1,721,021 research outputs found
Bellman neural networks for the class of optimal control problems with integral quadratic cost
No full textThis article introduces Bellman neural networks (BeNNs) and employs them to learn the optimal control actions for the class of optimal control problems (OCPs) with integral quadratic cost. BeNNs represent a particular family of physicsinformed neural networks specifically designed and trained to tackle OCPs via applying the Bellman principle of optimality (BPO). The BPO provides necessary and sufficient optimality conditions, which result in a nonlinear partial differential equation known as the Hamilton-Jacobi-Bellman (HJB) equation. BeNNs learn the optimal control actions from the unknown solution of the arising HJB equation (i.e., the value function), where the unknown solution is modeled using a neural network. In addition, this article shows how to estimate the upper bounds on the generalization error of BeNNs while learning the solutions for the OCP class under consideration. The generalization error estimate is provided in terms of the choice and number of the training points as well as the training error. Numerical studies show that BeNNs can be successfully applied to learn the feedback control actions for the class of OCPs considered and, after the training is completed, deployed to control the system in a closed-loop fashion. Impact Statement-The proposed research improves our understanding of how to solve optimal control problems with closed-loop solutions and has potentially a countless number of applications in several different areas. The study is at the intersection between optimal control theory and artificial intelligence connected with mathematical tools for functional interpolation. This advances the ability to implement a higher level of autonomy in decision-making for practical applications with a beneficial impact on our society
An Overview of X-TFC Applications for Aerospace Optimal Control Problems
No full textThis paper is an overview of Optimal Control Problems (OCPs) for aerospace applications tackled via the indirect method and a particular Physics-Informed Neural Networks (PINNs) framework, developed by the authors, named Extreme Theory of Functional Connections (X-TFC). X-TFC approximates the unknown OCP solutions via the Constrained Expressions, which are functionals made up of the sum of a free-function and a functional that analytically satisfies the boundary conditions. Thanks to this property, the framework is fast and accurate in learning the solution to the Two-Point Boundary Value Problem (TPBVP) arising after applying the Pontryagin Minimum Principle. The applications presented in this paper regard intercept problems, interplanetary planar orbit transfers, transfer trajectories within the Circular Restricted Three-Body Problem, and safe trajectories around asteroids with collision avoidance. The main results are presented and discussed, proving the efficiency of the proposed framework in solving OCPs and its low computational times, which can potentially enable a higher level of autonomy in decision-making for practical applications
Learning Fuel-Optimal Trajectories for Space Applications via Pontryagin Neural Networks
No full textThis paper demonstrates the utilization of Pontryagin Neural Networks (PoNNs) to acquire control strategies for achieving fuel-optimal trajectories. PoNNs, a subtype of Physics-Informed Neural Networks (PINNs), are tailored for solving optimal control problems through indirect methods. Specifically, PoNNs learn to solve the Two-Point Boundary Value Problem derived from the application of the Pontryagin Minimum Principle to the problem’s Hamiltonian. Within PoNNs, the Extreme Theory of Functional Connections (X-TFC) is leveraged to approximate states and costates using constrained expressions (CEs). These CEs comprise a free function, modeled by a shallow neural network trained via Extreme Learning Machine, and a functional component that consistently satisfies boundary conditions analytically. Addressing discontinuous control, a smoothing technique is employed, substituting the sign function with a hyperbolic tangent function and implementing a continuation procedure on the smoothing parameter. The proposed methodology is applied to scenarios involving fuel-optimal Earth−Mars interplanetary transfers and Mars landing trajectories. Remarkably, PoNNs exhibit convergence to solutions even with randomly initialized parameters, determining the number and timing of control switches without prior information. Additionally, an analytical approximation of the solution allows for optimal control computation at unencountered points during training. Comparative analysis reveals the efficacy of the proposed approach, which rivals state-of-the-art methods such as the shooting technique and the adaptive Gaussian quadrature collocation method
Machine Learning-based Light Curves Brightness Prediction for Space Objects in the Geostationary Belt
No full textPredicting the brightness of a space object is essential to ensure it can be visible from telescopes in the future and eventually also to reconstruct its light curve. Indeed, the analysis of satellite light curves, which represent the variation in brightness as a function of the phase angle or time, can be helpful to retrieve information about the object, such as its attitude, shape and configuration. This paper employs the light curves of some GEO satellites collected by the Space4 Center telescopes at the University of Arizona to generate a training dataset for neural networks. Specifically, the input of the neural network consists of the day of the year when the light curve was acquired as well as the longitudinal phase angle and the type of satellite, whereas the output is the brightness. Different types of training are carried out, considering first the type of satellite as input and then also the type of bus. Results show that recurrent neural networks are able to perform an accurate regression of the given light curves and predict the brightness. This framework will potentially be useful to synthetically generate several realistic light curves for more accurate neural network training, without the necessity to actually perform the observations through the telescopes
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Pontryagin neural networks with functional interpolation for optimal intercept problems
Get PDFIn this work, we introduce Pontryagin Neural Networks (PoNNs) and employ them to learn the optimal control actions for unconstrained and constrained optimal intercept problems. PoNNs represent a particular family of Physics-Informed Neural Networks (PINNs) specifically designed for tackling optimal control problems via the Pontryagin Minimum Principle (PMP) application (e.g., indirect method). The PMP provides first-order necessary optimality conditions, which result in a Two-Point Boundary Value Problem (TPBVP). More precisely, PoNNs learn the optimal control actions from the unknown solutions of the arising TPBVP, modeling them with Neural Networks (NNs). The characteristic feature of PoNNs is the use of PINNs combined with a functional interpolation technique, named the Theory of Functional Connections (TFC), which forms the so-called PINN-TFC based frameworks. According to these frameworks, the unknown solutions are modeled via the TFC’s constrained expressions using NNs as free functions. The results show that PoNNs can be successfully applied to learn optimal controls for the class of optimal intercept problems considered in this paper
Physics-Informed Neural Networks and Functional Interpolation for Solving the Matrix Differential Riccati Equation
No full textIn this manuscript, we explore how the solution of the matrix differential Riccati equation (MDRE) can be computed with the Extreme Theory of Functional Connections (X-TFC). X-TFC is a physics-informed neural network that uses functional interpolation to analytically satisfy linear constraints, such as the MDRE’s terminal constraint. We utilize two approaches for solving the MDRE with X-TFC: direct and indirect implementation. The first approach involves solving the MDRE directly with X-TFC, where the matrix equations are vectorized to form a system of first order differential equations and solved with iterative least squares. In the latter approach, the MDRE is first transformed into a matrix differential Lyapunov equation (MDLE) based on the anti-stabilizing solution of the algebraic Riccati equation. The MDLE is easier to solve with X-TFC because it is linear, while the MDRE is nonlinear. Furthermore, the MDLE solution can easily be transformed back into the MDRE solution. Both approaches are validated by solving a fluid catalytic reactor problem and comparing the results with several state-of-the-art methods. Our work demonstrates that the first approach should be performed if a highly accurate solution is desired, while the second approach should be used if a quicker computation time is needed
Orbit determination pipeline for geostationary objects using physics-informed neural networks
No full textDue to the importance of the geostationary orbit belt, tracking and identification of satellites in such orbits is of pivotal importance for space situational awareness. To address this problem, a comprehensive pipeline for satellite tracking is proposed, starting from raw observations to satellite identification and tracking. The pipeline includes "Stingray", an advanced hardware system with 15 cameras for high-resolution optical observations of the GEO belt. The astrometry component extracts the necessary information for orbit determination, while physics-informed neural networks (PINNs) estimate the object orbits, considering significant dynamics disturbances including third-body perturbations, solar radiation pressure and control maneuvers. The proposed framework is capable of processing the orbit determination of several objects in parallel and is able to automatically re-process all those observations for which the orbit determination previously failed by varying the PINN hyperparameters. Thus, the pipeline results to be accurate and efficient, thus being proper for catalog maintenance
Physics-Informed Neural Networks for Closed-Loop Guidance and Control in Aerospace Systems
No full textPhysics-Informed Neural Networks (PINNs) refer to recently defined a class of machine learning algorithms where the learning process for both regression and classification tasks is constrained to satisfy differential equations derived by the straightforward application of known physical laws. Indeed, Deep Neural Networks have been successfully employed to solve a variety of ODEs and PDEs arising in fluid mechanics, quantum mechanics, just to mention a few. Optimal control problems, i.e. finding a feasible control that minimizes a cost functional while satisfying physical, state and control constraints, are generally difficult to solve and one may need to resort to specialized numerical methods. In this work, we show how PINNs can be employed to synthesize closed-loop optimal guidance and control policies by learning the solution of the Hamilton-Jacobi-Bellman Equation (HJBE) via shallow and deep networks. We show that such methods can be coupled with the Theory of Functional Connections to create numerical frameworks that generate efficient and accurate solutions of the HJBE resulting in novel architectures for closed-loop G&C that may enable autonomy in a large class of aerospace systems
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