Optimal Control with Engineering Applications Episode 10 pot
Optimal Control with Engineering Applications Episode 10 pot
... 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...
Optimal Control with Engineering Applications Episode 2 potx
... 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...
Optimal Control with Engineering Applications Episode 8 potx
... 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...
Optimal Control with Engineering Applications Episode 12 ppsx
... problem with variable separation, the distinction
between Subproblem 1 and Subproblem 2 is no longer necessary. As in
optimal control problems, optimal open-loop strategies are equivalent to
optimal ... 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 maxi...
Optimal Control with Engineering Applications Episode 1 pps
... 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...
Optimal Control with Engineering Applications Episode 3 pdf
... 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. ... state
x
1
(0) = x
10
x
2
(0) = x
20
to a final state with
x
2
1
(t
b
)+x
2
2
(t
b
) ≤ d
2
and such that the cost functional
J(u, v)=t
b
is minimized with respect to u(.)...
Optimal Control with Engineering Applications Episode 4 ppt
... 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...
Optimal Control with Engineering Applications Episode 6 pdf
... 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...
Optimal Control with Engineering Applications Episode 9 ppt
... 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...
Optimal Control with Engineering Applications Episode 11 ppt
... 3.3.
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