added: `MultipleShooting` support for the `MovingHorizonEstimator` 🍾 by franckgaga · Pull Request #411 · JuliaControl/ModelPredictiveControl.jl

franckgaga · 2026-07-31T12:52:11Z

This is a humongous PR to introduce the support of a MultipleShooting transcription in the MovingHorizonEstimator, both for LinModel (QP) and NonLinModel (NLP). There is a new transcription keyword argument that supports only SingleShooting and MultipleShooting for now. This is a huge step toward #332 since the OrthogonalCollocation should be quite easy to implement now that the machinery for the linear and nonlinear equality constraints is there (it was non-existing before this PR). It is now fully functional and the new dimensions are pretty-printed in the optimization: section (similarly to NonLinMPC):

MovingHorizonEstimator estimator with a sample time Ts = 4.0 s:
├ model: LinModel
├ optimizer: OSQP 
├ transcription: MultipleShooting
├ arrival covariance: KalmanFilter 
├ direct: false
└ dimensions:
  │ ├ 2 estimation steps He
  │ ├ 2 manipulated inputs u (0 integrating states)
  │ ├ 6 estimated states x̂
  │ ├ 2 measured outputs ym (2 integrating states)
  │ ├ 0 unmeasured outputs yu
  │ └ 1 measured disturbances d
  └ optimization:
    ├ 30 decision variables Z̃ (0 slack variable, 3 bounds)
    ├  0 linear inequality constraints A
    ├ 12 linear equality constraints Aeq
    ├  0 nonlinear inequality constraints g (0 custom)
    └  0 nonlinear equality constraints geq

Ooof everything is more complex with the MHE, the growing windows complexify everything.

It is not strictly needed and it's an addition maintainability burden.

It was deleted by mistake.

codecov-commenter · 2026-07-31T18:28:15Z

Codecov Report

❌ Patch coverage is 96.60714% with 38 lines in your changes missing coverage. Please review.
✅ Project coverage is 98.20%. Comparing base (670f095) to head (5c0942b).
⚠️ Report is 65 commits behind head on main.

Files with missing lines	Patch %	Lines
src/estimator/mhe/transcription.jl	96.12%	24 Missing ⚠️
src/estimator/mhe/execute.jl	92.20%	12 Missing ⚠️
src/transcription.jl	96.77%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
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- Coverage   98.65%   98.20%   -0.46%     
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  Files          27       29       +2     
  Lines        5730     6130     +400     
==========================================
+ Hits         5653     6020     +367     
- Misses         77      110      +33

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github-actions · 2026-07-31T23:11:11Z

Benchmark Results (Julia v1)

Time benchmarks

	main	`5c0942b`...	main / `5c0942b`...
CASE STUDIES/PredictiveController/CSTR/LinMPC/With feedforward/DAQP/SingleShooting	5.15 ± 0.47 ms	5.12 ± 0.37 ms	1.01 ± 0.12
CASE STUDIES/PredictiveController/CSTR/LinMPC/With feedforward/OSQP/MultipleShooting	12.2 ± 0.74 ms	12 ± 0.74 ms	1.01 ± 0.088
CASE STUDIES/PredictiveController/CSTR/LinMPC/With feedforward/OSQP/SingleShooting	2.02 ± 0.1 ms	1.96 ± 0.095 ms	1.03 ± 0.072
CASE STUDIES/PredictiveController/CSTR/LinMPC/Without feedforward/DAQP/SingleShooting	5.08 ± 0.44 ms	5.07 ± 0.48 ms	1 ± 0.13
CASE STUDIES/PredictiveController/CSTR/LinMPC/Without feedforward/OSQP/MultipleShooting	8.36 ± 0.58 ms	8.33 ± 0.56 ms	1 ± 0.097
CASE STUDIES/PredictiveController/CSTR/LinMPC/Without feedforward/OSQP/SingleShooting	2.14 ± 0.097 ms	2.14 ± 0.019 ms	0.999 ± 0.046
CASE STUDIES/PredictiveController/Pendulum/LinMPC/Successive linearization/DAQP/SingleShooting	9.84 ± 1.7 ms	9.89 ± 1.7 ms	0.995 ± 0.24
CASE STUDIES/PredictiveController/Pendulum/LinMPC/Successive linearization/OSQP/MultipleShooting	0.133 ± 0.028 s	0.142 ± 0.036 s	0.935 ± 0.31
CASE STUDIES/PredictiveController/Pendulum/LinMPC/Successive linearization/OSQP/SingleShooting	15.6 ± 2.2 ms	15.2 ± 2.2 ms	1.03 ± 0.21
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Custom constraints/Ipopt/MultipleShooting	0.54 ± 0.0024 s	0.552 ± 0.014 s	0.979 ± 0.026
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Custom constraints/Ipopt/MultipleShooting (Hessian)	1.23 ± 0.059 s	1.18 ± 0.054 s	1.04 ± 0.069
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Custom constraints/Ipopt/SingleShooting	1.58 ± 0.022 s	1.58 ± 0.015 s	1 ± 0.017
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Custom constraints/Ipopt/TrapezoidalCollocation	1.01 ± 0.047 s	0.958 ± 0.028 s	1.05 ± 0.058
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Custom constraints/Ipopt/TrapezoidalCollocation (Hessian)	1.06 ± 0.1 s	0.989 ± 0.086 s	1.07 ± 0.14
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/MultipleShooting	0.37 ± 0.0031 s	0.366 ± 0.013 s	1.01 ± 0.037
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/MultipleShooting (Hessian)	0.417 ± 0.015 s	0.396 ± 0.01 s	1.05 ± 0.047
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/OrthogonalCollocation	0.569 ± 0.013 s	0.552 ± 0.013 s	1.03 ± 0.034
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/OrthogonalCollocation (Hessian)	0.564 ± 0.013 s	0.546 ± 0.015 s	1.03 ± 0.036
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/SingleShooting	0.533 ± 0.0048 s	0.537 ± 0.013 s	0.993 ± 0.026
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/SingleShooting (Hessian)	0.198 ± 0.0066 s	0.186 ± 0.003 s	1.06 ± 0.039
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/TrapezoidalCollocation	0.351 ± 0.004 s	0.34 ± 0.0083 s	1.03 ± 0.028
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/TrapezoidalCollocation (Hessian)	0.337 ± 0.029 s	0.328 ± 0.0089 s	1.03 ± 0.094
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/MadNLP/SingleShooting (Hessian)	0.0846 ± 0.0025 s	0.0841 ± 0.0057 s	1.01 ± 0.074
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Uno/MultipleShooting (Hessian)	0.131 ± 0.0038 s	0.134 ± 0.0096 s	0.977 ± 0.075
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/MultipleShooting	0.344 ± 0.00082 s	0.352 ± 0.0061 s	0.979 ± 0.017
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/MultipleShooting (Hessian)	0.367 ± 0.0057 s	0.355 ± 0.017 s	1.03 ± 0.051
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/MultipleShooting (threaded)	0.369 ± 0.0033 s	0.371 ± 0.0055 s	0.997 ± 0.017
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/OrthogonalCollocation	0.61 ± 0.01 s	0.603 ± 0.014 s	1.01 ± 0.028
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/OrthogonalCollocation (Hessian)	1.85 ± 0.06 s	1.91 ± 0.081 s	0.971 ± 0.052
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/SingleShooting	0.511 ± 0.0015 s	0.517 ± 0.0043 s	0.988 ± 0.0088
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/SingleShooting (Hessian)	0.191 ± 0.0047 s	0.189 ± 0.0021 s	1.01 ± 0.027
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/TrapezoidalCollocation	0.341 ± 0.0041 s	0.349 ± 0.011 s	0.976 ± 0.032
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/TrapezoidalCollocation (Hessian)	0.286 ± 0.0046 s	0.292 ± 0.015 s	0.979 ± 0.053
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/TrapezoidalCollocation (threaded)	0.371 ± 0.0063 s	0.374 ± 0.011 s	0.993 ± 0.033
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/MadNLP/MultipleShooting (Hessian)	0.22 ± 0.0052 s	0.222 ± 0.0062 s	0.993 ± 0.036
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/MadNLP/SingleShooting (Hessian)	0.074 ± 0.0003 s	0.0773 ± 0.0023 s	0.957 ± 0.028
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Uno/MultipleShooting (Hessian)	0.12 ± 0.002 s	0.114 ± 0.0039 s	1.05 ± 0.04
CASE STUDIES/StateEstimator/CSTR/MovingHorizonEstimator/DAQP/Current form	0.0854 ± 0.0061 s	0.0884 ± 0.0029 s	0.966 ± 0.075
CASE STUDIES/StateEstimator/CSTR/MovingHorizonEstimator/DAQP/Prediction form	0.0625 ± 0.0037 s	0.0653 ± 0.0037 s	0.957 ± 0.078
CASE STUDIES/StateEstimator/CSTR/MovingHorizonEstimator/OSQP/Current form	0.079 ± 0.0053 s	0.0827 ± 0.0052 s	0.956 ± 0.088
CASE STUDIES/StateEstimator/CSTR/MovingHorizonEstimator/OSQP/Prediction form	0.0553 ± 0.0071 s	0.0627 ± 0.0076 s	0.883 ± 0.16
CASE STUDIES/StateEstimator/Pendulum/MovingHorizonEstimator/Ipopt/Current form	0.0956 ± 0.0013 s	0.096 ± 0.00083 s	0.996 ± 0.016
CASE STUDIES/StateEstimator/Pendulum/MovingHorizonEstimator/Ipopt/Current form (Hessian)	0.0936 ± 0.00091 s	0.0944 ± 0.0013 s	0.992 ± 0.017
CASE STUDIES/StateEstimator/Pendulum/MovingHorizonEstimator/Ipopt/Prediction form	0.0725 ± 0.0013 s	0.0716 ± 0.0013 s	1.01 ± 0.026
CASE STUDIES/StateEstimator/Pendulum/MovingHorizonEstimator/Ipopt/Prediction form (Hessian)	0.0934 ± 0.0017 s	0.0919 ± 0.0026 s	1.02 ± 0.034
CASE STUDIES/StateEstimator/Pendulum/MovingHorizonEstimator/MadNLP/Current form (Hessian)	0.0503 ± 0.00051 s	0.0517 ± 0.00074 s	0.974 ± 0.017
CASE STUDIES/StateEstimator/Pendulum/MovingHorizonEstimator/MadNLP/Prediction form (Hessian)	0.0473 ± 0.00057 s	0.0452 ± 0.00041 s	1.05 ± 0.016
UNIT TESTS/PredictiveController/ExplicitMPC/moveinput!	4.51 ± 0.04 μs	4.38 ± 0.04 μs	1.03 ± 0.013
UNIT TESTS/PredictiveController/LinMPC/getinfo!	0.0995 ± 0.0024 ms	0.0999 ± 0.0025 ms	0.996 ± 0.034
UNIT TESTS/PredictiveController/LinMPC/moveinput!/MultipleShooting	0.14 ± 0.01 ms	0.142 ± 0.0095 ms	0.988 ± 0.098
UNIT TESTS/PredictiveController/LinMPC/moveinput!/SingleShooting	17.9 ± 0.41 μs	16.8 ± 0.42 μs	1.06 ± 0.036
UNIT TESTS/PredictiveController/NonLinMPC/getinfo!/LinModel	0.173 ± 0.013 ms	0.175 ± 0.013 ms	0.988 ± 0.1
UNIT TESTS/PredictiveController/NonLinMPC/getinfo!/NonLinModel	0.524 ± 0.076 ms	0.328 ± 0.12 ms	1.6 ± 0.63
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/LinModel/MultipleShooting	1.16 ± 0.26 ms	1.16 ± 0.25 ms	1 ± 0.31
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/LinModel/SingleShooting	0.485 ± 0.024 ms	0.482 ± 0.025 ms	1.01 ± 0.072
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/NonLinModel/MultipleShooting	10.8 ± 0.54 ms	10.6 ± 0.3 ms	1.02 ± 0.058
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/NonLinModel/MultipleShootingHessian	10.9 ± 0.48 ms	10.8 ± 0.56 ms	1.01 ± 0.069
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/NonLinModel/OrthogonalCollocation	10.4 ± 0.66 ms	11.7 ± 1.4 ms	0.887 ± 0.12
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/NonLinModel/OrthogonalCollocationHessian	11.1 ± 0.74 ms	11.2 ± 0.75 ms	0.989 ± 0.094
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/NonLinModel/SingleShooting	9.25 ± 1.1 ms	7.52 ± 0.22 ms	1.23 ± 0.16
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/NonLinModel/SingleShootingHessian	9.26 ± 1 ms	7.43 ± 0.14 ms	1.25 ± 0.14
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/NonLinModel/TrapezoidalCollocation	7.49 ± 0.25 ms	7.45 ± 0.63 ms	1 ± 0.091
UNIT TESTS/SimModel/LinModel/evaloutput	0.15 ± 0.001 μs	0.14 ± 0 μs	1.07 ± 0.0071
UNIT TESTS/SimModel/LinModel/updatestate!	0.201 ± 0.01 μs	0.19 ± 0.001 μs	1.06 ± 0.053
UNIT TESTS/SimModel/NonLinModel/evaloutput	0.33 ± 0.01 μs	0.36 ± 0.001 μs	0.917 ± 0.028
UNIT TESTS/SimModel/NonLinModel/linearize!	1.81 ± 0.051 μs	1.84 ± 0.05 μs	0.984 ± 0.038
UNIT TESTS/SimModel/NonLinModel/updatestate!	0.381 ± 0.011 μs	0.41 ± 0.01 μs	0.929 ± 0.035
UNIT TESTS/StateEstimator/ExtendedKalmanFilter/evaloutput/LinModel	0.47 ± 0.01 μs	0.481 ± 0.011 μs	0.977 ± 0.031
UNIT TESTS/StateEstimator/ExtendedKalmanFilter/evaloutput/NonLinModel	1.67 ± 0.02 μs	1.74 ± 0.021 μs	0.96 ± 0.016
UNIT TESTS/StateEstimator/ExtendedKalmanFilter/preparestate!/LinModel	0.631 ± 0 μs	0.26 ± 0.01 μs	2.43 ± 0.093
UNIT TESTS/StateEstimator/ExtendedKalmanFilter/preparestate!/NonLinModel	1.3 ± 0.01 μs	1.24 ± 0.01 μs	1.05 ± 0.012
UNIT TESTS/StateEstimator/ExtendedKalmanFilter/updatestate!/LinModel	4.08 ± 0.069 μs	3.98 ± 0.05 μs	1.03 ± 0.022
UNIT TESTS/StateEstimator/ExtendedKalmanFilter/updatestate!/NonLinModel	8.01 ± 0.08 μs	8.13 ± 0.071 μs	0.985 ± 0.013
UNIT TESTS/StateEstimator/InternalModel/evaloutput/LinModel	0.401 ± 0.001 μs	0.32 ± 0.001 μs	1.25 ± 0.005
UNIT TESTS/StateEstimator/InternalModel/evaloutput/NonLinModel	0.501 ± 0.01 μs	0.511 ± 0.011 μs	0.98 ± 0.029
UNIT TESTS/StateEstimator/InternalModel/preparestate!/LinModel	0.621 ± 0.01 μs	0.41 ± 0.01 μs	1.51 ± 0.044
UNIT TESTS/StateEstimator/InternalModel/preparestate!/NonLinModel	0.621 ± 0.019 μs	0.621 ± 0.02 μs	1 ± 0.044
UNIT TESTS/StateEstimator/InternalModel/updatestate!/LinModel	0.601 ± 0.011 μs	0.641 ± 0.01 μs	0.938 ± 0.023
UNIT TESTS/StateEstimator/InternalModel/updatestate!/NonLinModel	1.15 ± 0.02 μs	1.19 ± 0.02 μs	0.966 ± 0.023
UNIT TESTS/StateEstimator/KalmanFilter/evaloutput	0.26 ± 0.001 μs	0.26 ± 0.01 μs	1 ± 0.039
UNIT TESTS/StateEstimator/KalmanFilter/preparestate!	0.14 ± 0 μs	0.15 ± 0 μs	0.933 ± 0
UNIT TESTS/StateEstimator/KalmanFilter/updatestate!	2.59 ± 0.051 μs	2.61 ± 0.04 μs	0.992 ± 0.025
UNIT TESTS/StateEstimator/Luenberger/evaloutput	0.22 ± 0.001 μs	0.39 ± 0.01 μs	0.564 ± 0.015
UNIT TESTS/StateEstimator/Luenberger/preparestate!	0.271 ± 0.01 μs	0.431 ± 0.011 μs	0.629 ± 0.028
UNIT TESTS/StateEstimator/Luenberger/updatestate!	0.36 ± 0.02 μs	0.43 ± 0.01 μs	0.837 ± 0.05
UNIT TESTS/StateEstimator/MovingHorizonEstimator/getinfo!/LinModel	0.316 ± 0.019 ms	0.316 ± 0.02 ms	0.997 ± 0.087
UNIT TESTS/StateEstimator/MovingHorizonEstimator/getinfo!/NonLinModel	0.389 ± 0.033 ms	0.461 ± 0.059 ms	0.845 ± 0.13
UNIT TESTS/StateEstimator/MovingHorizonEstimator/preparestate!/LinModel/Constant arr. cov.	0.0403 ± 0.024 s	0.0437 ± 0.03 s	0.921 ± 0.83
UNIT TESTS/StateEstimator/MovingHorizonEstimator/preparestate!/LinModel/Current form	0.0397 ± 0.0022 s	0.0421 ± 0.03 s	0.942 ± 0.68
UNIT TESTS/StateEstimator/MovingHorizonEstimator/preparestate!/LinModel/Prediction form	0.441 ± 0.001 μs	0.391 ± 0.001 μs	1.13 ± 0.0039
UNIT TESTS/StateEstimator/MovingHorizonEstimator/preparestate!/NonLinModel/Current form	0.346 ± 0.019 ms	0.357 ± 0.019 ms	0.969 ± 0.074
UNIT TESTS/StateEstimator/MovingHorizonEstimator/preparestate!/NonLinModel/Prediction form	1.31 ± 0.01 μs	1.44 ± 0.01 μs	0.91 ± 0.0094
UNIT TESTS/StateEstimator/MovingHorizonEstimator/updatestate!/LinModel/Constant arr. cov.	14.2 ± 1.5 μs	13.7 ± 2.7 μs	1.03 ± 0.23
UNIT TESTS/StateEstimator/MovingHorizonEstimator/updatestate!/LinModel/Current form	0.0378 ± 0.0032 ms	0.0374 ± 0.0054 ms	1.01 ± 0.17
UNIT TESTS/StateEstimator/MovingHorizonEstimator/updatestate!/LinModel/Prediction form	15.6 ± 29 ms	0.0354 ± 0.024 s	0.44 ± 0.87
UNIT TESTS/StateEstimator/MovingHorizonEstimator/updatestate!/NonLinModel/Current form	19.1 ± 0.45 μs	18.9 ± 0.54 μs	1.01 ± 0.038
UNIT TESTS/StateEstimator/MovingHorizonEstimator/updatestate!/NonLinModel/Prediction form	0.348 ± 0.018 ms	0.381 ± 0.031 ms	0.913 ± 0.088
UNIT TESTS/StateEstimator/SteadyKalmanFilter/evaloutput	0.26 ± 0.01 μs	0.25 ± 0.01 μs	1.04 ± 0.058
UNIT TESTS/StateEstimator/SteadyKalmanFilter/preparestate!	0.481 ± 0.019 μs	0.33 ± 0.02 μs	1.46 ± 0.11
UNIT TESTS/StateEstimator/SteadyKalmanFilter/updatestate!	0.791 ± 0.011 μs	0.351 ± 0.011 μs	2.25 ± 0.077
UNIT TESTS/StateEstimator/UnscentedKalmanFilter/evaloutput/LinModel	0.3 ± 0.01 μs	0.301 ± 0.02 μs	0.997 ± 0.074
UNIT TESTS/StateEstimator/UnscentedKalmanFilter/evaloutput/NonLinModel	0.851 ± 0.019 μs	0.882 ± 0.03 μs	0.965 ± 0.039
UNIT TESTS/StateEstimator/UnscentedKalmanFilter/preparestate!/LinModel	3.7 ± 0.05 μs	3.72 ± 0.06 μs	0.994 ± 0.021
UNIT TESTS/StateEstimator/UnscentedKalmanFilter/preparestate!/NonLinModel	4.92 ± 0.05 μs	4.94 ± 0.059 μs	0.996 ± 0.016
UNIT TESTS/StateEstimator/UnscentedKalmanFilter/updatestate!/LinModel	3.72 ± 0.06 μs	3.73 ± 0.059 μs	0.997 ± 0.023
UNIT TESTS/StateEstimator/UnscentedKalmanFilter/updatestate!/NonLinModel	6.8 ± 0.1 μs	6.66 ± 0.12 μs	1.02 ± 0.024
time_to_load	6.5 ± 0.024 s	6.69 ± 0.036 s	0.971 ± 0.0064

Memory benchmarks

	main	`5c0942b`...	main / `5c0942b`...
CASE STUDIES/PredictiveController/CSTR/LinMPC/With feedforward/DAQP/SingleShooting	0.0489 M allocs: 1.86 MB	0.0489 M allocs: 1.86 MB	1
CASE STUDIES/PredictiveController/CSTR/LinMPC/With feedforward/OSQP/MultipleShooting	0.126 M allocs: 3.16 MB	0.126 M allocs: 3.16 MB	1
CASE STUDIES/PredictiveController/CSTR/LinMPC/With feedforward/OSQP/SingleShooting	12.6 k allocs: 0.356 MB	12.6 k allocs: 0.356 MB	1
CASE STUDIES/PredictiveController/CSTR/LinMPC/Without feedforward/DAQP/SingleShooting	0.0487 M allocs: 1.85 MB	0.0487 M allocs: 1.85 MB	1
CASE STUDIES/PredictiveController/CSTR/LinMPC/Without feedforward/OSQP/MultipleShooting	0.0879 M allocs: 2.23 MB	0.0879 M allocs: 2.23 MB	1
CASE STUDIES/PredictiveController/CSTR/LinMPC/Without feedforward/OSQP/SingleShooting	12.5 k allocs: 0.35 MB	12.5 k allocs: 0.35 MB	1
CASE STUDIES/PredictiveController/Pendulum/LinMPC/Successive linearization/DAQP/SingleShooting	0.119 M allocs: 6.38 MB	0.119 M allocs: 6.38 MB	1
CASE STUDIES/PredictiveController/Pendulum/LinMPC/Successive linearization/OSQP/MultipleShooting	4.76 M allocs: 0.257 GB	4.76 M allocs: 0.257 GB	1
CASE STUDIES/PredictiveController/Pendulum/LinMPC/Successive linearization/OSQP/SingleShooting	0.148 M allocs: 8.23 MB	0.148 M allocs: 8.23 MB	1
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Custom constraints/Ipopt/MultipleShooting	0.369 M allocs: 25.5 MB	0.369 M allocs: 25.6 MB	0.996
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Custom constraints/Ipopt/MultipleShooting (Hessian)	2.2 M allocs: 0.244 GB	2.2 M allocs: 0.244 GB	1
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Custom constraints/Ipopt/SingleShooting	0.306 M allocs: 0.0435 GB	0.306 M allocs: 0.0435 GB	1
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Custom constraints/Ipopt/TrapezoidalCollocation	2.17 M allocs: 0.212 GB	2.17 M allocs: 0.212 GB	0.998
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Custom constraints/Ipopt/TrapezoidalCollocation (Hessian)	2.17 M allocs: 0.212 GB	2.17 M allocs: 0.212 GB	0.998
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/MultipleShooting	0.316 M allocs: 22 MB	0.316 M allocs: 22.1 MB	0.996
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/MultipleShooting (Hessian)	0.741 M allocs: 0.0843 GB	0.741 M allocs: 0.0843 GB	1
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/OrthogonalCollocation	1.36 M allocs: 0.122 GB	1.36 M allocs: 0.122 GB	1
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/OrthogonalCollocation (Hessian)	1.36 M allocs: 0.122 GB	1.36 M allocs: 0.122 GB	1
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/SingleShooting	0.0965 M allocs: 17.6 MB	0.0965 M allocs: 17.9 MB	0.982
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/SingleShooting (Hessian)	0.0812 M allocs: 16.9 MB	0.0812 M allocs: 17 MB	0.996
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/TrapezoidalCollocation	0.314 M allocs: 21.9 MB	0.314 M allocs: 21.9 MB	1
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Ipopt/TrapezoidalCollocation (Hessian)	0.757 M allocs: 0.0765 GB	0.757 M allocs: 0.0766 GB	0.998
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/MadNLP/SingleShooting (Hessian)	0.0926 M allocs: 20 MB	0.0926 M allocs: 20 MB	0.997
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Economic/Uno/MultipleShooting (Hessian)	0.339 M allocs: 0.036 GB	0.339 M allocs: 0.036 GB	1
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/MultipleShooting	0.277 M allocs: 19 MB	0.277 M allocs: 19.1 MB	0.996
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/MultipleShooting (Hessian)	0.709 M allocs: 0.0739 GB	0.709 M allocs: 0.0739 GB	1
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/MultipleShooting (threaded)	0.296 M allocs: 28 MB	0.296 M allocs: 28 MB	0.997
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/OrthogonalCollocation	1.4 M allocs: 0.126 GB	1.4 M allocs: 0.126 GB	1
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/OrthogonalCollocation (Hessian)	5.71 M allocs: 0.694 GB	5.71 M allocs: 0.694 GB	1
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/SingleShooting	0.0754 M allocs: 13.3 MB	0.0754 M allocs: 13.5 MB	0.982
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/SingleShooting (Hessian)	0.0808 M allocs: 16.9 MB	0.0808 M allocs: 17 MB	0.996
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/TrapezoidalCollocation	0.276 M allocs: 19 MB	0.276 M allocs: 19 MB	1
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/TrapezoidalCollocation (Hessian)	0.72 M allocs: 0.0656 GB	0.72 M allocs: 0.0657 GB	0.998
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Ipopt/TrapezoidalCollocation (threaded)	0.295 M allocs: 28.1 MB	0.295 M allocs: 28.1 MB	1
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/MadNLP/MultipleShooting (Hessian)	0.587 M allocs: 0.0728 GB	0.587 M allocs: 0.0728 GB	1
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/MadNLP/SingleShooting (Hessian)	0.0927 M allocs: 20 MB	0.0927 M allocs: 20.1 MB	0.997
CASE STUDIES/PredictiveController/Pendulum/NonLinMPC/Noneconomic/Uno/MultipleShooting (Hessian)	0.334 M allocs: 0.0325 GB	0.334 M allocs: 0.0325 GB	1
CASE STUDIES/StateEstimator/CSTR/MovingHorizonEstimator/DAQP/Current form	1.25 M allocs: 0.213 GB	1.26 M allocs: 0.221 GB	0.963
CASE STUDIES/StateEstimator/CSTR/MovingHorizonEstimator/DAQP/Prediction form	1.16 M allocs: 0.136 GB	1.16 M allocs: 0.137 GB	0.998
CASE STUDIES/StateEstimator/CSTR/MovingHorizonEstimator/OSQP/Current form	1.13 M allocs: 0.21 GB	1.13 M allocs: 0.213 GB	0.983
CASE STUDIES/StateEstimator/CSTR/MovingHorizonEstimator/OSQP/Prediction form	1.07 M allocs: 0.134 GB	1.07 M allocs: 0.134 GB	1
CASE STUDIES/StateEstimator/Pendulum/MovingHorizonEstimator/Ipopt/Current form	0.0714 M allocs: 16.7 MB	0.0772 M allocs: 13.4 MB	1.25
CASE STUDIES/StateEstimator/Pendulum/MovingHorizonEstimator/Ipopt/Current form (Hessian)	0.0702 M allocs: 16.5 MB	0.0745 M allocs: 13 MB	1.27
CASE STUDIES/StateEstimator/Pendulum/MovingHorizonEstimator/Ipopt/Prediction form	0.0517 M allocs: 11.7 MB	0.0532 M allocs: 9.1 MB	1.28
CASE STUDIES/StateEstimator/Pendulum/MovingHorizonEstimator/Ipopt/Prediction form (Hessian)	0.0705 M allocs: 16.6 MB	0.0748 M allocs: 13 MB	1.27
CASE STUDIES/StateEstimator/Pendulum/MovingHorizonEstimator/MadNLP/Current form (Hessian)	0.0918 M allocs: 21.1 MB	0.0964 M allocs: 17 MB	1.24
CASE STUDIES/StateEstimator/Pendulum/MovingHorizonEstimator/MadNLP/Prediction form (Hessian)	0.0868 M allocs: 19.2 MB	0.0909 M allocs: 15.5 MB	1.24
UNIT TESTS/PredictiveController/ExplicitMPC/moveinput!	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/PredictiveController/LinMPC/getinfo!	0.326 k allocs: 15.6 kB	0.326 k allocs: 15.6 kB	1
UNIT TESTS/PredictiveController/LinMPC/moveinput!/MultipleShooting	1.62 k allocs: 0.0403 MB	1.62 k allocs: 0.0403 MB	1
UNIT TESTS/PredictiveController/LinMPC/moveinput!/SingleShooting	0.114 k allocs: 2.98 kB	0.114 k allocs: 2.98 kB	1
UNIT TESTS/PredictiveController/NonLinMPC/getinfo!/LinModel	0.408 k allocs: 0.0579 MB	0.408 k allocs: 0.0579 MB	1
UNIT TESTS/PredictiveController/NonLinMPC/getinfo!/NonLinModel	0.571 k allocs: 0.077 MB	0.571 k allocs: 0.077 MB	1
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/LinModel/MultipleShooting	1.79 k allocs: 0.105 MB	1.79 k allocs: 0.105 MB	1
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/LinModel/SingleShooting	0.254 k allocs: 10.1 kB	0.254 k allocs: 10.1 kB	1
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/NonLinModel/MultipleShooting	4.76 k allocs: 0.368 MB	4.76 k allocs: 0.368 MB	1
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/NonLinModel/MultipleShootingHessian	5.34 k allocs: 0.423 MB	5.34 k allocs: 0.423 MB	1
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/NonLinModel/OrthogonalCollocation	9.59 k allocs: 0.609 MB	9.59 k allocs: 0.611 MB	0.998
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/NonLinModel/OrthogonalCollocationHessian	0.0459 M allocs: 4.44 MB	0.0459 M allocs: 4.44 MB	1
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/NonLinModel/SingleShooting	0.957 k allocs: 0.233 MB	0.957 k allocs: 0.233 MB	1
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/NonLinModel/SingleShootingHessian	0.957 k allocs: 0.233 MB	0.957 k allocs: 0.233 MB	1
UNIT TESTS/PredictiveController/NonLinMPC/moveinput!/NonLinModel/TrapezoidalCollocation	3.42 k allocs: 0.241 MB	3.42 k allocs: 0.241 MB	1
UNIT TESTS/SimModel/LinModel/evaloutput	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/SimModel/LinModel/updatestate!	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/SimModel/NonLinModel/evaloutput	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/SimModel/NonLinModel/linearize!	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/SimModel/NonLinModel/updatestate!	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/ExtendedKalmanFilter/evaloutput/LinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/ExtendedKalmanFilter/evaloutput/NonLinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/ExtendedKalmanFilter/preparestate!/LinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/ExtendedKalmanFilter/preparestate!/NonLinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/ExtendedKalmanFilter/updatestate!/LinModel	4 allocs: 0.0938 kB	4 allocs: 0.0938 kB	1
UNIT TESTS/StateEstimator/ExtendedKalmanFilter/updatestate!/NonLinModel	4 allocs: 0.0938 kB	4 allocs: 0.0938 kB	1
UNIT TESTS/StateEstimator/InternalModel/evaloutput/LinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/InternalModel/evaloutput/NonLinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/InternalModel/preparestate!/LinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/InternalModel/preparestate!/NonLinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/InternalModel/updatestate!/LinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/InternalModel/updatestate!/NonLinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/KalmanFilter/evaloutput	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/KalmanFilter/preparestate!	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/KalmanFilter/updatestate!	4 allocs: 0.0938 kB	4 allocs: 0.0938 kB	1
UNIT TESTS/StateEstimator/Luenberger/evaloutput	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/Luenberger/preparestate!	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/Luenberger/updatestate!	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/MovingHorizonEstimator/getinfo!/LinModel	1.42 k allocs: 0.0529 MB	1.42 k allocs: 0.053 MB	0.998
UNIT TESTS/StateEstimator/MovingHorizonEstimator/getinfo!/NonLinModel	1.3 k allocs: 0.174 MB	1.42 k allocs: 0.252 MB	0.689
UNIT TESTS/StateEstimator/MovingHorizonEstimator/preparestate!/LinModel/Constant arr. cov.	0.159 M allocs: 0.117 GB	0.158 M allocs: 0.116 GB	1.01
UNIT TESTS/StateEstimator/MovingHorizonEstimator/preparestate!/LinModel/Current form	0.158 M allocs: 0.115 GB	0.158 M allocs: 0.118 GB	0.98
UNIT TESTS/StateEstimator/MovingHorizonEstimator/preparestate!/LinModel/Prediction form	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/MovingHorizonEstimator/preparestate!/NonLinModel/Current form	0.997 k allocs: 26.2 kB	1.04 k allocs: 27.8 kB	0.944
UNIT TESTS/StateEstimator/MovingHorizonEstimator/preparestate!/NonLinModel/Prediction form	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/MovingHorizonEstimator/updatestate!/LinModel/Constant arr. cov.	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/MovingHorizonEstimator/updatestate!/LinModel/Current form	2 allocs: 0.0469 kB	2 allocs: 0.0469 kB	1
UNIT TESTS/StateEstimator/MovingHorizonEstimator/updatestate!/LinModel/Prediction form	6.75 k allocs: 0.45 MB	7.55 k allocs: 0.475 MB	0.948
UNIT TESTS/StateEstimator/MovingHorizonEstimator/updatestate!/NonLinModel/Current form	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/MovingHorizonEstimator/updatestate!/NonLinModel/Prediction form	0.926 k allocs: 26.2 kB	1.04 k allocs: 27.8 kB	0.944
UNIT TESTS/StateEstimator/SteadyKalmanFilter/evaloutput	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/SteadyKalmanFilter/preparestate!	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/SteadyKalmanFilter/updatestate!	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/UnscentedKalmanFilter/evaloutput/LinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/UnscentedKalmanFilter/evaloutput/NonLinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/UnscentedKalmanFilter/preparestate!/LinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/UnscentedKalmanFilter/preparestate!/NonLinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/UnscentedKalmanFilter/updatestate!/LinModel	0 allocs: 0 B	0 allocs: 0 B
UNIT TESTS/StateEstimator/UnscentedKalmanFilter/updatestate!/NonLinModel	0 allocs: 0 B	0 allocs: 0 B
time_to_load	0.149 k allocs: 11.2 kB	0.149 k allocs: 11.2 kB	1

franckgaga added 30 commits July 14, 2026 14:26

changed: new general transcription.jl file

6f6643c

doc: SingleShooting decision var. for MHE

d34b413

doc: minor correction

cc14cb9

doc: wip transcription for MHE

3fbb6de

Merge branch 'main' into ms_mhe

4d69551

Merge branch 'main' into ms_mhe

613f575

Merge branch 'main' into ms_mhe

ce2cee7

doc: MultipleShooting for MovingHorizonEstimator

6faff9a

Merge branch 'main' into ms_mhe

6b35182

doc: mistake UnscentedKalmanFilter correction equations

4390346

added: transcription field in MovingHorizonEstimator

8c6b691

wip: support MultipleShooting in MHE

267673c

wip: idem

3b72b79

wip: idem

0c7ceec

wip: idem

0195ef8

Merge branch 'main' into ms_mhe

4680bc1

wip: support MultipleShooting in MHE

bdbcd02

wip: idem

0307ec9

wip: idem

e96d656

added: warm-starting for MHE with MultipleShooting

6be6e5a

debug: warm-starting MHE MS

7c49622

added: MultipleShooting for MHE starts to work 🍾🍾🍾

bcfe2b5

Ooof everything is more complex with the MHE, the growing windows complexify everything.

changed: output argument order in trunc_windows

5a12238

changed: more efficient eq. lin. constraint

91b923f

removed: estim.Ŵ field in MovingHorizonEstimator

8a90b28

It is not strictly needed and it's an addition maintainability burden.

changed: code cleaning and new docstrings

a5012d9

removed: useless argument in init_predmat_mhe

73213e1

added: treat X̂ bounds as box constraints for MHE w/o SingleShooting

258ec86

doc: add transcription kwarg in MovingHorizonEstimator

d318c30

doc: re-add covestim details in the extended help

325259e

It was deleted by mistake.

franckgaga added 12 commits July 30, 2026 11:28

added: generate geq_oracle for MovingHorizonEstimator

4f47b7f

debug: correct eq for MultipleShooting and MHE

87ed494

doc: minor precisions

6fa5c01

deleted: old outdated getŴ! method

aad77fb

added: MultipleShooting and NonLinModel with MHE work🥳🥳🥳

e624458

added: NL equality constraints info in getinfo(mhe)

137d950

doc: getinfo fields about NL eq. constraints for MHE

4cf4f8f

changed: minor format modification

02921ba

debug: correct variable name

ebe6c6e

removed: print

054eb56

Merge branch 'main' into ms_mhe

4a7db59

debug: replying merged bugfix on each TranscriptionMethod

ad6b723

franckgaga linked an issue Jul 31, 2026 that may be closed by this pull request

Multiple shooting transcription for MovingHorizonEstimator #293

Closed

franckgaga added 3 commits July 31, 2026 09:25

debug: truncate :Ŷ field in getinfo(mhe)

6ec44c1

debug: avoid undefined elements in Ŵ

f1eca6b

test: debug tests

98653e6

franckgaga added the benchmark label Jul 31, 2026

franckgaga added 5 commits July 31, 2026 12:02

doc: update jldoctests

576fe92

doc: debug doc

6be4552

doc: debug cross-ref

a38fa6a

doc: more precise definition of the decision vector for the MHE

5fe5483

doc: similar precisions fot MHE warm-starting

33f8d6c

franckgaga removed the benchmark label Jul 31, 2026

test: MultipleShooting tests for MovingHorizonEstimator

5c0942b

franckgaga added the benchmark label Jul 31, 2026

franckgaga merged commit dee00d3 into main Jul 31, 2026
6 checks passed

franckgaga deleted the ms_mhe branch August 4, 2026 19:05

franckgaga mentioned this pull request Aug 7, 2026

added: 🟨📐 TrapezoidalCollocation 🟨📐 for MovingHorizonEstimator #425

Merged

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added: `MultipleShooting` support for the `MovingHorizonEstimator` 🍾 - #411

added: `MultipleShooting` support for the `MovingHorizonEstimator` 🍾#411
franckgaga merged 64 commits into
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