4. Consider a linear-quadratic regular in the context of Section 13.4, but with the following variations: 0 The state dynamics is now st+1 = c + Ast +But, t = 0,1, .. .,N 1. o The cost function is now Nl E (St atlTQ(St at) + utTRut + (SN aNlTleN aN): t=0 Where at is a given deterministic trajectory. Intuitively, the problem is to nd inu ence the system such that st is close to at. Extend the computations in Section 13.4 to obtain the recursion of the value function via Bellman's equation. Also derive the optimal control for each stage