A method for monitoring and controlling a hybrid gas turbine system , wherein the hybrid gas turbine system includes at least one gas turbine , to be operated by fuel, at least one electric motor/generator , capable of operating as a generator or as a motor, and a plurality of actuators for their control, and wherein the method is implemented by a control logic unit , characterized in that the method includes the following steps: receiving a set of operating variables x, for detecting the operating states of the gas turbine , and of the electric motor/generator ; receiving a set of external variables w; selecting a set of control variables u, for controlling the operating states of the gas turbine and of the electric motor/generator ; setting a set of optimizing variables y, wherein the values of the optimizing variables y depend on the operating variables x, the control variables u, and the external variables w, and wherein the values of the optimizing variables y have to be adjusted for being optimized; processing one or more of the operating variables x, the control variables u, and the external variables w, by optimizing the values of the optimizing variables y; and generating and transmitting one or more control signals based on the control variables u as obtained by the optimization of the optimizing variables y , to control the actuators of the hybrid gas turbine system ; wherein the optimizing variables y i are function of the operating variables x and/or the control variables u and/or the external variables w by control functions f i ( x, u, w ) , and wherein the optimizing step is carried out minimizing the sum of the module of the optimizing variables y i and the control function f i ( x, u, w ) , according to the following equation: min u ∑ i = 1 N α i ⋅ y i − f i x u w ∑ i = 1 N α i = 1 where α i are weight factors. receiving a set of operating variables x, for detecting the operating states of the gas turbine , and of the electric motor/generator ; receiving a set of external variables w; selecting a set of control variables u, for controlling the operating states of the gas turbine and of the electric motor/generator ; setting a set of optimizing variables y, wherein the values of the optimizing variables y depend on the operating variables x, the control variables u, and the external variables w, and wherein the values of the optimizing variables y have to be adjusted for being optimized; wherein the values of the optimizing variables y depend on the operating variables x, the control variables u, and the external variables w, and wherein the values of the optimizing variables y have to be adjusted for being optimized; processing one or more of the operating variables x, the control variables u, and the external variables w, by optimizing the values of the optimizing variables y; and generating and transmitting one or more control signals based on the control variables u as obtained by the optimization of the optimizing variables y , to control the actuators of the hybrid gas turbine system ; wherein the optimizing variables y i are function of the operating variables x and/or the control variables u and/or the external variables w by control functions f i ( x, u, w ) , and wherein the optimizing step is carried out minimizing the sum of the module of the optimizing variables y i and the control function f i ( x, u, w ) , according to the following equation: min u ∑ i = 1 N α i ⋅ y i − f i x u w ∑ i = 1 N α i = 1 where α i are weight factors. <EOS>