Physics-Informed Neural Nets for Control of Dynamical Systems

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by Ordinary Differential Equations (ODEs), the conventional PINN has a continuous time input variable and outputs the solution of the corresponding ODE. In their original form, PINNs do not allow control inputs neither can they simulate for long-range intervals without serious degradation in their predictions. In this context, this work presents a new framework called Physics-Informed Neural Nets for Control (PINC), which proposes a novel PINN-based architecture that is amenable to \emph{control} problems and able to simulate for longer-range time horizons that are not fixed beforehand. The framework has new inputs to account for the initial state of the system and the control action. In PINC, the response over the complete time horizon is split such that each smaller interval constitutes a solution of the ODE conditioned on the fixed values of initial state and control action for that interval. The whole response is formed by feeding back the predictions of the terminal state as the initial state for the next interval. This proposal enables the optimal control of dynamic systems, integrating a priori knowledge from experts and data collected from plants into control applications. We showcase our proposal in the control of two nonlinear dynamic systems: the Van der Pol oscillator and the four-tank system

Neural Networks: Training and Application to Nonlinear System Identification and Control

This dissertation investigates training neural networks for system identification and classification. The research contains two main contributions as follow:1. Reducing number of hidden layer nodes using a feedforward componentThis research reduces the number of hidden layer nodes and training time of neural networks to make them more suited to online identification and control applications by adding a parallel feedforward component. Implementing the feedforward component with a wavelet neural network and an echo state network provides good models for nonlinear systems.The wavelet neural network with feedforward component along with model predictive controller can reliably identify and control a seismically isolated structure during earthquake. The network model provides the predictions for model predictive control. Simulations of a 5-story seismically isolated structure with conventional lead-rubber bearings showed significant reductions of all response amplitudes for both near-field (pulse) and far-field ground motions, including reduced deformations along with corresponding reduction in acceleration response. The controller effectively regulated the apparent stiffness at the isolation level. The approach is also applied to the online identification and control of an unmanned vehicle. Lyapunov theory is used to prove the stability of the wavelet neural network and the model predictive controller. 2. Training neural networks using trajectory based optimization approachesTraining neural networks is a nonlinear non-convex optimization problem to determine the weights of the neural network. Traditional training algorithms can be inefficient and can get trapped in local minima. Two global optimization approaches are adapted to train neural networks and avoid the local minima problem. Lyapunov theory is used to prove the stability of the proposed methodology and its convergence in the presence of measurement errors. The first approach transforms the constraint satisfaction problem into unconstrained optimization. The constraints define a quotient gradient system (QGS) whose stable equilibrium points are local minima of the unconstrained optimization. The QGS is integrated to determine local minima and the local minimum with the best generalization performance is chosen as the optimal solution. The second approach uses the QGS together with a projected gradient system (PGS). The PGS is a nonlinear dynamical system, defined based on the optimization problem that searches the components of the feasible region for solutions. Lyapunov theory is used to prove the stability of PGS and QGS and their stability under presence of measurement noise

LSTM networks for the implementation of an internal model control strategy in WWTPs

Water resources are one of the most important environmental issues due to the vulnerability of water to contamination and its direct effect on human health. Improving their management depends largely on the treatment of wastewater. For that reason, there are strict pollution limits set for the effluent of wastewater treatment plants (WWTPs), which is discharged into streams or other receiving waters. In order to improve the treatment quality, meet the standards imposed by authorities and to maintain low cost of operations, control strategies are implemented in these plants. This project presents a control system based on internal model controllers (IMCs) adopting artificial neural networks (ANNs), as an alternative to the default control strategy of the Benchmark Simulation Model no. 1 (BSM1), a framework emulating the behavior of a general purpose WWTP that uses proportional integral (PI) controllers. With the proposed control approach, the real plant behavior is modeled with only influent and effluent data to take under control the dissolved oxygen and nitrate and nitrite nitrogen concentrations, also offering a better performance in terms of integral absolute error (IAE) and integral square error (ISE) with respect to the default controllers.Els recursos hídrics són un dels assumptes ambientals més importants degut a la vulnerabilitat de l'aigua a ser contaminada i el seu efecte directe en la salut humana. La millora de la seva gestió depèn en gran mesura del tractament d'aigües residuals. Per aquest motiu, hi ha estrictes límits de contaminació establerts per l'efluent de les estacions depuradores d'aigües residuals (EDAR), el qual ́es abocat en rierols o altres aigües receptores. Amb la finalitat de millorar la qualitat del tractament, complir les normes imposades per les autoritats i mantenir un baix cost de les operacions, s'apliquen estratègies de control en aquestes estacions. Aquest projecte presenta un sistema de control basat en controladors per model intern(IMC) que empren xarxes neuronals artificials (ANN), com alternativa a l'estratègia de control per defecte del Benchmark Simulation Model no. 1 (BSM1), un marc que emula el comportament d'una EDAR de propòsit general que utilitza controladors proporcionals integrals (PI). Amb el mètode de control proposat, el comportament real de l'estació es modela amb només les dades de l'influent i de l'efluent per tenir sota control les concentracions d'oxigen dissolt i de nitrat i nitrit de nitrogen, oferint també un millor rendiment en termes de la integral de l'error absolut (IAE) i de la integral de l'error quadràtic (ISE) respecte als controladors per defecte.Los recursos hídricos son uno de los asuntos ambientales más importantes debido a la vulnerabilidad del agua a ser contaminada y su efecto directo en la salud humana. La mejora de su gestión depende en gran medida del tratamiento de aguas residuales. Por este motivo, hay estrictos límites de contaminación establecidos para el efluente de las estaciones depuradoras de aguas residuales (EDAR), el cual es vertido en arroyos u otras aguas receptoras. Con elfin de mejorar la calidad del tratamiento, cumplir las normas impuestas por las autoridades y mantener un bajo costo de las operaciones, se aplican estrategias de control en estas estaciones. Este proyecto presenta un sistema de control basado en controladores por modelo interno (IMC) que emplean redes neuronales artificiales (ANN), como alternativa a la estrategia de control por defecto del Benchmark Simulation Model no. 1 (BSM1), un marco que emula el comportamiento de una EDAR de propósito general que utiliza controladores proporcionales integrales (PI). Con el método de control propuesto, el comportamiento real de la estación se modela con sólo los datos del influente y del efluente para tener bajo control las concentraciones de oxígeno disuelto y de nitrato y nitrito de nitrógeno, ofreciendo también un mejor rendimiento en términos de la integral del error absoluto (IAE) y de la integral del error cuadrático (ISE) con respecto a los controladores por defecto

Hybrid and Electric Vehicles Optimal Design and Real-time Control based on Artificial Intelligence

L'abstract è presente nell'allegato / the abstract is in the attachmen

State-of-the-art on research and applications of machine learning in the building life cycle

Fueled by big data, powerful and affordable computing resources, and advanced algorithms, machine learning has been explored and applied to buildings research for the past decades and has demonstrated its potential to enhance building performance. This study systematically surveyed how machine learning has been applied at different stages of building life cycle. By conducting a literature search on the Web of Knowledge platform, we found 9579 papers in this field and selected 153 papers for an in-depth review. The number of published papers is increasing year by year, with a focus on building design, operation, and control. However, no study was found using machine learning in building commissioning. There are successful pilot studies on fault detection and diagnosis of HVAC equipment and systems, load prediction, energy baseline estimate, load shape clustering, occupancy prediction, and learning occupant behaviors and energy use patterns. None of the existing studies were adopted broadly by the building industry, due to common challenges including (1) lack of large scale labeled data to train and validate the model, (2) lack of model transferability, which limits a model trained with one data-rich building to be used in another building with limited data, (3) lack of strong justification of costs and benefits of deploying machine learning, and (4) the performance might not be reliable and robust for the stated goals, as the method might work for some buildings but could not be generalized to others. Findings from the study can inform future machine learning research to improve occupant comfort, energy efficiency, demand flexibility, and resilience of buildings, as well as to inspire young researchers in the field to explore multidisciplinary approaches that integrate building science, computing science, data science, and social science

Overløpskontroll i avløpsnett med forskjellige modelleringsteknikker og internet of things

Increased urbanization and extreme rainfall events are causing more frequent instances of sewer overflow, leading to the pollution of water resources and negative environmental, health, and fiscal impacts. At the same time, the treatment capacity of wastewater treatment plants is seriously affected. The main aim of this Ph.D. thesis is to use the Internet of Things and various modeling techniques to investigate the use of real-time control on existing sewer systems to mitigate overflow. The role of the Internet of Things is to provide continuous monitoring and real-time control of sewer systems. Data collected by the Internet of Things are also useful for model development and calibration. Models are useful for various purposes in real-time control, and they can be distinguished as those suitable for simulation and those suitable for prediction. Models that are suitable for a simulation, which describes the important phenomena of a system in a deterministic way, are useful for developing and analyzing different control strategies. Meanwhile, models suitable for prediction are usually employed to predict future system states. They use measurement information about the system and must have a high computational speed. To demonstrate how real-time control can be used to manage sewer systems, a case study was conducted for this thesis in Drammen, Norway. In this study, a hydraulic model was used as a model suitable for simulation to test the feasibility of different control strategies. Considering the recent advances in artificial intelligence and the large amount of data collected through the Internet of Things, the study also explored the possibility of using artificial intelligence as a model suitable for prediction. A summary of the results of this work is presented through five papers. Paper I demonstrates that one mainstream artificial intelligence technique, long short-term memory, can precisely predict the time series data from the Internet of Things. Indeed, the Internet of Things and long short-term memory can be powerful tools for sewer system managers or engineers, who can take advantage of real-time data and predictions to improve decision-making. In Paper II, a hydraulic model and artificial intelligence are used to investigate an optimal in-line storage control strategy that uses the temporal storage volumes in pipes to reduce overflow. Simulation results indicate that during heavy rainfall events, the response behavior of the sewer system differs with respect to location. Overflows at a wastewater treatment plant under different control scenarios were simulated and compared. The results from the hydraulic model show that overflows were reduced dramatically through the intentional control of pipes with in-line storage capacity. To determine available in-line storage capacity, recurrent neural networks were employed to predict the upcoming flow coming into the pipes that were to be controlled. Paper III and Paper IV describe a novel inter-catchment wastewater transfer solution. The inter-catchment wastewater transfer method aims at redistributing spatially mismatched sewer flows by transferring wastewater from a wastewater treatment plant to its neighboring catchment. In Paper III, the hydraulic behaviors of the sewer system under different control scenarios are assessed using the hydraulic model. Based on the simulations, inter-catchment wastewater transfer could efficiently reduce total overflow from a sewer system and wastewater treatment plant. Artificial intelligence was used to predict inflow to the wastewater treatment plant to improve inter-catchment wastewater transfer functioning. The results from Paper IV indicate that inter-catchment wastewater transfer might result in an extra burden for a pump station. To enhance the operation of the pump station, long short-term memory was employed to provide multi-step-ahead water level predictions. Paper V proposes a DeepCSO model based on large and high-resolution sensors and multi-task learning techniques. Experiments demonstrated that the multi-task approach is generally better than single-task approaches. Furthermore, the gated recurrent unit and long short-term memory-based multi-task learning models are especially suitable for capturing the temporal and spatial evolution of combined sewer overflow events and are superior to other methods. The DeepCSO model could help guide the real-time operation of sewer systems at a citywide level.publishedVersio

Nonlinear model predictive control using automatic differentiation

Although nonlinear model predictive control (NMPC) might be the best choice for a nonlinear plant, it is still not widely used. This is mainly due to the computational burden associated with solving online a set of nonlinear differential equations and a nonlinear dynamic optimization problem in real time. This thesis is concerned with strategies aimed at reducing the computational burden involved in different stages of the NMPC such as optimization problem, state estimation, and nonlinear model identification. A major part of the computational burden comes from function and derivative evaluations required in different parts of the NMPC algorithm. In this work, the problem is tackled using a recently introduced efficient tool, the automatic differentiation (AD). Using the AD tool, a function is evaluated together with all its partial derivative from the code defining the function with machine accuracy. A new NMPC algorithm based on nonlinear least square optimization is proposed. In a first–order method, the sensitivity equations are integrated using a linear formula while the AD tool is applied to get their values accurately. For higher order approximations, more terms of the Taylor expansion are used in the integration for which the AD is effectively used. As a result, the gradient of the cost function against control moves is accurately obtained so that the online nonlinear optimization can be efficiently solved. In many real control cases, the states are not measured and have to be estimated for each instance when a solution of the model equations is needed. A nonlinear extended version of the Kalman filter (EKF) is added to the NMPC algorithm for this purpose. The AD tool is used to calculate the required derivatives in the local linearization step of the filter automatically and accurately. Offset is another problem faced in NMPC. A new nonlinear integration is devised for this case to eliminate the offset from the output response. In this method, an integrated disturbance model is added to the process model input or output to correct the plant/model mismatch. The time response of the controller is also improved as a by–product. The proposed NMPC algorithm has been applied to an evaporation process and a two continuous stirred tank reactor (two–CSTR) process with satisfactory results to cope with large setpoint changes, unmeasured severe disturbances, and process/model mismatches. When the process equations are not known (black–box) or when these are too complicated to be used in the controller, modelling is needed to create an internal model for the controller. In this thesis, a continuous time recurrent neural network (CTRNN) in a state–space form is developed to be used in NMPC context. An efficient training algorithm for the proposed network is developed using AD tool. By automatically generating Taylor coefficients, the algorithm not only solves the differentiation equations of the network but also produces the sensitivity for the training problem. The same approach is also used to solve online the optimization problem of the NMPC. The proposed CTRNN and the predictive controller were tested on an evaporator and two–CSTR case studies. A comparison with other approaches shows that the new algorithm can considerably reduce network training time and improve solution accuracy. For a third case study, the ALSTOM gasifier, a NMPC via linearization algorithm is implemented to control the system. In this work a nonlinear state–space class Wiener model is used to identify the black–box model of the gasifier. A linear model of the plant at zero–load is adopted as a base model for prediction. Then, a feedforward neural network is created as the static gain for a particular output channel, fuel gas pressure, to compensate its strong nonlinear behavior observed in open–loop simulations. By linearizing the neural network at each sampling time, the static nonlinear gain provides certain adaptation to the linear base model. The AD tool is used here to linearize the neural network efficiently. Noticeable performance improvement is observed when compared with pure linear MPC. The controller was able to pass all tests specified in the benchmark problem at all load conditions.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Deep Learning-Based, Passive Fault Tolerant Control Facilitated by a Taxonomy of Cyber-Attack Effects

In the interest of improving the resilience of cyber-physical control systems to better operate in the presence of various cyber-attacks and/or faults, this dissertation presents a novel controller design based on deep-learning networks. This research lays out a controller design that does not rely on fault or cyber-attack detection. Being passive, the controller’s routine operating process is to take in data from the various components of the physical system, holistically assess the state of the physical system using deep-learning networks and decide the subsequent round of commands from the controller. This use of deep-learning methods in passive fault tolerant control (FTC) is unique in the research literature. The proposed controller is applied to both linear and nonlinear systems. Additionally, the application and testing are accomplished with both actuators and sensors being affected by attacks and /or faults