The stationary point of observer-based dynamic LQR is characterized by a pair of symmetric discrete-time Sylvester equations, and the usual separated LQR-plus-minimum-trace-observer design is not optimal.
Global convergence of policy gradient methods for the linear quadratic regulator
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Relearn LQR combines recursive least squares with policy gradient for on-policy data-driven LQR and proves stability of the full scheme via Lyapunov analysis with averaging and timescale separation.
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On the Optimization Landscape of Observer-based Dynamic Linear Quadratic Control
The stationary point of observer-based dynamic LQR is characterized by a pair of symmetric discrete-time Sylvester equations, and the usual separated LQR-plus-minimum-trace-observer design is not optimal.
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Stability-Certified On-Policy Data-Driven LQR via Recursive Learning and Policy Gradient
Relearn LQR combines recursive least squares with policy gradient for on-policy data-driven LQR and proves stability of the full scheme via Lyapunov analysis with averaging and timescale separation.