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Abstract
Microalgae are the most primitive plant-sized cellular organisms commonly known as phytoplankton. The habitat of its life is in waters or humid places. This organism is a primary producer of water that has any capability to photosynthesis like any other high-level plants. This study examines mathematically the optimal control of light intensity and liquid waste nutrition in microalgae growth. Growth liter is done by setting the intensity of light in the process of glucose formation and nutrition tofu liquid waste, tapioca, industry, and households as the additional nutrients of microalgae. The Pontryagin maximun principles is used to determine the optimal control solution. The solution is solved from the state and co-state equation that stationery evaluated using the indexed performance maks 𝐽[𝑢1 + 𝑢2 ] = ∫ 𝐺(𝑡) − 𝑡𝑓 𝑡0 𝑆(𝑡) − 1 2 𝑢1 (𝑡) 2 − 1 2 𝑢2 (𝑡) 2𝑑𝑡 with the stationer condition that gives the optimal control 𝑢1 ∗ = 𝛾2𝛼2𝑄𝐵 and 𝑢2 ∗ = −𝛾5𝜌1𝑆. The results shows that before the optimal control of light intensity and nutrition of liquid waste is applied, the concentration of microalgae biomass becomes 5.915 g / liter on the 20th day stayed at the 105th day. The lipid quota with an initial value of 0.6 g/liter will decrease to 0.2 g / liter at 4th day which is the equilibrium point. Optimal control of the regulation of light intensity of 2-9 klux and liquid waste nutrition provided a significant increase in the amount of microalgae biomass and lipid quota, with the regulation of light intensity of 2- 9 klux and tofu liquid waste nutrition which gave the largest increase in the amount of microalgae biomass and lipid quota