Reliability-based economic model predictive control for generalized flow-based networks including actuators' health-aware capabilities

This paper proposes a reliability-based economic model predictive control (MPC) strategy for the management of generalized flow-based networks, integrating some ideas on network service reliability, dynamic safety stock planning, and degradation of equipment health. The proposed strategy is based on a single-layer economic optimisation problem with dynamic constraints, which includes two enhancements with respect to existing approaches. The first enhancement considers chance-constraint programming to compute an optimal inventory replenishment policy based on a desired risk acceptability level, leading to dynamically allocate safety stocks in flow-based networks to satisfy non-stationary flow demands. The second enhancement computes a smart distribution of the control effort and maximises actuators’ availability by estimating their degradation and reliability. The proposed approach is illustrated with an application of water transport networks using the Barcelona network as the considered case study.Peer ReviewedPostprint (author's final draft

Data-driven Economic NMPC using Reinforcement Learning

Reinforcement Learning (RL) is a powerful tool to perform data-driven optimal control without relying on a model of the system. However, RL struggles to provide hard guarantees on the behavior of the resulting control scheme. In contrast, Nonlinear Model Predictive Control (NMPC) and Economic NMPC (ENMPC) are standard tools for the closed-loop optimal control of complex systems with constraints and limitations, and benefit from a rich theory to assess their closed-loop behavior. Unfortunately, the performance of (E)NMPC hinges on the quality of the model underlying the control scheme. In this paper, we show that an (E)NMPC scheme can be tuned to deliver the optimal policy of the real system even when using a wrong model. This result also holds for real systems having stochastic dynamics. This entails that ENMPC can be used as a new type of function approximator within RL. Furthermore, we investigate our results in the context of ENMPC and formally connect them to the concept of dissipativity, which is central for the ENMPC stability. Finally, we detail how these results can be used to deploy classic RL tools for tuning (E)NMPC schemes. We apply these tools on both a classical linear MPC setting and a standard nonlinear example from the ENMPC literature

Bayesian Updating, Model Class Selection and Robust Stochastic Predictions of Structural Response

A fundamental issue when predicting structural response by using mathematical models is how to treat both modeling and excitation uncertainty. A general framework for this is presented which uses probability as a multi-valued conditional logic for quantitative plausible reasoning in the presence of uncertainty due to incomplete information. The fundamental probability models that represent the structure’s uncertain behavior are specified by the choice of a stochastic system model class: a set of input-output probability models for the structure and a prior probability distribution over this set that quantifies the relative plausibility of each model. A model class can be constructed from a parameterized deterministic structural model by stochastic embedding utilizing Jaynes’ Principle of Maximum Information Entropy. Robust predictive analyses use the entire model class with the probabilistic predictions of each model being weighted by its prior probability, or if structural response data is available, by its posterior probability from Bayes’ Theorem for the model class. Additional robustness to modeling uncertainty comes from combining the robust predictions of each model class in a set of competing candidates weighted by the prior or posterior probability of the model class, the latter being computed from Bayes’ Theorem. This higherlevel application of Bayes’ Theorem automatically applies a quantitative Ockham razor that penalizes the data-fit of more complex model classes that extract more information from the data. Robust predictive analyses involve integrals over highdimensional spaces that usually must be evaluated numerically. Published applications have used Laplace's method of asymptotic approximation or Markov Chain Monte Carlo algorithms

On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to a nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system

Optimal management of bio-based energy supply chains under parametric uncertainty through a data-driven decision-support framework

This paper addresses the optimal management of a multi-objective bio-based energy supply chain network subjected to multiple sources of uncertainty. The complexity to obtain an optimal solution using traditional uncertainty management methods dramatically increases with the number of uncertain factors considered. Such a complexity produces that, if tractable, the problem is solved after a large computational effort. Therefore, in this work a data-driven decision-making framework is proposed to address this issue. Such a framework exploits machine learning techniques to efficiently approximate the optimal management decisions considering a set of uncertain parameters that continuously influence the process behavior as an input. A design of computer experiments technique is used in order to combine these parameters and produce a matrix of representative information. These data are used to optimize the deterministic multi-objective bio-based energy network problem through conventional optimization methods, leading to a detailed (but elementary) map of the optimal management decisions based on the uncertain parameters. Afterwards, the detailed data-driven relations are described/identified using an Ordinary Kriging meta-model. The result exhibits a very high accuracy of the parametric meta-models for predicting the optimal decision variables in comparison with the traditional stochastic approach. Besides, and more importantly, a dramatic reduction of the computational effort required to obtain these optimal values in response to the change of the uncertain parameters is achieved. Thus the use of the proposed data-driven decision tool promotes a time-effective optimal decision making, which represents a step forward to use data-driven strategy in large-scale/complex industrial problems.Peer ReviewedPostprint (published version

Stochastic Optimal Power Flow Based on Data-Driven Distributionally Robust Optimization

We propose a data-driven method to solve a stochastic optimal power flow (OPF) problem based on limited information about forecast error distributions. The objective is to determine power schedules for controllable devices in a power network to balance operation cost and conditional value-at-risk (CVaR) of device and network constraint violations. These decisions include scheduled power output adjustments and reserve policies, which specify planned reactions to forecast errors in order to accommodate fluctuating renewable energy sources. Instead of assuming the uncertainties across the networks follow prescribed probability distributions, we assume the distributions are only observable through a finite training dataset. By utilizing the Wasserstein metric to quantify differences between the empirical data-based distribution and the real data-generating distribution, we formulate a distributionally robust optimization OPF problem to search for power schedules and reserve policies that are robust to sampling errors inherent in the dataset. A simple numerical example illustrates inherent tradeoffs between operation cost and risk of constraint violation, and we show how our proposed method offers a data-driven framework to balance these objectives