1.
Introduction
Classical Optimal Control
2.
Bellman Principle
2.1.
Bellman Equation
2.2.
Hamilton-Jacobi-Bellman Equation
3.
Linear-Quadratic Regulator
3.1.
Discrete-time
3.2.
Continuous-time
Numerical Optimization
4.
Lagrangian Duality
5.
Karush-Kuhn-Tucker Conditions
6.
Linear Programming
6.1.
Examples
7.
Quadratic Programming
7.1.
Examples
8.
Non-Linear Programming
8.1.
Examples
Model Predictive Control
9.
Linear-Quadratic MPC
9.1.
Direct
9.2.
Indirect
9.3.
Examples
Modeling
10.
State-Space Representation of Mechanical Systems
10.1.
Cart-Pole
10.2.
Bi-Rotor
11.
Controllability of LTI systems
Software
12.
Optimization Modeling Languages
13.
Solvers
Bibliography
Light
Rust
Coal
Navy
Ayu
Optimal and Predictive Control
Indirect Linear-Quadratic MPC
{
u
k
}
0
N
min
s.t.
x
k
⊤
Q
x
k
+
u
k
⊤
R
u
k
u
m
i
n
≤
u
k
≤
u
m
a
x
,
where
x
k
=
A
k
x
0
+
i
=
0
∑
k
−
1
A
k
−
1
−
i
B
u
i
,
k
=
0
,
…
,
N
+
1