Hi @jstac , as I commented in #174 , there is a further issue in a Bellman equation in section Linked-Ricatti-equations-for-Markov-LQ-dynamic-programming of lecture markov_jump_lq and this PR corrects that issue:

• $-x' P_i x - \rho_i & = \max_u - [x'R_i x + u' Q_i u + 2 u' W_i x - \beta \sum_j \Pi_{ij}E ((A_i x + B_i u + C_i w)' P_j(A_i x + B_i u + C_i w) x + \rho_j)$ -->> $-x' P_i x - \rho_i & = \max_u - [x'R_i x + u' Q_i u + 2 u' W_i x + \beta \sum_j \Pi_{ij}E ((A_i x + B_i u + C_i w)' P_j(A_i x + B_i u + C_i w) x + \rho_j)$
• i.e., - -->> +

We should correct it because, in the setups above, we have

• $\min_{{u_t}{t=0}^\infty} E \sum{t=0}^{\infty} \beta^t r(x_t, s_t, u_t)$ with $r(x_t, s_t, u_t) = x_t' R_{s_t} x_t + u_t' Q_{s_t} u_t + 2 u_t' W_{s_t} x_t$
• the Bellman equation I modified is just obtained by turning the minimization problem in the above setting into a maximization problem
• so in the Bellman equation, we should only add a minus sign, -, in the front of the objective function from the minimization problem.