核心概念
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems with unknown dynamics, globally convergent to the optimal solution, unbiased under noisy measurements, and computationally efficient.
摘要
The content discusses an iterative learning algorithm for optimal control in continuous-time symmetric systems with unknown dynamics. It covers the background of linear-quadratic regulation problems, state-of-the-art methods, convergence conditions, measurement noise considerations, and extension to infinite-horizon problems. The algorithm's key features include global convergence, unbiasedness under noise, and low computational complexity.
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Introduction
- Linear-quadratic regulation (LQR) problem aims to minimize a quadratic cost subject to system dynamics.
- Direct approach focuses on solving optimal control without knowing the system model.
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State-of-the-Art
- Kleinman’s algorithm sets a foundation for solving LQR problems without system model access.
- Model-free algorithms emerged from Kleinman’s algorithm for LQR problems.
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Symmetric Systems
- Definition of external symmetry in systems based on input-output relations.
- Completely symmetric systems are internally and externally symmetric.
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Main Results
- Algorithm presented solves optimal control problem without prior model knowledge.
- Convergence analysis shows the algorithm's effectiveness in reaching the optimal solution.
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Extension to Infinite-Horizon Problems
- Algorithm adapted for infinite-horizon problems with state feedback gain derivation.
- Theoretical analysis ensures convergence and reliability under noisy measurements.
統計資料
It is shown that limk→+∞ ∥uk − u⋆∥2,tf = 0 holds from Lemma 1.
Condition (45) ensures limk→+∞ ∥uk − u⋆∥∞,tf = 0 as per Lemma 3.