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An adaptive decentralized control scheme is proposed for real-time control of oscillatory dynamics and overall stability improvement of an interconnected power system. A standard framework of continuous-time (CT) infinite-horizon optimal control paradigm is defined and an extended online actor-critic (AC) algorithm based on policy iteration is used for its solution. The AC structure uses neural networks (NNs) whose weights are updated adaptively. The proof for the convergence of the scheme guarantees the system stability. The unobservable internal states of the synchronous machine are estimated using a numerically stable, swift and relatively accurate decentralized dynamic state estimator (DDSE) based on spherical-radial cubature rule. Applicability of the developed scheme has been demonstrated on a benchmark power system (IEEE 2.2, 16 machine 68 bus system) model via nonlinear time-domain simulations. Multi-processor technology based scaled laboratory setup was used for controller performance validation in real-time. [ABSTRACT FROM AUTHOR]