Tang, D.Chen, L.Tian, Z.Hu, E.2020-05-202020-05-202021International Journal of Control, 2021; 94(5):1321-13330020-71791366-5820http://hdl.handle.net/2440/124816Published online: 11 Aug 2019.This study proposes a modified value-function-approximation (MVFA) and investi-gates its use under a single-critic configuration based on neural networks (NNs) for synchronous policy iteration (SPI) to deliver compact implementation of optimal control online synthesis for control-affine continuous-time nonlinear systems. Exist-ing single-critic algorithms require stabilising critic tuning laws while eliminating actor tuning. This paper thus studies alternative single-critic realisation aiming to relax the needs for stabilising mechanisms in the critic tuning law. Optimal control laws are determined from the Hamilton-Jacobi-Bellman equality by solving for the associated value function via SPI in a single-critic configuration. Different from other existing single-critic methods, an MVFA is proposed to deal with closed-loop stabil-ity during online learning. Gradient-descent tuning is employed to adjust the critic NN parameters in the interests of not complicating the problem. Parameters conver-gence and closed-loop stability are examined. The proposed MVFA-based approach yields an alternative single-critic SPI method with uniformly ultimately bounded closed-loop stability during online learning without the need for stabilising mecha-nisms in the critic tuning law. The proposed approach is verified via simulations.en© 2019 Informa UK Limited, trading as Taylor & Francis GroupAdaptive dynamic programming; approximate dynamic programming; neural networks; nonlinear control; optimal control; policy iterationJournal article003013347010.1080/00207179.2019.16488740004811623000012-s2.0-85070798623485418Tang, D. [0000-0002-7143-0441]Chen, L. [0000-0002-2269-2912]Tian, Z. [0000-0001-9847-6004]Hu, E. [0000-0002-7390-0961]