A Unified Approach to the Finite-Horizon Linear Quadratic Optimal Control Problem**
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Cited by (14)
Free finite horizon LQR: A bilevel perspective and its application to model predictive control
2019, AutomaticaCitation Excerpt :Hence, we restrict ourselves to this case, in which the initial state of the system is given and an affine constraint on the state might be imposed at the final time as in (2). However, the analysis can be easily extended to deal with the free final time version of more general finite-horizon LQR problems, e.g. Ferrante and Ntogramatzidis (2007). Problem 1 can be casted into an equivalent bilevel optimization problem, whose upper level reads:
On the exact solution of the matrix Riccati differential equation
2011, IFAC Proceedings Volumes (IFAC-PapersOnline)On the solution of the Riccati differential equation arising from the LQ optimal control problem
2010, Systems and Control LettersCitation Excerpt :Moreover, sign-controllability is also the weakest known assumption for which the associated algebraic Riccati equation is guaranteed to admit a symmetric solution. Under this assumption, a formula parameterising in finite terms all the trajectories originating from the Hamiltonian differential equation, introduced by the same authors in [18], is exploited to derive a non-recursive formula for the solution of the Riccati differential equation. This parameterisation of the trajectories of the Hamiltonian differential equation generalises those proposed in [19,20] for controllable and stabilisable systems, respectively; see also [21,22] for the discrete-time counterpart.
Unified Control Parameterization Approach for Finite-Horizon Feedback Control with Trajectory Shaping
2022, IEEE Transactions on Aerospace and Electronic SystemsImproved Performance for PMSM Control System Based on LQR Controller and Computational Intelligence
2021, International Conference on Electrical, Computer, and Energy Technologies, ICECET 2021Stability robustness of linear quadratic regulators
2016, International Journal of Robust and Nonlinear Control
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Partially supported by the Ministry of Higher Education of Italy (MIUR) under the project Identification and Control of Industrial Systems any by the Australian Research Council (DP0664789).