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arxiv: 1907.09136 · v1 · pith:OMTMPRL4new · submitted 2019-07-18 · 📡 eess.SY · cs.SY

Combustion Phasing Modelling and Control for Compression Ignition Engines with High Dilution and Boost Levels

Wenbo Sui , Carrie M. Hall This is my paper

Pith reviewed 2026-05-24 19:19 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords combustion phasingCA50 controldiesel enginemodel-based controladaptive controlEGRboostknock integral model
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The pith

A simplified nonlinear model supports controllers that regulate diesel combustion phasing to within 0.5 CAD in five cycles.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a nonlinear model for predicting combustion phasing in compression ignition engines at high exhaust gas recirculation and boost levels. This model is calibrated using simulation and experimental data and then used to design both an adaptive closed-loop controller and a feedforward open-loop controller. In simulations of transient conditions, the adaptive controller brings CA50 to steady state in no more than five cycles with errors under 0.1 CAD, while the feedforward approach achieves the same settling with errors under 0.5 CAD. Precise combustion phasing control is important because it affects fuel efficiency in these engines.

Core claim

The combustion phasing model combines a knock integral model, burn duration model, and Wiebe function, simplified for control purposes and calibrated for high dilution and boost conditions. Based on this model, an adaptive nonlinear model-based controller for closed-loop control and a feedforward model-based controller for open-loop control are designed and tested in simulations, demonstrating rapid convergence and low steady-state errors for CA50.

What carries the argument

The simplified nonlinear combustion phasing model that integrates knock integral, burn duration, and Wiebe function elements to predict CA50 for controller design.

If this is right

  • The model predicts CA50 accurately enough for control under high EGR and boost.
  • Adaptive control achieves steady-state errors less than 0.1 CAD.
  • Feedforward control achieves steady-state errors less than 0.5 CAD.
  • Both controllers settle CA50 within 5 engine cycles during transients.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The control strategies might reduce the need for extensive calibration in production engines.
  • Similar modeling could support control in other advanced combustion modes if recalibrated.
  • Real-world testing would be needed to confirm performance beyond simulation.

Load-bearing premise

The simplified nonlinear model remains sufficiently accurate during unmeasured transients after calibration on available data.

What would settle it

Engine test data during transient operation where CA50 does not reach steady state within 5 cycles or exceeds the reported error bounds.

Figures

Figures reproduced from arXiv: 1907.09136 by Carrie M. Hall, Wenbo Sui.

Figure 1
Figure 1. Figure 1: Schematic of diesel engine system With the inclusion of technologies like EGR, variable geometry turbochargers (VGT), diesel engines are becoming increasingly complicated. As such, simple rule-based control strategies or methods based on look-up tables [5, 6] are not always satisfactory on these more complex engines and the automotive industry has turned to model-based and closed loop control techniques on… view at source ↗
Figure 2
Figure 2. Figure 2: Speed-load map of experimental operating points [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Model calibration procedure The optimized parameters of the CA50 prediction model in Eqn. (20) are given in [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of SOC prediction and GT simulations [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of CA50 prediction and GT simulations [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of SOC prediction and experimental data [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of CA50 prediction and experimental data [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Prediction accuracy during an a) engine speed transient, b) EGR fraction [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Structure of CA50 adaptive feedback control system [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Structure of CA50 feedforward model-based control system [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Simulation result for Case 1 No fuel is injected into the cylinder in first 2 cycles, but after fuel injection begins, both control systems reach steady state in 5 cycles. The adaptive controller has a 0.46 CAD overshoot, and the steady state error ranges from -0.08 to 0.02 CAD. This oscillation of the error is mainly from the precision of SOI rather than the control algorithm. Compared with the adaptive … view at source ↗
Figure 12
Figure 12. Figure 12: Simulation result for Case 2 C. Case 3: Reference Intake Manifold Temperature Change In Case 3, changes in the intake manifold temperatures are simulated as shown in [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Simulation result in Case 3 Like Case 1 and Case 2, no fuel injection in the first 2 cycles results in the zero CA50s in the first 2 cycles, but in the first 5 seconds, both control systems can reach steady quickly. The system based on adaptive control has an overshoot which is 0.46 CAD, and a steady state error from -0.08 CAD to 0.02 CAD. The system with feedforward model￾based controller has a -0.40 CAD… view at source ↗
Figure 15
Figure 15. Figure 15: These changes also take several cycles to get to their new steady state values. [PITH_FULL_IMAGE:figures/full_fig_p029_15.png] view at source ↗
Figure 14
Figure 14. Figure 14: Simulation result in Case 4 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 Time [s] Actual CA50 [CAD] Reference CA50 Adaptive Control Model-based Control [PITH_FULL_IMAGE:figures/full_fig_p029_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Pressure and temperature at IVC in Case 4 [PITH_FULL_IMAGE:figures/full_fig_p030_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Simulation result in Case 5 Similar to the other 4 cases, zero fuel injection leads to no combustion in the first 2 cycles and both control systems reach the steady state after 5 cycles. The steady state error is - 0.05 – 0.05 CAD for adaptive control, while the error for the feedforward model-based control is -0.26 CAD. The EGR fraction is changed from 0 to 0.5 after 5 seconds and both control approaches… view at source ↗
Figure 17
Figure 17. Figure 17: Pressure and temperature at IVC in Case 5 [PITH_FULL_IMAGE:figures/full_fig_p032_17.png] view at source ↗
read the original abstract

Because fuel efficiency is significantly impacted by the timing of combustion in internal combustion engines, accurate control of combustion phasing is critical. In this paper, a nonlinear combustion phasing model is introduced and calibrated, and both a feedforward model-based control strategy and an adaptive model-based control strategy are investigated for combustion phasing control. The combustion phasing model combines a knock integral model, burn duration model and a Wiebe function to predict the combustion phasing of a diesel engine. This model is simplified to be more suitable for combustion phasing control and is calibrated and validated using simulations and experimental data that include conditions with high exhaust gas recirculation fractions and high boost levels. Based on this model, an adaptive nonlinear model-based controller is designed for closed-loop control, and a feedforward model-based controller is designed for open-loop control. These two control approaches were tested in simulations. The simulation results show that during transient changes the CA50 (the crank angle at which 50% of the mass of fuel has burned) can reach steady state in no more than 5 cycles and the steady state errors are less than +/-0.1 crank angle degree (CAD) for adaptive control, and less than +/-0.5 CAD for feedforward model-based control.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces a simplified nonlinear combustion phasing model (knock integral + burn duration + Wiebe) for diesel engines at high EGR and boost levels. The model is calibrated on experimental data, then used to design a feedforward model-based controller and an adaptive nonlinear model-based controller for CA50. Both are evaluated only in simulation on the design model, where CA50 settles in ≤5 cycles with steady-state errors <±0.5 CAD (feedforward) and <±0.1 CAD (adaptive).

Significance. If the model remains accurate during unmeasured transients, the adaptive controller could provide a practical, low-error approach to combustion phasing under varying dilution and boost. The simulation metrics are quantitatively strong, but the absence of any reported transient model validation or closed-loop hardware results limits the immediate engineering significance.

major comments (2)
  1. [Abstract; simulation section] Abstract and simulation-results section: the headline claims (settling ≤5 cycles, errors <±0.1 CAD adaptive / <±0.5 CAD feedforward) are obtained by closing the loop on the identical calibrated model used for controller synthesis. No open-loop transient validation (measured vs. predicted CA50 during the boost/EGR steps) or closed-loop engine experiments are reported, so the metrics are not independent of the model assumptions.
  2. [Model calibration and validation] Model-calibration section: the manuscript states that the simplified model is “calibrated and validated using … experimental data,” yet no quantitative fit metrics (RMS CA50 error, R², or residual plots) are supplied for the transient conditions exercised by the controllers. This leaves the central assumption that the model remains sufficiently accurate during unmeasured fast transients untested.
minor comments (1)
  1. [Model equations] Notation for the knock-integral threshold and Wiebe shape parameters should be defined once at first use rather than re-introduced in the controller section.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their thorough review and valuable comments. We address each major comment below with clarifications and indicate where revisions will be incorporated.

read point-by-point responses

  1. Referee: [Abstract; simulation section] Abstract and simulation-results section: the headline claims (settling ≤5 cycles, errors <±0.1 CAD adaptive / <±0.5 CAD feedforward) are obtained by closing the loop on the identical calibrated model used for controller synthesis. No open-loop transient validation (measured vs. predicted CA50 during the boost/EGR steps) or closed-loop engine experiments are reported, so the metrics are not independent of the model assumptions.

    Authors: We agree that the reported controller metrics are obtained from simulation closing the loop on the calibrated model used for synthesis. This is standard practice for initial verification of model-based controller designs. The underlying model was calibrated on experimental engine data at high EGR and boost levels. We will revise the abstract and simulation section to explicitly state that results are simulation-based on the design model and to note the absence of hardware closed-loop experiments as a limitation of the current study. revision: partial

  2. Referee: [Model calibration and validation] Model-calibration section: the manuscript states that the simplified model is “calibrated and validated using … experimental data,” yet no quantitative fit metrics (RMS CA50 error, R², or residual plots) are supplied for the transient conditions exercised by the controllers. This leaves the central assumption that the model remains sufficiently accurate during unmeasured fast transients untested.

    Authors: The calibration used experimental data at the relevant high-dilution and boost conditions. We acknowledge that explicit quantitative transient fit metrics (RMS error, R², residuals) for the specific boost/EGR steps are not reported. In the revised manuscript we will add these metrics and residual plots for the transient conditions to strengthen support for model accuracy during fast transients. revision: yes

standing simulated objections not resolved
  • Closed-loop hardware experiments on the physical engine, which were not performed in this study.

Circularity Check

0 steps flagged

No significant circularity; model calibrated to external data with independent simulation testing

full rationale

The paper calibrates its nonlinear combustion phasing model (knock integral + burn duration + Wiebe) to experimental data under high EGR/boost conditions and reports separate validation. Controller performance metrics (CA50 settling ≤5 cycles, steady-state errors <±0.1 CAD adaptive / <±0.5 CAD feedforward) are obtained from closed-loop simulations on that model, which is standard model-based design practice and does not reduce any claimed result to the fitted constants by construction. No self-definitional equations, fitted-input predictions, or load-bearing self-citations appear in the derivation chain. The work remains self-contained against the external experimental benchmarks used for calibration/validation.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The model rests on standard combustion-modeling assumptions and a set of parameters fitted to experimental data whose exact values and fitting procedure are not visible in the abstract.

free parameters (3)
  • Knock-integral threshold and scaling constants
    Calibrated to match ignition timing on the supplied experimental data set.
  • Burn-duration coefficients
    Fitted for high-EGR, high-boost conditions.
  • Wiebe shape parameters
    Adjusted during model simplification for control use.
axioms (1)
  • domain assumption The Wiebe function form accurately describes mass-fraction-burned profiles under the tested dilution and boost levels.
    Invoked when the combined model is assembled and simplified.

pith-pipeline@v0.9.0 · 5749 in / 1402 out tokens · 23955 ms · 2026-05-24T19:19:58.771245+00:00 · methodology

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Reference graph

Works this paper leans on

35 extracted references · 35 canonical work pages

  1. [1]

    Heywood, J. B. Internal Combustion Engine Fundamentals. Indian Edition 2011. New York: McGraw-Hill Companies, Inc, 2011, p. 390, 501 – 502, 586 – 592

    work page 2011

  2. [2]

    Introduction to Internal Combustion Engines

    Stone R. Introduction to Internal Combustion Engines. Third Edition. Warrendale: Society of Automotive Engineers, Inc., 1999, p. 97, 424

    work page 1999

  3. [3]

    M., Bohac S

    Ickes A. M., Bohac S. V., and Assanis D. N. Effect of Fuel Cetane Number on a Premixed Diesel Combustion Mode. International Journal of Engine Research, 2009, 10(4): 251-263

    work page 2009

  4. [4]

    A Diesel Engine Combustion Phasing Optimization Using a Model Guided Extremum Seeking Approach

    Tan Q., Divekar P., Tan Y., et al. A Diesel Engine Combustion Phasing Optimization Using a Model Guided Extremum Seeking Approach. 35th Chinese Control Conference, Chengdu, China, 2837-2842, 2016, New York: IEEE Control Systems Society

    work page 2016

  5. [5]

    and Saito, T

    Kataoka, M., Terazawa, Y., Hayashibara, H. and Saito, T. Combustion control apparatus for an engine. U.S. Patent 6,964,256, issued November 15, 2005

    work page 2005

  6. [6]

    Combustion control apparatus of diesel engine

    Kataoka, M., Kobayashi, A., and Saito, T. Combustion control apparatus of diesel engine. U.S. Patent 6,725,829, issued April 27, 2004. 37

    work page 2004

  7. [7]

    Diesel combustion control with closed-loop control of the injection strategy

    Schnorbus, T., Pischinger, S., Körfer, T., et al. Diesel combustion control with closed-loop control of the injection strategy. SAE Technical Paper No. 2008-01- 0651, 2008

    work page 2008

  8. [8]

    R., Mannal, S

    Saracino, R., Gaballo, M. R., Mannal, S. et al. Cylinder pressure-based closed loop combustion control: A valid support to fulfill current and future requirements of diesel powertrain systems. SAE Technical Paper No. 2015-24-2423, 2015

    work page 2015

  9. [9]

    Relationship Between Ignition Processes and the Lift-Off Length of Diesel Fuel Jets

    Pickett, L., Siebers, D., and Idicheria, C. Relationship Between Ignition Processes and the Lift-Off Length of Diesel Fuel Jets. SAE Technical Paper 2005-01-3843, doi:10.4271/2005-01-3843

    work page doi:10.4271/2005-01-3843 2005

  10. [10]

    The Influence of Charge Dilution and Injection Timing on Low-Temperature Diesel Combustion and Emissions

    Kook, S., Bae, C., Miles, P., et al. The Influence of Charge Dilution and Injection Timing on Low-Temperature Diesel Combustion and Emissions. SAE Technical Paper 2005-01-3837, doi:10.4271/2005-01-3837

    work page doi:10.4271/2005-01-3837 2005

  11. [11]

    A Predictive Real Time NOx Model for Conventional and Partially Premixed Diesel Combustion

    Andersson, M., Johansson, B., Hultqvist, A., et al. A Predictive Real Time NOx Model for Conventional and Partially Premixed Diesel Combustion. SAE Technical Paper 2006-01-3329, doi:10.4271/2006-01-3329

    work page doi:10.4271/2006-01-3329 2006

  12. [12]

    Direct Injection Diesel Engine Rate of Heat Release Prediction using Universal Load Correction 38 Factor in Double Wiebe Function for Performance Simulation

    Loganathan, S., Murali Manohar, R., Thamaraikannan, R., et al. Direct Injection Diesel Engine Rate of Heat Release Prediction using Universal Load Correction Factor in Double Wiebe Function for Performance Simulation. SAE Technical Paper 2011-01-2456, doi:10.4271/2011-01-2456

    work page doi:10.4271/2011-01-2456 2011

  13. [13]

    Modeling of Diesel Engine Components for Model-Based Control (Second Report): Prediction of Combustion with High Speed Calculation Diesel Combustion Model

    Suzuki, Y., Kusaka, J., Ogawa, M., et al. Modeling of Diesel Engine Components for Model-Based Control (Second Report): Prediction of Combustion with High Speed Calculation Diesel Combustion Model. SAE Technical Paper 2011-01- 2044, doi:10.4271/2011-01-2044

    work page doi:10.4271/2011-01-2044 2011

  14. [14]

    M., et al

    Hernandez JJ., Sanz-Argent J., Carot J. M., et al. Ignition Delay Time Correlations for a Diesel Fuel with Application to Engine Combustion Modelling. International Journal of Engine Research, 2010, 11(3):199-206

    work page 2010

  15. [15]

    Modeling of HCCI engine combustion for control analysis

    Bengtsson J., Gafvert M., Strandh P. Modeling of HCCI engine combustion for control analysis. In: 43rd IEEE Conference on Decision and Control, Atlantis, Paradise Island, Bahamas, 2004, 2: 1682 - 1687, 2004, New York: IEEE

    work page 2004

  16. [16]

    Correlation of Autoignition Phenomena in Internal Combustion Engines and Rapid Compression Machines

    Livengood JC., and Wu PC. Correlation of Autoignition Phenomena in Internal Combustion Engines and Rapid Compression Machines. Symposium (International) on Combustion, 1955, 5(1): 347 – 356

    work page 1955

  17. [17]

    Combustion Control of Diesel Engines Using Injection Timing

    Hillion, M., Buhlbuck, H., Chauvin, J., et al. Combustion Control of Diesel Engines Using Injection Timing. SAE Technical Paper 2009-01-0367, doi:10.4271/2009-01-0367. 38

    work page doi:10.4271/2009-01-0367 2009

  18. [18]

    Development and Application of a 0D D.I

    Lafossas, F., Marbaix, M., and Menegazzi, P. Development and Application of a 0D D.I. Diesel combustion model for Emissions Prediction. SAE Technical Paper 2007-01-1841, doi:10.4271/2007-01-1841

    work page doi:10.4271/2007-01-1841 2007

  19. [19]

    Multi-Zone Predictive Modeling of Common Rail Multi-Injection Diesel Engines

    Arsie, I., Di Genova, F., Mogavero, A., et al. Multi-Zone Predictive Modeling of Common Rail Multi-Injection Diesel Engines. SAE Technical Paper 2006-01- 1384, doi:10.4271/2006-01-1384

    work page doi:10.4271/2006-01-1384 2006

  20. [20]

    Modeling and Experimental Study of an HCCI Engine for Combustion Timing Control

    Shahbakhti M. Modeling and Experimental Study of an HCCI Engine for Combustion Timing Control. PhD dissertation, University of Alberta, Canada, 2009

    work page 2009

  21. [21]

    Thermodynamic based modeling for nonlinear control of combustion

    Bettis J.B. Thermodynamic based modeling for nonlinear control of combustion. Master Thesis, Missouri University of Science and Technology, MO, USA, 2010

    work page 2010

  22. [22]

    and Stola, F., Instantaneous engine speed measurement and processing for MFB50 evaluation

    Ponti, F., Ravaglioli, V., Serra, G. and Stola, F., Instantaneous engine speed measurement and processing for MFB50 evaluation. SAE International Journal of Engines, 2(2), pp.235-244, 2010

    work page 2010

  23. [23]

    and Serra, G

    Ponti, F., Ravaglioli, V., Moro, D. and Serra, G. MFB50 on-board estimation methodology for combustion control. Control Engineering Practice, 21(12), pp.1821-1829, 2013

    work page 2013

  24. [24]

    Cylinder Pressure-Based Control in Heavy-Duty EGR Diesel Engines Using a Virtual Heat Release and Emission Sensor

    Willems, F., Doosje, E., Engels, F., et al. Cylinder Pressure-Based Control in Heavy-Duty EGR Diesel Engines Using a Virtual Heat Release and Emission Sensor. SAE Technical Paper 2010-01-0564, doi: 10.4271/2010-01-0564

    work page doi:10.4271/2010-01-0564 2010

  25. [25]

    Development of engine control using the in-cylinder pressure signal in a high speed direct injection diesel engine

    Yu S., Choi H., Cho S., et al. Development of engine control using the in-cylinder pressure signal in a high speed direct injection diesel engine. International Journal of Automotive Technology, 2013, 14(2): 175-182

    work page 2013

  26. [26]

    Closed-loop diesel engine combustion phasing control based on crankshaft torque measurements

    Thor M., Egardt B., McKelvey T., et al. Closed-loop diesel engine combustion phasing control based on crankshaft torque measurements. Control Engineering Practice, 2014, 33: 115-124

    work page 2014

  27. [27]

    Fuzzy Logic Control of Diesel Combustion Phasing Using Ion Current Signal

    Badawy T., Khaled N., and Henein N. Fuzzy Logic Control of Diesel Combustion Phasing Using Ion Current Signal. ASME 2012 Internal Combustion Engine Division Spring Technical Conference, Torino, Piemonte, Italy, 645-658, 2012, New York: ASME

    work page 2012

  28. [28]

    A method for combustion phasing control using cylinder pressure measurement in a CRDI diesel engine

    Yoon M., Lee K., and Sunwoo M. A method for combustion phasing control using cylinder pressure measurement in a CRDI diesel engine. Mechatronics, 2007, 17(9): 469-479. 39

    work page 2007

  29. [29]

    Finesso and E

    R. Finesso and E. Spessa, A Feed-Forward Approach for the Real-Time Estimation and Control of MFB50 and SOI In Diesel Engines. SAE International Journal of Engines, 7(1), pp.528-549, 2014

    work page 2014

  30. [30]

    Adaptive Control of a Recompression Four-Cylinder HCCI engine

    Larimore J., Jade S., Hellstrom E., et al. Adaptive Control of a Recompression Four-Cylinder HCCI engine. IEEE Transactions on Control Systems Technology, 2015, 23(6): 2144-2154

    work page 2015

  31. [31]

    M., Shaver G

    Hall C. M., Shaver G. M., Chauvin J., et al. Combustion phasing model for control of a gasoline-ethanol fueled SI engine with variable valve timing. American Control Conference (ACC), 2012, Montreal, QC, Canada, 2012

    work page 2012

  32. [32]

    A Mean-value Model for Control of Homogeneous Charge Compression Ignition (HCCI) Engines

    Rausen D.J., Stefanopoulou A.G., Kang J.-M., et al. A Mean-value Model for Control of Homogeneous Charge Compression Ignition (HCCI) Engines. Journal of Dynamic Systems, Measurement and Control, 2004, 127(3): 355-362

    work page 2004

  33. [33]

    Analysis and Control of Compression-Ignition and Spark-Ignited Engines Operations with Dual-Fuel Combustion Strategy

    Kassa M. Analysis and Control of Compression-Ignition and Spark-Ignited Engines Operations with Dual-Fuel Combustion Strategy. PhD dissertation, Illinois Institute of Technology, IL, USA, 2017

    work page 2017

  34. [34]

    Modeling the Impact of Natural Gas Variation on Combustion in a Dual-Fuel Engine Master Thesis, Illinois Institute of Technology, IL, USA, 2017

    Hulbert M. Modeling the Impact of Natural Gas Variation on Combustion in a Dual-Fuel Engine Master Thesis, Illinois Institute of Technology, IL, USA, 2017

    work page 2017

  35. [35]

    A., and Gallestey E

    Hokayem P. A., and Gallestey E. Lecture Notes on Nonlinear Systems and Control. http://control.ee.ethz.ch/~apnoco/Lectures2017/NLSC_lecture_notes_2017.pdf. (2017, accessed 24 September 2017)

    work page 2017