Infinite-Horizon Linear-Quadratic Control by Forward Propagation of the Differential Riccati Equation

Date

2015-04-01

Author

Prach, Anna
Tekinalp, Ozan
Bernstein, Dennis S.

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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One of the foundational principles of optimal control theory is that optimal control laws are propagated backward in time. For linear-quadratic control, this means that the solution of the Riccati equation must be obtained from backward integration from a final-time condition. These features are a direct consequence of the transversality conditions of optimal control, which imply that a free final state corresponds to a fixed final adjoint state [1], [2]. In addition, the principle of dynamic programming and the associated Hamilton-Jacobi-Bellman equation is an inherently backward-propagating methodology [3].

Subject Keywords

Riccati equations , Optimal control, Quadratic control, Stability analysis, Dynamic programming, Kalman filters

URI

https://hdl.handle.net/11511/49239

Journal

IEEE CONTROL SYSTEMS MAGAZINE

DOI

https://doi.org/10.1109/mcs.2014.2385252

Collections

Department of Aerospace Engineering, Article

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Citation Formats

A. Prach, O. Tekinalp, and D. S. Bernstein, “Infinite-Horizon Linear-Quadratic Control by Forward Propagation of the Differential Riccati Equation,” IEEE CONTROL SYSTEMS MAGAZINE, pp. 78–93, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/49239.