Tutorial: Problem Set 6 - Numerical Methods
J. Jerez
Institut für Automatik
ETH Zürich
Spring Semester 2016
J. Jerez
Tutorial: Problem Set 6 - Numerical Methods
Spring Semester 2016
Example MPC problem
min
u
s.t.
N
−1
X
>
(xk> Qxk + uk> Ruk ) + xN
PxN
k=0
umin ≤ uk ≤ umax
xk+1 = Axk + Buk
xmin ≤ xk ≤ xmax
where
0.7115
A=
0.4345
−0.4345
,
0.8853
0.2173
0
B=
, x0 =
,
0.0573
6
−∞
∞
umin = −5, umax = 5, xmin =
, xmax =
,
−∞
∞
10 0
N = 10, Q =
, R = 1, P = PLQR ,
0 10
and in case of state constraints
xmin,2 = 0 .
J. Jerez
Tutorial: Problem Set 6 - Numerical Methods
Spring Semester 2016
Overview
Develop algorithms in MATLAB
Exercise 1
Exercise 2
Exercise 3
Use software to create production code controllers
Exercise 4
J. Jerez
Tutorial: Problem Set 6 - Numerical Methods
Spring Semester 2016
Exercise 1 - Primal Gradient Method in MATLAB
MATLAB programming exercise
Write a solver based on the primal gradient method
Solve input-constrained MPC problem formulated as a dense QP
Analyze the sensitivity of the solver
Use the lecture notes from this morning
Suggested amount of time to solve the exercise: 45 min
J. Jerez
Tutorial: Problem Set 6 - Numerical Methods
Spring Semester 2016
Exercise 2 - Barrier Interior-Point Method in MATLAB
MATLAB programming exercise
Write a solver based on the primal barrier interior-point method
Test your solver on example random problems and visualize its behaviour
Analyze the sensitivity of the solver
Use the lecture notes from this morning
Suggested amount of time to solve the exercise: 45 min
J. Jerez
Tutorial: Problem Set 6 - Numerical Methods
Spring Semester 2016
Exercise 3 - Dual ADMM in MATLAB
MATLAB programming exercise
Write a solver based on the Alternating Direction Method of Multipliers
Solve input- and state-constrained MPC problems formulated as sparse QPs
Analyze the sensitivity of the solver
Use the lecture notes from this morning
Suggested amount of time to solve the exercise: 60 min
J. Jerez
Tutorial: Problem Set 6 - Numerical Methods
Spring Semester 2016
Exercise 4 - Code Generation for Various Methods
Software tools exercise
Use different interfaces to generate high-performance C code based on the
Primal-Dual Interior-Point Method and ADMM
Solve input- and state-constrained MPC problems formulated as sparse QPs
Compare the performance of different solvers
Use online documentation
C compiler needed
Suggested amount of time to solve the exercise: 45 min
J. Jerez
Tutorial: Problem Set 6 - Numerical Methods
Spring Semester 2016