e di сe еquation 3-2. A first-order discrete system is described by the x(k + 1) = -0.5x(k) + u(k). The performance measure to be minimized is J = E |x(k)\, k=0 and the admissible states and controls...

Extracted text: e di сe еquation 3-2. A first-order discrete system is described by the x(k + 1) = -0.5x(k) + u(k). The performance measure to be minimized is J = E |x(k)\, k=0 and the admissible states and controls are constrained by -0.2 < x(k)="">< 0.2,="" k="0," 1,="" 2="" -0.1="">< u(k)="">< 0.1,="" k="0," 1.="" (a)="" carry="" out="" by="" hand="" the="" computational="" steps="" required="" to="" determine="" the="" optimal="" control="" law="" by="" using="" dynamic="" programming.="" quantize="" both="" u(k)="" and="" x(k)="" in="" steps="" of="" 0.1="" about="" zero,="" and="" use="" linear="" interpolation.="" (b)="" what="" is="" the="" optimal="" control="" sequence="" for="" an="" initial="" state="" value="" of="">