much harder. For complementarity problems, we develop a first-order approximation algorithm to efficiently approximate the covariance of the decision in a stochastic complementarity problem. The method can be used to approximate the covariance for large-scale problems by solving a system of linear equations. We also provide bounds to the error incurred in this technique. We then use the technique to analyze policies related to the North American natural gas market. Further, we use this branch of nonconvex problems in the Ethiopian food market to analyze the regional effects of exogenous shocks on the market. We develop a detailed model of the food production, transportation, trade, storage, and consumption in Ethiopia, and test it against exogenous shocks. These shocks are motivated by the prediction that teff, a food grain whose export is banned now, could become a super grain. We present the regional effects of different government policies in response to this shock. For mixed-integer bilevel programming, we develop algorithms that run in polynomial time, provided a subset of the input parameters are fixed. Besides the $\Sigma^p_2$-hardness of the general version of the problem, we show polynomial solvability and $NP$-completeness of certain restricted versions of this problem. Finally, we completely characterize the feasible regions represented by each of these different types of nonconvex optimization problems. We show that the representability of linear complementarity problems, continuous bilevel programs, and polyhedral reverse-convex programs are the same, and they coincide with that of mixed-integer programs if the feasible region is bounded. We also show that the feasible region of any mixed-integer bilevel program is a union of the feasible regions of finitely many mixed-integer programs up to projections and closures

Sampling-Based Algorithms for Two-Stage Stochastic Programs and Applications

In this dissertation, we present novel sampling-based algorithms for solving two-stage stochastic programming problems. Sampling-based methods provide an efficient approach to solving large-scale stochastic programs where uncertainty is possibly defined on continuous support. When sampling-based methods are employed, the process is usually viewed in two steps - sampling and optimization. When these two steps are performed in sequence, the overall process can be computationally very expensive. In this dissertation, we utilize the framework of internal-sampling where sampling and optimization steps are performed concurrently. The dissertation comprises of two parts. In the first part, we design a new sampling technique for solving two-stage stochastic linear programs with continuous recourse. We incorporate this technique within an internal-sampling framework of stochastic decomposition. In the second part of the dissertation, we design an internal-sampling-based algorithm for solving two-stage stochastic mixed-integer programs with continuous recourse. We design a new stochastic branch-and-cut procedure for solving this class of optimization problems. Finally, we show the efficiency of this method for solving large-scale practical problems arising in logistics and finance

Modelling construction business performance

Searching academic databases for records on ‘business failure’, ‘business distress’ or ‘bankruptcy’ yields a large body of studies on qualitative, empirical, theoretical and simulation aspects. It is a central part of this research to distil from this large quantity of potentially relevant reports and methodologies those which can both flag and predict business failure in the construction industry. An additional search term, such as, ‘construction’, ‘construction industry’ or ‘contractor’ yields a much smaller number of hits, many of which emphasize the construction industry’s distinctive characteristics. We scientists need first to understand the subject of investigation and the environment in which it lives. To do so, an analysis of existing successful and failed approaches to particular research questions is helpful before embarking on new territory. This guides the structure of the following report for we first review papers that specifically report on aspects of business failure in the construction industry followed by, (a) an overview of promising candidates borrowed from other disciplines and industries, and (b) a possible novel approach. An Australian (Queensland) perspective on the topic will also drive this investigation as most of the published research has been applied to the US and UK construction industries