Cubic performance index. Let x_k+1 = ax_k + bu_k where x_k and u_k are scalars, and J = 1/3 s_N x_N^3 + 1/3 sigma_k=0^N-1 (qx_k^3 + ru_k^3) Write state and costate equations and stationarity condition. When can we solve for u_k? Under this condition, eliminate u_k from the state equation. Solve the open-loop control problem (i.e., x_N fixed, s_N 0, q = 0) Cubic performance index. Let x_k+1 = ax_k + bu_k where x_k and u_k are scalars, and J = 1/3 s_N x_N^3 + 1/3 sigma_k=0^N-1 (qx_k^3 + ru_k^3) Write state and costate equations and stationarity condition. When can we solve for u_k? Under this condition, eliminate u_k from the state equation. Solve the open-loop control problem (i.e., x_N fixed, s_N 0, q = 0)