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1. Consider the system that minimizes PI P I=\int_{0}^{1} \frac{u^{2}}{2}+\frac{x_{1}^{2}}{2} d t subject to the constraints \dot{x}_{1}=x_{2} \dot{x}_{2}=-a x_{1}-b x_{2}+u using the State Function of Pontryagin. a.Determine the state function of Pontryagin H. b.Find the optimal input u and the optimal Hº C.Find the matrix A that will yield the governing equations of the form
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