Direct methods are well known to have a large convergence rate in the solution of optimal control problems and thanks to the availability of efficient Non-Linear Programming (NLP) algorithms that are widely adopted. Additionally, it has been proved that thanks to the Covector Mapping Principle (CMP) there is essentially no distinction between direct and indirect methods when Pseudo Spectral collocation is used. In this work, inspired by CMP, a map is proposed to connect the discretized equations of the indirect method with those resulting from the direct transcription with the same trapezoidal scheme. The indirect method will benefit this new formulation since it can adopt the same regularization techniques typically implemented in direct approaches while still maintaining the explicit solution of the control as a function of the states and co-states in a bi-level optimization solution strategy. Finally, the proposed mapping is also derived for the implicit dynamics.
Direct methods are well known to have a large convergence rate in the solution of optimal control problems and thanks to the availability of efficient Non-Linear Programming (NLP) algorithms that are widely adopted. Additionally, it has been proved that thanks to the Covector Mapping Principle (CMP) there is essentially no distinction between direct and indirect methods when Pseudo Spectral collocation is used. In this work, inspired by CMP, a map is proposed to connect the discretized equations of the indirect method with those resulting from the direct transcription with the same trapezoidal scheme. The indirect method will benefit this new formulation since it can adopt the same regularization techniques typically implemented in direct approaches while still maintaining the explicit solution of the control as a function of the states and co-states in a bi-level optimization solution strategy. Finally, the proposed mapping is also derived for the implicit dynamics.
A Direct/Indirect Approach to Optimal Control Problems / Bertolazzi, Enrico; Biral, Francesco. - ELETTRONICO. - 14477:(2025), pp. 47-62. ( NUMTA 2023 Pizzo Calabro, Italy 14-20 June) [10.1007/978-3-031-81244-6_4].
A Direct/Indirect Approach to Optimal Control Problems
Enrico Bertolazzi
;Francesco Biral
2025-01-01
Abstract
Direct methods are well known to have a large convergence rate in the solution of optimal control problems and thanks to the availability of efficient Non-Linear Programming (NLP) algorithms that are widely adopted. Additionally, it has been proved that thanks to the Covector Mapping Principle (CMP) there is essentially no distinction between direct and indirect methods when Pseudo Spectral collocation is used. In this work, inspired by CMP, a map is proposed to connect the discretized equations of the indirect method with those resulting from the direct transcription with the same trapezoidal scheme. The indirect method will benefit this new formulation since it can adopt the same regularization techniques typically implemented in direct approaches while still maintaining the explicit solution of the control as a function of the states and co-states in a bi-level optimization solution strategy. Finally, the proposed mapping is also derived for the implicit dynamics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
