Runge-Kutta methods in optimal control and the transformed adjoint system

By William W. Hager. Numerische Mathematik, 2000

500 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/456afcebaae661bb1aa8ebd56d4d13ab6d70abfb

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

Pseudospectral Optimal Control and Its Convergence Theorems (2008, background): “the Karush-Kuhn-Tucker conditions) [13].”
Pseudospectral Methods for Infinite-Horizon Nonlinear Optimal Control Problems (2005, methodology): “Note, however, that the primal-space conditions [35,38] are obtained through dual-space considerations.”
Optimal control problems with delays in state and control variables subject to mixed control–state constraints (2009, methodology): “For undelayed optimal control problems, Hager [24] has given a detailed consistency analysis for higher-order Runge–Kutta schemes.”
Adjoint sensitivity analysis of regional air quality models (2005, methodology): “Runge–Kutta and Rosenbrock methods on the other hand are well suited for adjoint computations [22,43].”
A unified framework for the numerical solution of optimal control problems using pseudospectral methods (2010, methodology): “Second, we show that the LG and LGR transformed adjoint systems (analogous to the definition in Hager (2000)) are full rank while the LGL transformed adjoint system is rank-deficient.”
Universal Differential Equations for Scientific Machine Learning (2020, methodology): “Care has to be taken as the stability of an adjoint approach can be dependent on the chosen discretization method [59, 60, 61, 62, 63], and our software contribution helps researchers switch between all of these optimization approaches in combination with hundreds of diﬀerential equation solver…”
DISCRETE MECHANICS AND OPTIMAL CONTROL: AN ANALYSIS ∗ (2008, methodology): “This leads in Hager’s terminology to a Runge-Kutta scheme of order κ for optimal control , and therefore Hager’s convergence result for standard Runge-Kutta schemes in Hager [2000], Theorem 2.1, is directly applicable.”
Rate of convergence for the Legendre pseudospectral optimal control of feedback linearizable systems (2010, methodology): “They are essential to other computational methods such as those based on Euler [11] and Runge-Kutta [ 12 ] discretization.”
Approximation of reachable sets using optimal control algorithms (2013, background): “Results concerning the convergence of discretized optimal control problems can be found in [42, 19, 30] and the references stated therein.”
A Gauss pseudospectral transcription for optimal control (2005, methodology): “In these methods, piecewise polynomials can be used to approximate the differential equations at collocation points ([35] [7] [46] [21] [65] [33]).”
Legendre Pseudospectral Approximations of Optimal Control Problems (2003, methodology): “In fact, the popular Hermite-Simpson collocation method and even some Runge-Kutta methods do not converge to the solution of the optimal control problem [10].”