Consider the general optimal control problem: V(xo) : min u(t)eRm te[to,tf] s.t. for some initial condition XO E R and f

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Consider The General Optimal Control Problem V Xo Min U T Erm Te To Tf S T For Some Initial Condition Xo E R And F 1 (157.88 KiB) Viewed 34 times

Consider the general optimal control problem: V(xo) : min u(t)eRm te[to,tf] s.t. for some initial condition XO E R and free final time tf. a) To obtain a solution u*(.) to the given problem (OCP) one can use the Ha- milton formalism or the Dynamic Programming principle. Briefly state the difference in philosophy between both approaches in deriving the optimality conditions, considering the optimal state x* (.) and V. b) tf Sot 10 c) l(x(t), u(t)) dt + F(x(tf)) x(t)=f(x(t), u(t)), x(to) = xo, State two properties of the Hamiltonian H along an optimal trajectory set {x* (t), u* (t), λ* (t)} at any t = [to, tf] associated with the specifications of (OCP). Vo(xo) : min u(t)em te[t0,00) State a requirement on the terminal cost function in (OCP) for the minimizing sequence u*(-), [to, tf], to also be optimal on the first time interval [to, tf] of the infinite horizon problem S l(x(t), u(t)) dt s.t. x(t)=f(x(t), u(t)), (OCP) d) Why are continuous-time problems referred to as blems? x(to) = xo. infinite dimensional pro- e) Explain Bellman's Principle of Optimality using the ackwards dynamic pro- gramming recursion! State two advantages ADP has over MPC! (1) ensure stability (2) guarantee recursive feasibility (3) satisfy input constraints (4) achieve global optimality f) For which of the following objectives can terminal costs be utilized in discrete- time optimal control problems?