Pmj Paul van den Hof

Predictor input selection for direct identification in dynamic networks

In the literature methods have been proposed which enable consistent estimates of modules embedded in complex dynamic networks. In this paper the network extension of the so called closed-loop Direct Method is investigated. Currently, for this method the variables which must be included in the predictor model are not considered as a user choice. In this paper it is shown that there is some freedom as to which variables to include in the predictor model as inputs, and still obtain consistent estimates of the module of interest. Conditions on this choice of predictor inputs are presented.

Risk management in oil reservoir water-flooding under economic uncertainty

Model-based economic optimization of the water-flooding process in oil reservoirs suffers from high levels of uncertainty. The achievable economic objective is highly uncertain due to the varying economic conditions and the limited knowledge of the reservoir model parameters. For improving robustness, different approaches, e.g., mean or mean-variance optimization have been proposed. One of the drawbacks of the mean-variance approach is the symmetric nature of the variance and hence the reduction of the best cases. In this work, we focus only on the lower tail, i.e., the worst-case(s) and aims to maximize the lower tail of the economic objective function without heavily compromising the best cases. Concepts from robust optimization (max-min approach) and the theory of risk (a risk averse mean-CVaR approach) are considered to offer an asymmetric shaping of the objective function distribution with respect to the given uncertainty. A scenario-based approach is used, where an ensemble of oil price scenarios characterizes the economic uncertainty.

Identifiability of linear dynamic networks

Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we need to make sure that the network model set is identifiable. We introduce the notion of network identifiability, as a property of a parametrized model set, that ensures that different network models can be distinguished from each other when performing identification on the basis of measured data. Different from the classical notion of (parameter) identifiability, we focus on the distinction between network models in terms of their transfer functions. For a given structured model set with a pre-chosen topology, identifiability typically requires conditions on the presence and location of excitation signals, and on presence, location and correlation of disturbance signals. Because in a dynamic network, disturbances cannot always be considered to be of full-rank, the reduced-rank situation is also covered, meaning that the number of driving white noise processes can be strictly less than the number of disturbance variables. This includes the situation of having noise-free nodes.

Data-driven and model-based verification via Bayesian identification and reachability analysis

This work develops a measurement-driven and model-based formal verification approach, applicable to dynamical systems with partly unknown dynamics. We provide a new principled method, grounded on Bayesian inference and on reachability analysis respectively, to compute the confidence that a physical system driven by external inputs and accessed under noisy measurements verifies a given property expressed as a temporal logic formula. A case study discusses the bounded- and unbounded-time safety verification of a partly unknown system, encompassed within a class of linear, time-invariant dynamical models with inputs and output measurements.

Verification of General Markov Decision Processes by Approximate Similarity Relations and Policy Refinement

In this work we introduce new approximate similarity relations that are shown to be key for policy (or control) synthesis over general Markov decision processes. The models of interest are discrete-time Markov decision processes, endowed with uncountably-infinite state spaces and metric output (or observation) spaces. The new relations, underpinned by the use of metrics, allow in particular for a useful trade-off between deviations over probability distributions on states, and distances between model outputs. We show that the new probabilistic similarity relations can be effectively employed over general Markov decision processes for verification purposes, and specifically for control refinement from abstract models.

Identification in dynamic networks

Abstract System identification is a common tool for estimating (linear) plant models as a basis for model-based predictive control and optimization. The current challenges in process industry, however, ask for data-driven modelling techniques that go beyond the single unit/plant models. While optimization and control problems become more and more structured in the form of decentralized and/or distributed solutions, the related modelling problems will need to address structured and interconnected systems. An introduction will be given to the current state of the art and related developments in the identification of linear dynamic networks. Starting from classical prediction error methods for open-loop and closed-loop systems, several consequences for the handling of network situations will be presented and new research questions will be highlighted.

Handling Geological and Economic Uncertainties in Balancing Short-Term and Long-Term Objectives in Waterflooding Optimization

Model-based economic optimization of oil production has a significant scope to increase financial life-cycle performance. The net-present-value (NPV) objective in this optimization, because of its nature, focuses on long-term gains, whereas short-term production is not explicitly addressed. At the same time, the achievable NPV is highly uncertain because of strongly varying economic conditions and limited knowledge of the reservoir-model parameters. The prime focus of this work is to develop optimization strategies that balance both long-term and short-term economic objectives and also offer robustness to the long-term NPV. An earlier robust hierarchical optimization method honoring geological uncertainty with robust long-term and short-term NPV objectives serves as a starting base of this work. We address the issue of extending this approach to include economic uncertainty and aim to analyze how the optimal solution reduces the uncertainty in the achieved average NPV. An ensemble of varying oil prices is used to model economic uncertainty with average NPVs as robust objectives in the hierarchical approach. A weighted-sum approach is used with the same objectives to quantify the effect of uncertainty. To reduce uncertainty, a mean-variance-optimization (MVO) objective is then considered to maximize the mean and also minimize the variance. A reduced effect of uncertainty on the long-term NPV is obtained compared with the uncertainty in the mean-optimization (MO) objectives. Last, it is investigated whether, because of the better handling of uncertainty in MVO, a balance between short-term and long-term gains can be naturally obtained by solving a single-objective MVO. Simulation examples show that a faster NPV buildup is naturally achieved by choosing appropriate weighting of the variance term in the MVO objective. Copyright [2017], Society of Petroleum Engineers.

Identification of dynamic networks operating in the presence of algebraic loops

When identifying all modules in a dynamic network it is natural to treat all node variables in a symmetric way, i.e. not having pre-assigned roles of `inputs and `outputs. In a prediction error setting this implies that every node signal is predicted on the basis of all other nodes. A usual restriction in direct and joint-io methods for dynamic network and closed-loop identification is the need for a delay to be present in every loop (absence of algebraic loops). It is shown that the classical one-step-ahead predictor that incorporates direct feedt-hrough terms in models can not be used in a dynamic network setting. It has to be replaced by a network predictor, for which consistency results are shown when applied in a direct identification method. The result is a one-stage direct/joint-io method that can handle the presence of algebraic loops. It is illustrated that the identified models have improved variance properties over instrumental variable estimation methods.

Non-parametric identification in dynamic networks

In this paper we present a non-parametric approach to identification in networks. The main advantage of a non-parametric approach is that consistent estimates can be obtained with very little prior knowledge about the system. This is a particularly important consideration for a network identification problem which can easily become very complex with high order dynamics and many inputs. We consider a very general framework for dynamic networks that includes measured variables, external excitation variables, process noise, and sensor noise.

Prediction error identification with rank-reduced output noise

In data-driven modelling in dynamic networks, it is commonly assumed that all measured node variables in the network are noise-disturbed and that the network (vector) noise process is full rank. However when the scale of the network increases, this full rank assumption may not be considered as realistic, as noises on different node signals can be strongly correlated. In this paper it is analyzed how a prediction error method can deal with a noise disturbance whose dimension is strictly larger than the number of white noise signals than is required to generate it (rank-reduced noise). Based on maximum likelihood considerations, an appropriate prediction error identification criterion will be derived and consistency will be shown, while variance results will be demonstrated in a simulation example.