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This paper presents an approach using a high-performance feedback neural network optimizer based on a new idea of successive approximation, for the control of interconnected multi-reservoir systems. The main advantages of the proposed neural network optimizer over the existing neural network optimization models are that no dual variables, penalty parameters, or Lagrange multipliers are required. It is very simple in structure and has the least number of state variables. In particular, the projected optimization network has better asymptotic stability. For an arbitrarily given initial point, the trajectory of the network converges to an optimal solution of the convex nonlinear programming problem. The proposed neural network optimizer has been tested on a practical system consisting of a set of ten linked reservoirs where the objective is to find out the optimal amounts of water releases from each hydro-plant during each interval in the interconnected system. Also to minimize and distribute uniformly the energy deficit if any, subject to a number of governing constraints such as demand-supply balance, flow balance equation, bounds on reservoir storage, bounds on water releases and coupling constraints.