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High energy efficiency for low operating cost of desalination can be obtained from operational optimizations as well as component-wise innovations. This paper is concerned with an energy-efficient operation for reverse osmosis (RO) desalination process involving a joint control of multiple modules. Energy resource considered for desalination is of two types: intermittent solar energy and steady grid energy. With solar energy, the energy efficiency is measured by total permeate production obtained while the solar energy is available. With grid energy, the energy efficiency is measured by the power consumed to get unit permeate production rate. Achieving maximum energy efficiency is equivalent to solving constrained optimization. For the constrained optimization, obligatory constraints are given by the permissible ranges of trans-membrane pressure on RO membrane and total dissolved solids of permeate, and optional constraint is given by the permissible range of permeate production rate. Constraints as well as the objective function are modeled by the empirical second order equations in terms of control variables of multiple modules. Jointly optimal values of the control variables are found by the sequential quadratic programming. Experimental results obtained by the jointly optimal control demonstrate superior performances as compared to those acquired by marginally optimal control schemes. [ABSTRACT FROM AUTHOR]