Skip to content

Commit d53e583

Browse files
jbcaillaujbcaillau
committed
jlesc17
1 parent 1531341 commit d53e583

1 file changed

Lines changed: 324 additions & 10 deletions

File tree

‎docs/src/jlesc17.md‎

Lines changed: 324 additions & 10 deletions
Original file line numberDiff line numberDiff line change
@@ -14,11 +14,15 @@
1414

1515
- Nonlinear optimal control of ODEs:
1616

17-
$$ g(x(t_0),x(t_f)) + \int_{t_0}^{t_f} f^0(x(t), u(t))\, \mathrm{d}t \to \min $$
17+
```math
18+
g(x(t_0),x(t_f)) + \int_{t_0}^{t_f} f^0(x(t), u(t))\, \mathrm{d}t \to \min
19+
```
1820

1921
subject to
2022

21-
$$ \dot{x}(t) = f(x(t), u(t)),\quad t \in [t_0, t_f] $$
23+
```math
24+
\dot{x}(t) = f(x(t), u(t)),\quad t \in [t_0, t_f]
25+
```
2226

2327
plus boundary, control and state constraints
2428

@@ -33,37 +37,347 @@ plus boundary, control and state constraints
3337

3438
- Discretising an OCP into an NLP: $h_i := t_{i+1}-t_i$,
3539

36-
$$ g(X_0,X_N) + \sum_{i=0}^{N} h_i f^0(X_i,U_i) \to \min $$
40+
```math
41+
g(X_0,X_N) + \sum_{i=0}^{N} h_i f^0(X_i,U_i) \to \min
42+
```
3743

3844
subject to
3945

40-
$$ X_{i+1} - X_i - h_i f(X_i, U_i) = 0,\quad i = 0,\dots,N-1 $$
46+
```math
47+
X_{i+1} - X_i - h_i f(X_i, U_i) = 0,\quad i = 0,\dots,N-1
48+
```
4149

4250
plus other constraints on $X := (X_i)_{i=0,N}$ and $U := (U_i)_{i=0,N}$ such as boundary and path (state and / or control) constraints :
4351

44-
$$ b(t_0, X_0, t_N, X_N) = 0 $$
52+
```math
53+
b(t_0, X_0, t_N, X_N) = 0
54+
```
4555

46-
$$ g(t_i, X_i, U_i) = 0,\quad i = 0,\dots,N $$
56+
```math
57+
g(t_i, X_i, U_i) = 0,\quad i = 0,\dots,N
58+
```
4759

4860
- SIMD parallelism ($f0$, $f$, $g$) + sparsity: Kernels for GPU ([KernelAbstraction.jl](https://juliagpu.github.io/KernelAbstractions.jl/stable/)) and sparse linear algebra ([CUDSS.jl](https://github.com/exanauts/CUDSS.jl))
4961
- Modelling and optimising for GPU: [ExaModels.jl](https://exanauts.github.io/ExaModels.jl/dev/guide) + [MadNLP.jl](https://madnlp.github.io/MadNLP.jl), with **built-in AD**
5062
- [Simple example, DSL](@ref tutorial-double-integrator-energy)
5163
- Compile into an ExaModel (one pass compiler, [syntax + semantics](https://github.com/control-toolbox/CTParser.jl/blob/20c6be5c953587fef10b054a95f9dc8c66b90577/src/onepass.jl#L145))
52-
- Simple example, generated code
64+
65+
66+
```@raw html
67+
<details><summary>Simple example, generated code</summary>
68+
```
69+
5370
```julia
54-
XXXX
71+
begin
72+
#= /data/caillau/CTParser.jl/src/onepass.jl:1003 =#
73+
function (; scheme = :trapezoidal, grid_size = 200, backend = nothing, init = (0.1, 0.1, 0.1), base_type = Float64)
74+
#= /data/caillau/CTParser.jl/src/onepass.jl:1003 =#
75+
#= /data/caillau/CTParser.jl/src/onepass.jl:1004 =#
76+
LineNumberNode(0, "box constraints: variable")
77+
#= /data/caillau/CTParser.jl/src/onepass.jl:1005 =#
78+
begin
79+
LineNumberNode(0, "box constraints: state")
80+
begin
81+
var"##235" = -Inf * ones(3)
82+
#= /data/caillau/CTParser.jl/src/onepass.jl:461 =#
83+
var"##236" = Inf * ones(3)
84+
end
85+
end
86+
#= /data/caillau/CTParser.jl/src/onepass.jl:1006 =#
87+
begin
88+
LineNumberNode(0, "box constraints: control")
89+
begin
90+
var"##237" = -Inf * ones(1)
91+
#= /data/caillau/CTParser.jl/src/onepass.jl:512 =#
92+
var"##238" = Inf * ones(1)
93+
end
94+
end
95+
#= /data/caillau/CTParser.jl/src/onepass.jl:1007 =#
96+
var"##230" = ExaModels.ExaCore(base_type; backend = backend)
97+
#= /data/caillau/CTParser.jl/src/onepass.jl:1008 =#
98+
begin
99+
#= /data/caillau/CTParser.jl/test/test_onepass_exa.jl:23 =#
100+
var"##232" = begin
101+
#= /data/caillau/CTParser.jl/src/onepass.jl:111 =#
102+
local ex
103+
#= /data/caillau/CTParser.jl/src/onepass.jl:112 =#
104+
try
105+
#= /data/caillau/CTParser.jl/src/onepass.jl:113 =#
106+
(1 - 0) / grid_size
107+
catch ex
108+
#= /data/caillau/CTParser.jl/src/onepass.jl:115 =#
109+
println("Line ", 1, ": ", "(t ∈ [0, 1], time)")
110+
#= /data/caillau/CTParser.jl/src/onepass.jl:116 =#
111+
throw(ex)
112+
end
113+
end
114+
#= /data/caillau/CTParser.jl/test/test_onepass_exa.jl:24 =#
115+
x = begin
116+
#= /data/caillau/CTParser.jl/src/onepass.jl:111 =#
117+
local ex
118+
#= /data/caillau/CTParser.jl/src/onepass.jl:112 =#
119+
try
120+
#= /data/caillau/CTParser.jl/src/onepass.jl:113 =#
121+
ExaModels.variable(var"##230", 3, 0:grid_size; lvar = [var"##235"[i] for (i, j) = Base.product(1:3, 0:grid_size)], uvar = [var"##236"[i] for (i, j) = Base.product(1:3, 0:grid_size)], start = init[2])
122+
catch ex
123+
#= /data/caillau/CTParser.jl/src/onepass.jl:115 =#
124+
println("Line ", 2, ": ", "(x ∈ R ^ 3, state)")
125+
#= /data/caillau/CTParser.jl/src/onepass.jl:116 =#
126+
throw(ex)
127+
end
128+
end
129+
#= /data/caillau/CTParser.jl/test/test_onepass_exa.jl:25 =#
130+
var"u##239" = begin
131+
#= /data/caillau/CTParser.jl/src/onepass.jl:111 =#
132+
local ex
133+
#= /data/caillau/CTParser.jl/src/onepass.jl:112 =#
134+
try
135+
#= /data/caillau/CTParser.jl/src/onepass.jl:113 =#
136+
ExaModels.variable(var"##230", 1, 0:grid_size; lvar = [var"##237"[i] for (i, j) = Base.product(1:1, 0:grid_size)], uvar = [var"##238"[i] for (i, j) = Base.product(1:1, 0:grid_size)], start = init[3])
137+
catch ex
138+
#= /data/caillau/CTParser.jl/src/onepass.jl:115 =#
139+
println("Line ", 3, ": ", "(u ∈ R, control)")
140+
#= /data/caillau/CTParser.jl/src/onepass.jl:116 =#
141+
throw(ex)
142+
end
143+
end
144+
#= /data/caillau/CTParser.jl/test/test_onepass_exa.jl:26 =#
145+
begin
146+
#= /data/caillau/CTParser.jl/src/onepass.jl:111 =#
147+
local ex
148+
#= /data/caillau/CTParser.jl/src/onepass.jl:112 =#
149+
try
150+
#= /data/caillau/CTParser.jl/src/onepass.jl:113 =#
151+
ExaModels.constraint(var"##230", (x[i, 0] for i = 1:3); lcon = [-1, 0, 0], ucon = [-1, 0, 0])
152+
catch ex
153+
#= /data/caillau/CTParser.jl/src/onepass.jl:115 =#
154+
println("Line ", 4, ": ", "x(0) == [-1, 0, 0]")
155+
#= /data/caillau/CTParser.jl/src/onepass.jl:116 =#
156+
throw(ex)
157+
end
158+
end
159+
#= /data/caillau/CTParser.jl/test/test_onepass_exa.jl:27 =#
160+
begin
161+
#= /data/caillau/CTParser.jl/src/onepass.jl:111 =#
162+
local ex
163+
#= /data/caillau/CTParser.jl/src/onepass.jl:112 =#
164+
try
165+
#= /data/caillau/CTParser.jl/src/onepass.jl:113 =#
166+
ExaModels.constraint(var"##230", (x[i, grid_size] for i = 1:2); lcon = [0, 0], ucon = [0, 0])
167+
catch ex
168+
#= /data/caillau/CTParser.jl/src/onepass.jl:115 =#
169+
println("Line ", 5, ": ", "(x[1:2])(1) == [0, 0]")
170+
#= /data/caillau/CTParser.jl/src/onepass.jl:116 =#
171+
throw(ex)
172+
end
173+
end
174+
#= /data/caillau/CTParser.jl/test/test_onepass_exa.jl:28 =#
175+
begin
176+
#= /data/caillau/CTParser.jl/src/onepass.jl:111 =#
177+
local ex
178+
#= /data/caillau/CTParser.jl/src/onepass.jl:112 =#
179+
try
180+
#= /data/caillau/CTParser.jl/src/onepass.jl:113 =#
181+
begin
182+
#= /data/caillau/CTParser.jl/src/onepass.jl:735 =#
183+
if scheme == :trapezoidal
184+
#= /data/caillau/CTParser.jl/src/onepass.jl:736 =#
185+
ExaModels.constraint(var"##230", ((x[1, j + 1] - x[1, j]) - (var"##232" * (x[2, j] + x[2, j + 1])) / 2 for j = 0:grid_size - 1))
186+
elseif #= /data/caillau/CTParser.jl/src/onepass.jl:737 =# scheme == :euler
187+
#= /data/caillau/CTParser.jl/src/onepass.jl:738 =#
188+
ExaModels.constraint(var"##230", ((x[1, j + 1] - x[1, j]) - var"##232" * x[2, j] for j = 0:grid_size - 1))
189+
elseif #= /data/caillau/CTParser.jl/src/onepass.jl:739 =# scheme == :euler_b
190+
#= /data/caillau/CTParser.jl/src/onepass.jl:740 =#
191+
ExaModels.constraint(var"##230", ((x[1, j + 1] - x[1, j]) - var"##232" * x[2, j + 1] for j = 0:grid_size - 1))
192+
else
193+
#= /data/caillau/CTParser.jl/src/onepass.jl:742 =#
194+
throw("unknown numerical scheme")
195+
end
196+
end
197+
catch ex
198+
#= /data/caillau/CTParser.jl/src/onepass.jl:115 =#
199+
println("Line ", 6, ": ", "(∂(x₁))(t) == x₂(t)")
200+
#= /data/caillau/CTParser.jl/src/onepass.jl:116 =#
201+
throw(ex)
202+
end
203+
end
204+
#= /data/caillau/CTParser.jl/test/test_onepass_exa.jl:29 =#
205+
begin
206+
#= /data/caillau/CTParser.jl/src/onepass.jl:111 =#
207+
local ex
208+
#= /data/caillau/CTParser.jl/src/onepass.jl:112 =#
209+
try
210+
#= /data/caillau/CTParser.jl/src/onepass.jl:113 =#
211+
begin
212+
#= /data/caillau/CTParser.jl/src/onepass.jl:735 =#
213+
if scheme == :trapezoidal
214+
#= /data/caillau/CTParser.jl/src/onepass.jl:736 =#
215+
ExaModels.constraint(var"##230", ((x[2, j + 1] - x[2, j]) - (var"##232" * (var"u##239"[1, j] + var"u##239"[1, j + 1])) / 2 for j = 0:grid_size - 1))
216+
elseif #= /data/caillau/CTParser.jl/src/onepass.jl:737 =# scheme == :euler
217+
#= /data/caillau/CTParser.jl/src/onepass.jl:738 =#
218+
ExaModels.constraint(var"##230", ((x[2, j + 1] - x[2, j]) - var"##232" * var"u##239"[1, j] for j = 0:grid_size - 1))
219+
elseif #= /data/caillau/CTParser.jl/src/onepass.jl:739 =# scheme == :euler_b
220+
#= /data/caillau/CTParser.jl/src/onepass.jl:740 =#
221+
ExaModels.constraint(var"##230", ((x[2, j + 1] - x[2, j]) - var"##232" * var"u##239"[1, j + 1] for j = 0:grid_size - 1))
222+
else
223+
#= /data/caillau/CTParser.jl/src/onepass.jl:742 =#
224+
throw("unknown numerical scheme")
225+
end
226+
end
227+
catch ex
228+
#= /data/caillau/CTParser.jl/src/onepass.jl:115 =#
229+
println("Line ", 7, ": ", "(∂(x₂))(t) == u(t)")
230+
#= /data/caillau/CTParser.jl/src/onepass.jl:116 =#
231+
throw(ex)
232+
end
233+
end
234+
#= /data/caillau/CTParser.jl/test/test_onepass_exa.jl:30 =#
235+
begin
236+
#= /data/caillau/CTParser.jl/src/onepass.jl:111 =#
237+
local ex
238+
#= /data/caillau/CTParser.jl/src/onepass.jl:112 =#
239+
try
240+
#= /data/caillau/CTParser.jl/src/onepass.jl:113 =#
241+
begin
242+
#= /data/caillau/CTParser.jl/src/onepass.jl:735 =#
243+
if scheme == :trapezoidal
244+
#= /data/caillau/CTParser.jl/src/onepass.jl:736 =#
245+
ExaModels.constraint(var"##230", ((x[3, j + 1] - x[3, j]) - (var"##232" * (0.5 * var"u##239"[1, j] ^ 2 + 0.5 * var"u##239"[1, j + 1] ^ 2)) / 2 for j = 0:grid_size - 1))
246+
elseif #= /data/caillau/CTParser.jl/src/onepass.jl:737 =# scheme == :euler
247+
#= /data/caillau/CTParser.jl/src/onepass.jl:738 =#
248+
ExaModels.constraint(var"##230", ((x[3, j + 1] - x[3, j]) - var"##232" * (0.5 * var"u##239"[1, j] ^ 2) for j = 0:grid_size - 1))
249+
elseif #= /data/caillau/CTParser.jl/src/onepass.jl:739 =# scheme == :euler_b
250+
#= /data/caillau/CTParser.jl/src/onepass.jl:740 =#
251+
ExaModels.constraint(var"##230", ((x[3, j + 1] - x[3, j]) - var"##232" * (0.5 * var"u##239"[1, j + 1] ^ 2) for j = 0:grid_size - 1))
252+
else
253+
#= /data/caillau/CTParser.jl/src/onepass.jl:742 =#
254+
throw("unknown numerical scheme")
255+
end
256+
end
257+
catch ex
258+
#= /data/caillau/CTParser.jl/src/onepass.jl:115 =#
259+
println("Line ", 8, ": ", "(∂(x₃))(t) == 0.5 * u(t) ^ 2")
260+
#= /data/caillau/CTParser.jl/src/onepass.jl:116 =#
261+
throw(ex)
262+
end
263+
end
264+
#= /data/caillau/CTParser.jl/test/test_onepass_exa.jl:31 =#
265+
begin
266+
#= /data/caillau/CTParser.jl/src/onepass.jl:111 =#
267+
local ex
268+
#= /data/caillau/CTParser.jl/src/onepass.jl:112 =#
269+
try
270+
#= /data/caillau/CTParser.jl/src/onepass.jl:113 =#
271+
ExaModels.objective(var"##230", x[3, grid_size])
272+
catch ex
273+
#= /data/caillau/CTParser.jl/src/onepass.jl:115 =#
274+
println("Line ", 9, ": ", "x₃(1) → min")
275+
#= /data/caillau/CTParser.jl/src/onepass.jl:116 =#
276+
throw(ex)
277+
end
278+
end
279+
end
280+
#= /data/caillau/CTParser.jl/src/onepass.jl:1009 =#
281+
begin
282+
#= /data/caillau/CTParser.jl/src/onepass.jl:994 =#
283+
!(isempty([1, 2, 3])) || throw(CTBase.ParsingError("dynamics not defined"))
284+
#= /data/caillau/CTParser.jl/src/onepass.jl:995 =#
285+
sort([1, 2, 3]) == 1:3 || throw(CTBase.ParsingError("some coordinates of dynamics undefined"))
286+
end
287+
#= /data/caillau/CTParser.jl/src/onepass.jl:1010 =#
288+
return ExaModels.ExaModel(var"##230")
289+
end
290+
end
55291
```
292+
293+
```@raw html
294+
</details>
295+
```
296+
56297
- **Remark.** Automated scalarisation of (linear) range constraints
57298
```julia
58299
XXXX
59300
```
60301
- Solving (MadNLP + CUDSS)
61302
```julia
62-
XXXX
303+
This is MadNLP version v0.8.7, running with cuDSS v0.4.0
304+
305+
Number of nonzeros in constraint Jacobian............: 12005
306+
Number of nonzeros in Lagrangian Hessian.............: 9000
307+
308+
Total number of variables............................: 4004
309+
variables with only lower bounds: 0
310+
variables with lower and upper bounds: 0
311+
variables with only upper bounds: 0
312+
Total number of equality constraints.................: 3005
313+
Total number of inequality constraints...............: 0
314+
inequality constraints with only lower bounds: 0
315+
inequality constraints with lower and upper bounds: 0
316+
inequality constraints with only upper bounds: 0
317+
318+
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
319+
0 1.0000000e-01 1.10e+00 1.00e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
320+
1 1.0001760e-01 1.10e+00 3.84e-03 -1.0 6.88e+02 -4.0 1.00e+00 2.00e-07h 2
321+
2 -5.2365072e-03 1.89e-02 1.79e-07 -1.0 6.16e+00 -4.5 1.00e+00 1.00e+00h 1
322+
3 5.9939627e+00 2.28e-03 1.66e-04 -3.8 6.00e+00 -5.0 9.99e-01 1.00e+00h 1
323+
4 5.9996194e+00 3.00e-06 1.05e-06 -3.8 7.77e-02 - 1.00e+00 1.00e+00h 1
324+
325+
Number of Iterations....: 4
326+
327+
(scaled) (unscaled)
328+
Objective...............: 5.9996194116826898e+00 5.9996194116826898e+00
329+
Dual infeasibility......: 1.0504883830561350e-06 1.0504883830561350e-06
330+
Constraint violation....: 2.9972943093481582e-06 2.9972943093481582e-06
331+
Complementarity.........: 2.0007458990898193e-06 2.0007458990898193e-06
332+
Overall NLP error.......: 2.9972943093481582e-06 2.9972943093481582e-06
333+
334+
Number of objective function evaluations = 6
335+
Number of objective gradient evaluations = 5
336+
Number of constraint evaluations = 6
337+
Number of constraint Jacobian evaluations = 5
338+
Number of Lagrangian Hessian evaluations = 4
339+
Total wall-clock secs in solver (w/o fun. eval./lin. alg.) = 0.423
340+
Total wall-clock secs in linear solver = 0.055
341+
Total wall-clock secs in NLP function evaluations = 0.005
342+
Total wall-clock secs = 0.483
63343
```
64344
- [Goddard problem](https://control-toolbox.org/Tutorials.jl/stable/tutorial-goddard/)
65345
```julia
66-
XXXX
346+
This is MadNLP version v0.8.4, running with cuDSS v0.3.0
347+
348+
Number of nonzeros in constraint Jacobian............: 135017
349+
Number of nonzeros in Lagrangian Hessian.............: 130008
350+
351+
Total number of variables............................: 35008
352+
variables with only lower bounds: 0
353+
variables with lower and upper bounds: 0
354+
variables with only upper bounds: 0
355+
Total number of equality constraints.................: 30007
356+
Total number of inequality constraints...............: 15004
357+
inequality constraints with only lower bounds: 5002
358+
inequality constraints with lower and upper bounds: 10002
359+
inequality constraints with only upper bounds: 0
360+
361+
[...]
362+
363+
Number of Iterations....: 35
364+
365+
(scaled) (unscaled)
366+
Objective...............: -1.0142336978192805e+00 -1.0142336978192805e+00
367+
Dual infeasibility......: 4.7384318691001681e-13 4.7384318691001681e-13
368+
Constraint violation....: 1.4068322357215250e-09 1.4068322357215250e-09
369+
Complementarity.........: 9.0909295306344959e-09 9.0909295306344959e-09
370+
Overall NLP error.......: 9.0909295306344959e-09 9.0909295306344959e-09
371+
372+
Number of objective function evaluations = 36
373+
Number of objective gradient evaluations = 36
374+
Number of constraint evaluations = 36
375+
Number of constraint Jacobian evaluations = 36
376+
Number of Lagrangian Hessian evaluations = 35
377+
Total wall-clock secs in solver (w/o fun. eval./lin. alg.) = 0.911
378+
Total wall-clock secs in linear solver = 0.227
379+
Total wall-clock secs in NLP function evaluations = 0.059
380+
Total wall-clock secs = 1.198
67381
```
68382

69383
## Wrap up

0 commit comments

Comments
 (0)