The study of dynamic systems without resorting to or any knowledge of differential equations is known as the direct method. In this method, algebraic equations of motion characterize the system dynamics. The algebraic optimal control laws can be derived in an explicit form for general nonlinear time-varying and time-invariant systems by minimizing an algebraic performance measure. The essence of the approach is based on using assumed-time-modes expansions of generalized coordinates and inputs in conjunction with the variational work-energy principles that govern the physical system. The resulting algebraic optimal control laws are in the form of digitally implementable generalized algebraic state feedback. However, to implement these control laws an algebraic state estimator must be designed. The development of such an estimator is proposed by utilizing neural networks within a hybrid algebraic equation of motion for general nonlinear systems. To prove the concept, numerical simulations are validated on linear systems in the deterministic, noisy and modelling uncertainty cases and a nonlinear flexible structure.