Fuel-Efficient Powered Descent Guidance on Large Planetary Bodies via Theory of Functional Connections

Johnston, Hunter; Schiassi, Enrico; Furfaro, Roberto; Mortari, Daniele

doi:10.1007/s40295-020-00228-x

Cited by 35 publications

(29 citation statements)

References 62 publications

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“…Primarily, TFC is used for the solution of DEs because the CEs eliminate the "curse of the equation constraints" [39][40][41]. Moreover, TFC has already been used to solve different classes of optimal control space guidance problems such as energy optimal landing on large and small planetary bodies [42,43], fuel optimal landing on large planetary bodies [44], energy optimal relative motion problems subject to Clohessy-Wiltshire dynamics [45], and classes of transport theory problems, such as radiative transfer [46] and rarefied-gas dynamics [47]. For tackling DEs, the standard (or Vanilla as defined in [48,49]) TFC method employs a linear combination of orthogonal polynomials, such as Legendre or Chebyshev polynomials [39,40], as a free function.…”

Section: Physics-informed Neural Network and Functional Interpolationmentioning

confidence: 99%

Physics-Informed Neural Networks and Functional Interpolation for Data-Driven Parameters Discovery of Epidemiological Compartmental Models

et al. 2021

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In this work, we apply a novel and accurate Physics-Informed Neural Network Theory of Functional Connections (PINN-TFC) based framework, called Extreme Theory of Functional Connections (X-TFC), for data-physics-driven parameters’ discovery of problems modeled via Ordinary Differential Equations (ODEs). The proposed method merges the standard PINNs with a functional interpolation technique named Theory of Functional Connections (TFC). In particular, this work focuses on the capability of X-TFC in solving inverse problems to estimate the parameters governing the epidemiological compartmental models via a deterministic approach. The epidemiological compartmental models treated in this work are Susceptible-Infectious-Recovered (SIR), Susceptible-Exposed-Infectious-Recovered (SEIR), and Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIRS). The results show the low computational times, the high accuracy, and effectiveness of the X-TFC method in performing data-driven parameters’ discovery systems modeled via parametric ODEs using unperturbed and perturbed data.

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Section: Physics-informed Neural Network and Functional Interpolationmentioning

confidence: 99%

Physics-Informed Neural Networks and Functional Interpolation for Data-Driven Parameters Discovery of Epidemiological Compartmental Models

et al. 2021

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“…The detailed derivation of the switching functions is reported in the work of Johnston et al [21]. Here, for the convenience of the reader we just report them.…”

Section: Appendix a Switching Functionsmentioning

confidence: 99%

“…In particular, TFC is widely used for the solution of DEs, because the CEs remove the "curse of the equation constraints" [16][17][18]. Additionally, TFC has already been used to solve several classes of optimal control space guidance problems such as energy optimal landing on large and small planetary bodies [19,20], fuel optimal landing on large planetary bodies [21], and energy optimal relative motion problems subject to Clohessy-Wiltshire dynamics [22]. For solving DEs, the standard TFC method uses a linear combination of orthogonal polynomials, such as Legendre or Chebyshev polynomials [16,17], as a free function.…”

Section: Introductionmentioning

confidence: 99%

Pontryagin Neural Networks with Functional Interpolation for Optimal Intercept Problems

et al. 2021

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In 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.

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“…TFC has been developed for univariate and multivariate scenarios [2,7,8] to solve a variety of mathematical problems: a homotopy continuation algorithm for dynamics and control problems [14], domain mapping [15], data-driven parameters discovery applied to epidemiological compartmental models [16], transport theory problems such as radiative transfer [17] and rarefied-gas dynamics [18], nonlinear programming under equality constraints [19], Timoshenko-Ehrenfest beam [20], boundary-value problems in hybrid systems [21], eighth-order boundary value problems [22], and in Support Vector Machine [23]. TFC has been widely used for solving optimal control problems for space application, solved via indirect methods [24]: orbit transfer and propagation [25][26][27][28], energy-optimal in relative motion [29], energy-optimal and fuel-efficient landing on small and large planetary bodies [30,31], the minimum time-energy optimal intercept problem [32].…”

Section: Introductionmentioning

confidence: 99%

Theory of Functional Connections Applied to Linear ODEs Subject to Integral Constraints and Linear Ordinary Integro-Differential Equations

Florio

Schiassi

D’Ambrosio

et al. 2021

MCA

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This study shows how the Theory of Functional Connections (TFC) allows us to obtain fast and highly accurate solutions to linear ODEs involving integrals. Integrals can be constraints and/or terms of the differential equations (e.g., ordinary integro-differential equations). This study first summarizes TFC, a mathematical procedure to obtain constrained expressions. These are functionals representing all functions satisfying a set of linear constraints. These functionals contain a free function, g(x), representing the unknown function to optimize. Two numerical approaches are shown to numerically estimate g(x). The first models g(x) as a linear combination of a set of basis functions, such as Chebyshev or Legendre orthogonal polynomials, while the second models g(x) as a neural network. Meaningful problems are provided. In all numerical problems, the proposed method produces very fast and accurate solutions.

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Fuel-Efficient Powered Descent Guidance on Large Planetary Bodies via Theory of Functional Connections

Cited by 35 publications

References 62 publications

Physics-Informed Neural Networks and Functional Interpolation for Data-Driven Parameters Discovery of Epidemiological Compartmental Models

Physics-Informed Neural Networks and Functional Interpolation for Data-Driven Parameters Discovery of Epidemiological Compartmental Models

Pontryagin Neural Networks with Functional Interpolation for Optimal Intercept Problems

Theory of Functional Connections Applied to Linear ODEs Subject to Integral Constraints and Linear Ordinary Integro-Differential Equations

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