Sampathirao, Ajay Kumar (2016) Parallel methods for solving stochastic optimal control problems: control of drinking water networks. Advisor: Bemporad, Prof. Alberto. Coadvisor: Sopasakis, Dr. Pantelis . pp. 199. [IMT PhD Thesis]

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Abstract
This thesis is concerned with the development of optimisation methods to solve stochastic Model Predictive Control (MPC) problem and employ them in the management of DrinkingWater Networks (DWNs). DWNs are largescale, complex both in topology and dynamics, energyintensive systems subjected to irregular demands. Managing these networks play a crucial role in the economic sustainability of urban cities. The main challenge associated with such infrastructures is to minimise the energy required for pumping water while simultaneously maintaining uninterrupted water supply. Stateoftheart control methodologies as well as the current engineering practices use predictive models to forecast upcoming water demands but do not take into consideration the inevitable forecasting error. This way, the water network is operated in a deterministic fashion disregarding its inherent stochastic behaviour which accrues from the volatility of water demand and, often, electricity prices. In this thesis, we address two challenges namely: optimisation methods for solving stochastic MPC problems and closedloop feedback control for the management of drinking water networks. MPC is an advanced control technology that copes with complex control problem by repeatedly solving a finite horizon constrained optimal control problem; uses only the first decision as input and discards the rest of the sequence. This methodology decides the control action based on present state of the system and thus provides an implicit feedback to the system. Instead of historical demand profile, timeseries models were developed to forecast the future water demand. The economic and the social aspects involved in operation of the DWN were captured in a cost function. Now the MPC controller combined with online forecaster minimise the cost function across a prediction horizon of 1 day with sampling time equal to 1 hour and thus the closedloop strategy for DWN management is devised. The forecasts are just nominal demands and differ from the actual demands. There exist several approaches when it comes to working with uncertain forecasts: (i) to assume that forecast errors are negligible and disregard them, (ii) to assume knowledge of their worstcase values (maximum errors), (iii) to assume knowledge of probabilistic information. These three approaches lead to the three principal flavours of MPC: the certaintyequivalent (CE), the worstcase robust and the stochastic MPC. CEMPC is simple but not realistic (because the errors are not negligible), worstcase MPC is more meaningful but it is too conservative (because it is highly improbable that the errors admit their worstcase values) and then we have stochastic MPC which is the approach pursued in this thesis. A stochastic MPC allows a systematic framework as tradeoff performance against constraint violation by modelling the uncertainty as stochastic process and quantifying its influence. However, this formulation is an infinite dimensional optimisation problem and its corresponding discrete approximation is deemed to be a largescale problem with millions of decision variables. Therefore, the applicability of stochastic MPC in control applications is limited due to the unavailability of algorithms that can solve them efficiently and within the sampling time of the controlled system. Here we developed optimisation algorithms that solve stochastic MPC problem by exploiting their structure and using parallelisation. These algorithms are (i) accelerated proximal gradient algorithm also known as forwardbackward splitting and (ii) LBFGS method for forwardbackward envelope (FBE) function. Both these algorithms employ decomposition to solve the Fenchel dual and make them suitable for parallel implementation. Graphics processing units (GPUs) are capable of perform parallel computation and are therefore perfect hardware to solve the stochastic MPC problem with the accelerated proximal gradient method. The water network of the city Barcelona is considered to study the validity of the proposed algorithm. The GPU implementation is found to be 10 times faster than commercial solvers like Gurobi running in multicore environment and made the problem computationally tractable in the sampling time. The efficiency of the stochastic MPC to manage theDWN is quantified in terms of key performance indicators like economic utility, network utility and quality of service. The forwardbackward splitting is a firstorder method and has slow convergence for illconditioned problems. We constructed a continuously differentiable realvalued forwardbackward envelope function that has the same set of minimisers as the actual problem. Then we use quasiNewton method, in particular LBFGS method, that utilises secondorder information to solve the FBE. The computations with this algorithm are also parallelisable and it demonstrated fast convergence compared to accelerated dual proximal gradient algorithm.
Item Type:  IMT PhD Thesis 

Subjects:  Q Science > QA Mathematics > QA75 Electronic computers. Computer science 
PhD Course:  Computer Decision and System Science 
Identification Number:  10.6092/imtlucca/etheses/203 
Date Deposited:  22 Mar 2017 11:29 
URI:  http://etheses.imtlucca.it/id/eprint/203 
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