Abstract-Despite the proven advantages of scenario-based stochastic model predictive control for the operational control of water networks, its applicability is limited by its considerable computational footprint. In this paper we fully exploit the structure of these problems and solve them using a proximal gradient algorithm parallelizing the involved operations. The proposed methodology is applied and validated on a case study: the water network of the city of Barcelona.
Drinking Water Networks (DWN) are large-scale multiple-input multiple-output systems with uncertain disturbances (such as the water demand from the consumers) and involve components of linear, non-linear and switching nature. Operating, safety and quality constraints deem it important for the state and the input of such systems to be constrained into a given domain. Moreover, DWNs' operation is driven by time-varying demands and involves an considerable consumption of electric energy and the exploitation of limited water resources. Hence, the management of these networks must be carried out optimally with respect to the use of available resources and infrastructure, whilst satisfying high service levels for the drinking water supply. To accomplish this task, this paper explores various methods for demand forecasting, such as Seasonal ARIMA, BATS and Support Vector Machine, and presents a set of statistically validated time series models. These models, integrated with a Model Predictive Control (MPC) strategy addressed in this paper, allow to account for an accurate on-line forecasting and flow management of a DWN.
Abstract-Stochastic optimal control problems arise in many applications and are, in principle, large-scale involving up to millions of decision variables. Their applicability in control applications is often limited by the availability of algorithms that can solve them efficiently and within the sampling time of the controlled system.In this paper we propose a dual accelerated proximal gradient algorithm which is amenable to parallelization and demonstrate that its GPU implementation affords high speedup values (with respect to a CPU implementation) and greatly outperforms well-established commercial optimizers such as Gurobi.
We present an open-source solution for the operational control of drinking water distribution networks which accounts for the inherent uncertainty in water demand and electricity prices in the day-ahead market of a volatile deregulated economy. As increasingly more energy markets adopt this trading scheme, the operation of drinking water networks requires uncertainty-aware control approaches that mitigate the effect of volatility and result in an economic and safe operation of the network that meets the consumers' need for uninterrupted water supply. We propose the use of scenario-based stochastic model predictive control: an advanced control methodology which comes at a considerable computation cost which is overcome by harnessing the parallelization capabilities of graphics processing units (GPUs) and using a massively parallelizable algorithm based on the accelerated proximal gradient method.
Abstract. We propose a decentralised hierarchical multi-rate control scheme for the control of large-scale systems with state and input constraints. The large-scale system is partitioned into sub-systems each one of which is locally controlled by a stabilizing linear controller which does not account for the prescribed constraints. A higher-level controller commands reference signals at a lower uniform sampling frequency so as to enforce linear constraints on the process variables. Worst-case subsystem interactions are modeled and accounted for in a robust manner. By optimally constraining the magnitude and rate of variation of the reference signals to each lower-level controller we prove that closed-loop stability is preserved and the fulfillment of the prescribed constraints is guaranteed. We apply the proposed methodology for the decentralised control of a quadraple-tank system, known as Johansson's system and we compare it to a centralised control approach.
Scenario-based stochastic optimal control problems suffer from the curse of dimensionality as they can easily grow to six and seven figure sizes. First-order methods are suitable as they can deal with such large-scale problems, but may fail to achieve accurate solutions within a reasonable number of iterations. To achieve solutions of higher accuracy and high speed, in this paper we propose two proximal quasi-Newtonian limited-memory algorithms -MINFBE applied to the dual problem and the Newtontype alternating minimization algorithm (NAMA) -which can be massively parallelized on lockstep hardware such as graphics processing units (GPUs). We demonstrate the performance of these methods, in terms of convergence speed and parallelizability, on large-scale problems involving millions of variables.
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