Optimal Control with Engineering Applications Episode 8 potx
Hans P. Geering Optimal Control with Engineering Applications pot
... Exercises 22
2 Optimal Control 23
2.1 Optimal Control Problems with a Fixed Final State 24
2.1.1TheOptimalControlProblemofTypeA 24
2.1.2Pontryagin’sMinimumPrinciple 25
2.1.3Proof 25
2.1.4 Time -Optimal, ... has been solved in [15].
Hans P. Geering, Ph.D.
Professor of Automatic Control and Mechatronics
Measurement and Control Laboratory
Department of Mechanical and Process...
Robust Control Theory and Applications Part 8 potx
... optimal problem
288
Robust Control, Theory and Applications
Advances in Reinforcement Learning
282
7. References
Bhattacharyya S. P., Chapellat H., and Keel L. H.(1994). Robust Control, The ... actuator effectiveness. IET Control Theory and Applications, 3(6):772– 788 ,
June 2009.
305
Passive Fault Tolerant Control
Simple Robust Normalized PI Control for Cont...
Optimal Control with Engineering Applications With 12 Figures Hans P. Geering potx
... game
problem:
State variables: x
1
and x
2
.
Control variables: u ∈ [−1, +1] and v ∈ [−π, π].
Hans P. Geering
Optimal Control
with Engineering
Applications
With 12 Figures
123
2 List of Symbols
Integers
i, ... 113
Solutions to Exercises 117
References 129
Index 131
Hans P. Geering
Optimal Control with Engineering Applications
26 2 Optimal Cont...
Optimal Control with Engineering Applications Hans P. Geering pptx
... been solved in [15].
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...
Optimal Control with Engineering Applications Episode 1 pps
... 92
3.3.4LQQSpeedControl 96
3.4 Exercises 99
4 Differential Games 10 3
4 .1 Theory 10 3
4 .1. 1 Problem Statement 10 4
4 .1. 2TheNash-PontryaginMinimaxPrinciple 10 5
4 .1. 3Proof 10 6
4 .1. 4Hamilton-Jacobi-IsaacsTheory 10 7
4.2 ... TheLQDifferentialGameProblem 10 9
4.2 .1 Solved with the Nash-Pontryagin Minimax Principle 10 9
4.2.2 Solved with the Hamilton-Jacobi-Isaacs Theory . ....
Optimal Control with Engineering Applications Episode 2 potx
... are fixed.
2) This problem 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 is often named “time -optimal control of
the double integrator”. It is analyzed in detail in Chapter 2. 1.4.
Problem 2: Time -optimal, horizontal motion of a mass with vi...
Optimal Control with Engineering Applications Episode 3 pdf
... 0andλ
2
=0
∂F
∂λ
3
= x
1
+ x
2
− 4
= 0 and λ
3
≥ 0
< 0andλ
3
=0
The optimal solution is:
x
o
1
=1
x
o
2
=1.5
λ
o
1
=0.5
λ
o
2
=3
λ
o
3
=0.
The third constraint is inactive.
14 1 Introduction
control ... corresponding necessary con-
ditions for the optimality of a solution of an optimal control problem. The
generalization from constrained static optimization to optimal...
Optimal Control with Engineering Applications Episode 4 ppt
... Introduction
1 .4 Exercises
1. In all of the optimal control problems stated in this chapter, the control
constraint Ω is required to be a time-invariant set in the control space
R
m
.
For the control ... equality
constraints x − y = 2 and x
2
+ y
2
=4.
2 Optimal Control
In this chapter, a set of necessary conditions for the optimality of a solution of
an optimal control...
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 interi...
Optimal Control with Engineering Applications Episode 8 potx
... — Thus, Theorem 2 covers our
time -optimal and fuel -optimal control problems as well.
2 .8 Non-Scalar-Valued Cost Functional 67
2 .8 Optimal Control Problems
with a Non-Scalar-Valued Cost Functional
Up ... 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 optima...
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 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 11 ppt
... −1012345
−150
−100
−50
50
100
150
Fig. 3.3. Approximatively optimal controller for a =3, q = 100.
92 3 Optimal State Feedback Control
3.3.3 Controller with a Progressive Characteristic
For a linear time-invariant ... following optimal control problem of Type B.1 where there
is an additional state constraint x(t
1
)∈ S
1
⊂R
n
at the fixed time t
1
within
thetimeinterval[t
a
,t
b
]:...
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