Experimental Implementation of Adaptive-Critic Based Infinite Time Optimal Neurocontrol for a Heat Diffusion System

Recently the synthesis methodology for the infinite time optimal neuro-controllers for PDE systems in the framework of adaptive-critic design has been developed. In this paper, first we model an experimental setup representing one dimensional heat diffusion problems. Then we synthesize and implement an adaptive-critic based neuro-controller for online temperature profile control of the experimental setup

Model Predictive Control Based on Deep Learning for Solar Parabolic-Trough Plants

En la actualidad, cada vez es mayor el interés por utilizar energías renovables, entre las que se encuentra la energía solar. Las plantas de colectores cilindro-parabólicos son un tipo de planta termosolar donde se hace incidir la radiación del Sol en unos tubos mediante el uso de unos espejos con forma de parábola. En el interior de estos tubos circula un fluido, generalmente aceite o agua, que se calienta para generar vapor y hacer girar una turbina, produciendo energía eléctrica. Uno de los métodos más utilizados para manejar estas plantas es el control predictivo basado en modelo (model predictive control, MPC), cuyo funcionamiento consiste en obtener las señales de control óptimas que se enviarán a la planta basándose en el uso de un modelo de la misma. Este método permite predecir el estado que adoptará el sistema según la estrategia de control escogida a lo largo de un horizonte de tiempo. El MPC tiene como desventaja un gran coste computacional asociado a la resolución de un problema de optimización en cada instante de muestreo. Esto dificulta su implementación en plantas comerciales y de gran tamaño, por lo que, actualmente, uno de los principales retos es la disminución de estos tiempos de cálculo, ya sea tecnológicamente o mediante el uso de técnicas subóptimas que simplifiquen el problema. En este proyecto, se propone el uso de redes neuronales que aprendan offline de la salida proporcionada por un controlador predictivo para luego poder aproximarla. Se han entrenado diferentes redes neuronales utilizando un conjunto de datos de 30 días de simulación y modificando el número de entradas. Los resultados muestran que las redes neuronales son capaces de proporcionar prácticamente la misma potencia que el MPC con variaciones más suaves de la salida y muy bajas violaciones de las restricciones, incluso disminuyendo el número de entradas. El trabajo desarrollado se ha publicado en Renewable Energy, una revista del primer cuartil en Green & sustainable science & technology y Energy and fuels.Nowadays, there is an increasing interest in using renewable energy sources, including solar energy. Parabolic trough plants are a type of solar thermal power plant in which solar radiation is reflected onto tubes with parabolic mirrors. Inside these tubes circulates a fluid, usually oil or water, which is heated to generate steam and turn a turbine to produce electricity. One of the most widely used methods to control these plants is model predictive control (MPC), which obtains the optimal control signals to send to the plant based on the use of a model. This method makes it possible to predict its future state according to the chosen control strategy over a time horizon. The MPC has the disadvantage of a significant computational cost associated with resolving an optimization problem at each sampling time. This makes it challenging to implement in commercial and large plants, so currently, one of the main challenges is to reduce these computational times, either technologically or by using suboptimal techniques that simplify the problem. This project proposes the use of neural networks that learn offline from the output provided by a predictive controller to then approximate it. Different neural networks have been trained using a 30-day simulation dataset and modifying the number of irradiance and temperature inputs. The results show that the neural networks can provide practically the same power as the MPC with smoother variations of the output and very low violations of the constraints, even when decreasing the number of inputs. The work has been published in Renewable Energy, a first quartile journal in Green & sustainable science & technology and Energy and fuels.Universidad de Sevilla. Máster en Ingeniería Industria

Backstepping PDE Design: A Convex Optimization Approach

Abstract\u2014Backstepping design for boundary linear PDE is formulated as a convex optimization problem. Some classes of parabolic PDEs and a first-order hyperbolic PDE are studied, with particular attention to non-strict feedback structures. Based on the compactness of the Volterra and Fredholm-type operators involved, their Kernels are approximated via polynomial functions. The resulting Kernel-PDEs are optimized using Sumof- Squares (SOS) decomposition and solved via semidefinite programming, with sufficient precision to guarantee the stability of the system in the L2-norm. This formulation allows optimizing extra degrees of freedom where the Kernel-PDEs are included as constraints. Uniqueness and invertibility of the Fredholm-type transformation are proved for polynomial Kernels in the space of continuous functions. The effectiveness and limitations of the approach proposed are illustrated by numerical solutions of some Kernel-PDEs

Optimization based control design techniques for distributed parameter systems

The study presents optimization based control design techniques for the systems that are governed by partial differential equations. A control technique is developed for systems that are actuated at the boundary. The principles of dynamic inversion and constrained optimization theory are used to formulate a feedback controller. This control technique is demonstrated for heat equations and thermal convection loops. This technique is extended to address a practical issue of parameter uncertainty in a class of systems. An estimator is defined for unknown parameters in the system. The Lyapunov stability theory is used to derive an update law of these parameters. The estimator is used to design an adaptive controller for the system. A second control technique is presented for a class of second order systems that are actuated in-domain. The technique of proper orthogonal decomposition is used first to develop an approximate model. This model is then used to design optimal feedback controller. Approximate dynamic programming based neural network architecture is used to synthesize a sub-optimal controller. This control technique is demonstrated to stabilize the heave dynamics of a flexible aircraft wings. The third technique is focused on the optimal control of stationary thermally convected fluid flows from the numerical point of view. To overcome the computational requirement, optimization is carried out using reduced order model. The technique of proper orthogonal decomposition is used to develop reduced order model. An example of chemical vapor deposition reactor is considered to examine this control technique --Abstract, page iii

Optimal Management of Beaver Population using a Reduced-Order Distributed Parameter Model and Single Network Adaptive Critics

Beavers are often found to be in conflict with human interests by creating nuisances like building dams on flowing water (leading to flooding), blocking irrigation canals, cutting down timbers, etc. At the same time they contribute to raising water tables, increased vegetation, etc. Consequently, maintaining an optimal beaver population is beneficial. Because of their diffusion externality (due to migratory nature), strategies based on lumped parameter models are often ineffective. Using a distributed parameter model for beaver population that accounts for their spatial and temporal behavior, an optimal control (trapping) strategy is presented in this paper that leads to a desired distribution of the animal density in a region in the long run. The optimal control solution presented, imbeds the solution for a large number of initial conditions (i.e., it has a feedback form), which is otherwise nontrivial to obtain. The solution obtained can be used in real-time by a nonexpert in control theory since it involves only using the neural networks trained offline. Proper orthogonal decomposition-based basis function design followed by their use in a Galerkin projection has been incorporated in the solution process as a model reduction technique. Optimal solutions are obtained through a single network adaptive critic (SNAC) neural-network architecture

Parallel computations and control of adaptive structures

The equations of motion for structures with adaptive elements for vibration control are presented for parallel computations to be used as a software package for real-time control of flexible space structures. A brief introduction of the state-of-the-art parallel computational capability is also presented. Time marching strategies are developed for an effective use of massive parallel mapping, partitioning, and the necessary arithmetic operations. An example is offered for the simulation of control-structure interaction on a parallel computer and the impact of the approach presented for applications in other disciplines than aerospace industry is assessed

Activities of the Institute for Computer Applications in Science and Engineering (ICASE)

This report summarizes research conducted at the Institute for Computer Applications Science and Engineering in applied mathematics, numerical analysis, and computer science during the period October 2, 1987 through March 31, 1988

Challenges in Optimization with Complex PDE-Systems (hybrid meeting)

The workshop concentrated on various aspects of optimization problems with systems of nonlinear partial differential equations (PDEs) or variational inequalities (VIs) as constraints. In particular, discussions around several keynote presentations in the areas of optimal control of nonlinear or non-smooth systems, optimization problems with functional and discrete or switching variables leading to mixed integer nonlinear PDE constrained optimization, shape and topology optimization, feedback control and stabilization, multi-criteria problems and multiple optimization problems with equilibrium constraints as well as versions of these problems under uncertainty or stochastic influences, and the respectively associated numerical analysis as well as design and analysis of solution algorithms were promoted. Moreover, aspects of optimal control of data-driven PDE constraints (e.g. related to machine learning) were addressed

QRnet: optimal regulator design with LQR-augmented neural networks

In this paper we propose a new computational method for designing optimal regulators for high-dimensional nonlinear systems. The proposed approach leverages physics-informed machine learning to solve high-dimensional Hamilton-Jacobi-Bellman equations arising in optimal feedback control. Concretely, we augment linear quadratic regulators with neural networks to handle nonlinearities. We train the augmented models on data generated without discretizing the state space, enabling application to high-dimensional problems. We use the proposed method to design a candidate optimal regulator for an unstable Burgers' equation, and through this example, demonstrate improved robustness and accuracy compared to existing neural network formulations.Comment: Added IEEE accepted manuscript with copyright notic

Stochastic Model Predictive Control via Fixed Structure Policies

In this work, the model predictive control problem is extended to include not only open-loop control sequences but also state-feedback control laws by directly optimizing parameters of a control policy. Additionally, continuous cost functions are developed to allow training of the control policy in making discrete decisions, which is typically done with model-free learning algorithms. This general control policy encompasses a wide class of functions and allows the optimization to occur both online and offline while adding robustness to unmodelled dynamics and outside disturbances. General formulations regarding nonlinear discrete-time dynamics and abstract cost functions are formed for both deterministic and stochastic problems. Analytical solutions are derived for linear cases and compared to existing theory, such as the classical linear quadratic regulator. It is shown that, given some assumptions hold, there exists a finite horizon in which a constant linear state-feedback control law will stabilize a nonlinear system around the origin. Several control policy architectures are used to regulate the cart-pole system in deterministic and stochastic settings, and neural network-based policies are trained to analyze and intercept bodies following stochastic projectile motion