In this paper, the minimisation of an unknown but measurable cost function with uncertain dynamics is considered. The drift term of the uncertain dynamical system and the gradient of the objective function are treated as unknown time-varying parameters. A novel estimation scheme based on almost invariant manifolds is proposed to estimate the time-varying parameters. A direct gradient-based adaptive extremum-seeking controller is designed to solve the uncertain optimisation problem. This approach is shown to improve the transient performance of real-time optimisation control systems.