Question Topics :

Answer: Question : This is possibly not a relevant question to the "Optimal Control" topic. However, the answer of this question is given below: (i) Reactance is real quantity and its unit is Ohm. While solve a ac network problem (excited with sinusoidal sources), we place (a) j operator before inductive reactance (say j2 this indicates "2" is real quantity (reactance of the ideal inductor) that is rotated 90deg. in CCW direction and it is presented in complex plane), (b) -j before capacitive reactance. Details you may refer to any standard book (say,Electrical and Electronic Technology ---> Edward Hughes). My sincere thanks to you. G Ray

Answer: Dear Mr. Prashant Rai, Answer of Q1. (i) Kindly read the objective function as f(x) = 2x1^2 + 4x1x2 + 4x2^2 - 4x1 + 2x2 + 16, (ii)grad(f)=0, gives two simultaneous equations as 4x1 + 4x2 -4 = 0 and 4x1 + 8x2 + 2 = 0. To solve this problem, follow the procedure as given in the example (video Lecture). My sincere thanks to you. G Ray

Answer: Question : This is possibly not a relevant question to the "Optimal Control" topic. However, the answer of this question is given below: (i) Reactance is real quantity and its unit is Ohm. While solve a ac network problem (excited with sinusoidal sources), we place (a) j operator before inductive reactance (say j2 this indicates "2" is real quantity (reactance of the ideal inductor) that is rotated 90deg. in CCW direction and it is presented in complex plane), (b) -j before capacitive reactance. Details you may refer to any standard book (say,Electrical and Electronic Technology ---> Edward Hughes). My sincere thanks to you. G Ray