Optimal Control with Engineering Applications Episode 12 ppsx

... minimizing control of the resulting optimal control problem of Type C.1 and, conversely, when the state feedback law u(t)=k u (x(t),t) is applied, v o (.) is a globally maximizing control of ... the optimal costate λ o (.) is free. Remark: The calculus of variations only requires the local minimization of the Hamiltonian H with respect to the control u and a local maximization o...

Ngày tải lên: 12/08/2014, 16:21

... open-loop optimal controls with the help of Pontryagin’s Minimum Principle, the conversion of optimal open-loop to optimal closed-loop controls, and the direct design of optimal closed-loop optimal controls ... P. Geering Optimal Control with Engineering Applications Contents ix 3.2.3 The LQ Regulator Problem 81 3.2.4 The Time-Invariant Case with Infinite Horizon 83 3.3...

Ngày tải lên: 12/08/2014, 16:21

... nicely reveals that the solution of an optimal control prob- lem always is “as bad” as the considered formulation of the optimal control problem. This optimal control problem lacks any sustainability ... functional. 1.1.1 The Optimal Control Problem We only consider optimal control problems where the initial time t a and the initial state x(t a )=x a are specified. Hence, t...

Ngày tải lên: 12/08/2014, 16:21

... corresponding necessary con- ditions for the optimality of a solution of an optimal control problem. The generalization from constrained static optimization to optimal control is very straightforward, indeed. ... γ 2 v T (t)v(t)  dt is simultaneously minimized with respect to u and maximized with respect to v, when both of the players are allowed to use state-feedback control....

Ngày tải lên: 12/08/2014, 16:21

... x o (·)andλ o (·). • Eliminate locally optimal solutions which are not globally optimal. • If possible, convert the resulting optimal open-loop control u o (t)intoan optimal closed-loop control u o (x o (t),t) ... (i.e., to be optimized). 2.1 Optimal Control Problems with a Fixed Final State In this section, Pontryagin’s Minimum Principle is derived for optimal control p...

Ngày tải lên: 12/08/2014, 16:21

... textbooks on linear optimal control, such as [1], [11], [16], and [25]. 50 2 Optimal Control Theorem D If the control u o :[t a ,t b ] → Ω is optimal (in the non-singular case with λ o 0 =1), then ... > 0. Using the optimal open-loop control law u o (t)=−bλ o (t)=−be −at λ o (0) , 46 2 Optimal Control 2) If the optimal control u o (t)attimet lies in the interior of...

Ngày tải lên: 12/08/2014, 16:21

... functional is J(u)=x 3 (t b ) , 66 2 Optimal Control Theorem 1. The following optimal control problem has a globally optimal solution: Find an unconstrained optimal control u :[t a ,t b ] → R m , such ... R m . — The following optimal control problem has a globally optimal solution: Find an optimal control u :[t a ,t b ] → Ω ⊂ R m , such that the dynamic system ˙x(t)=f...

Ngày tải lên: 12/08/2014, 16:21

... 3 Optimal State Feedback Control Proof 3) Otherwise, combining the optimal solution of the modified antecedent optimal control problem with the succedent part of the solution of the original optimal ... coincides with the succedent part of the optimal solution of the original problem. 2) The optimal solution of the antecedent optimal control problem coincides with the...

Ngày tải lên: 12/08/2014, 16:21

... time-invariant optimal control problem with an infinite horizon for a nonlinear dynamic system with a non-quadratic cost functional, which is structured as follows: Find a time-invariant optimal state ... Hamilton-Jacobi-Bellman Theory 83 3.2.4 The Time-Invariant Case with Infinite Horizon In this section, time-invariant optimal control problems with the uncon- strained contr...

Ngày tải lên: 12/08/2014, 16:21

... 3.3. ✲ ✻ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Ngày tải lên: 12/08/2014, 16:21