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Finite-Dimensional Characterization of Optimal Control Laws Over an Infinite Horizon for Nonlinear Systems
- Source :
- IEEE Transactions on Automatic Control; October 2023, Vol. 68 Issue: 10 p5954-5965, 12p
- Publication Year :
- 2023
-
Abstract
- Infinite-horizon optimal control problems for nonlinear systems are considered. Due to the nonlinear and intrinsically infinite-dimensional nature of the task, solving such optimal control problems is challenging. In this article, an exact finite-dimensional characterization of the optimal solution over the entire horizon is proposed. This is obtained via the (static) minimization of a suitably defined function of (projected) trajectories of the underlying Hamiltonian dynamics on a hypersphere of fixed radius. The result is achieved in the spirit of the so-called shooting methods by introducing, via simultaneous forward/backward propagation, an intermediate shooting point much closer to the origin, regardless of the actual initial state. A modified strategy allows one to determine an arbitrarily accurate approximate solution by means of standard gradient-descent algorithms over compact domains. Finally, to further increase the robustness of the control law, a receding-horizon architecture is envisioned by designing a sequence of shrinking hyperspheres. These aspects are illustrated by means of a benchmark numerical simulation.
Details
- Language :
- English
- ISSN :
- 00189286 and 15582523
- Volume :
- 68
- Issue :
- 10
- Database :
- Supplemental Index
- Journal :
- IEEE Transactions on Automatic Control
- Publication Type :
- Periodical
- Accession number :
- ejs64082397
- Full Text :
- https://doi.org/10.1109/TAC.2022.3230764