Reinforcement Learning in Continuous Time and Space
Neural Computation
Discrete-time control algorithms and adaptive intelligent systems designs
Discrete-time control algorithms and adaptive intelligent systems designs
Inexact Kleinman-Newton Method for Riccati Equations
SIAM Journal on Matrix Analysis and Applications
Reinforcement learning and adaptive dynamic programming for feedback control
IEEE Circuits and Systems Magazine
Generalized policy iteration for continuous-time systems
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem
Automatica (Journal of IFAC)
IEEE Transactions on Neural Networks
Continuous-Time Adaptive Critics
IEEE Transactions on Neural Networks
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
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This paper mathematically analyzes the integral generalized policy iteration (I-GPI) algorithms applied to a class of continuous-time linear quadratic regulation (LQR) problems with the unknown system matrix A. GPI is the general idea of interacting policy evaluation and policy improvement steps of policy iteration (PI), for computing the optimal policy. We first introduce the update horizon @?, and then show that (i) all of the I-GPI methods with the same @? can be considered equivalent and that (ii) the value function approximated in the policy evaluation step monotonically converges to the exact one as @?-~. This reveals the relation between the computational complexity and the update (or time) horizon of I-GPI as well as between I-PI and I-GPI in the limit @?-~. We also provide and discuss two modes of convergence of I-GPI; I-GPI behaves like PI in one mode, and in the other mode, it performs like value iteration for discrete-time LQR and infinitesimal GPI (@?-0). From these results, a new classification of the integral reinforcement learning is formed with respect to @?. Two matrix inequality conditions for stability, the region of local monotone convergence, and data-driven (adaptive) implementation methods are also provided with detailed discussion. Numerical simulations are carried out for verification and further investigations.