×

CasADi: a software framework for nonlinear optimization and optimal control. (English) Zbl 1411.90004

Summary: We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by differential equations, i.e. optimal control problems. CasADi is written in self-contained C++, but is most conveniently used via full-featured interfaces to Python, MATLAB or Octave. Since its inception in late 2009, it has been used successfully for academic teaching as well as in applications from multiple fields, including process control, robotics and aerospace. This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years.

MSC:

90-04 Software, source code, etc. for problems pertaining to operations research and mathematical programming
49-04 Software, source code, etc. for problems pertaining to calculus of variations and optimal control
65K05 Numerical mathematical programming methods
PDF BibTeX XML Cite
Full Text: DOI Link

References:

[1] Albersmeyer, J.; Diehl, M., The lifted Newton method and its application in optimization, SIAM J. Optim., 20, 1655-1684, (2010) · Zbl 1198.90396
[2] Albert, A.; Imsland, L.; Haugen, J., Numerical optimal control mixing collocation with single shooting: a case study, IFAC-PapersOnLine, 49, 290-295, (2016)
[3] Alexandrescu, A.: Modern C++ Design. Addison-Wesley, Reading (2001)
[4] Anderson, E., et al.: LAPACK Users’ Guide, 3rd edn. SIAM, Philadelphia (1999) · Zbl 0755.65028
[5] Andersson, J.: A General-Purpose Software Framework for Dynamic Optimization. Ph.D. thesis, Arenberg Doctoral School, KU Leuven (2013)
[6] Andersson, J., Kozma, A., Gillis, J., Diehl, M.: CasADi User Guide. http://guide.casadi.org. Accessed 2 June 2018
[7] Andersson, LE; Scibilia, F.; Imsland, L., An estimation-forecast set-up for iceberg drift prediction, Cold Reg. Sci. Technol., 131, 88-107, (2016)
[8] Axelsson, M., Magnusson, F., Henningsson, T.: A framework for nonlinear model predictive control in jmodelica.org. In: 11th International Modelica Conference, 118, pp. 301-310. Linköping University Electronic Press (2015)
[9] Bonmin. https://projects.coin-or.org/Bonmin. Accessed 1 Feb 2017
[10] Belkhir, F.; Cabo, DK; Feigner, F.; Frey, G., Optimal startup control of a steam power plant using the Jmodelica Platform, IFAC-PapersOnLine, 48, 204-209, (2015)
[11] Belousov, B., Neumann, G., Rothkopf, C.A., Peters, J.R.: Catching heuristics are optimal control policies. In: Lee, D.D., Sugiyama, M., Luxburg, U.V., Guyon, I., Garnett, R. (eds.) Advances in Neural Information Processing Systems, pp. 1426-1434. Curran Associates, Red Hook, NY (2016)
[12] Berntorp, K., Magnusson, F.: Hierarchical predictive control for ground-vehicle maneuvering. In: American Control Conference (ACC), pp. 2771-2776 (2015)
[13] Berx, K., Gadeyne, K., Dhadamus, M., Pipeleers, G., Pinte, G.: Model-based gearbox synthesis. In: Mechatronics Forum International Conference, pp. 599-605 (2014)
[14] Biegler, L., Solution of dynamic optimization problems by successive quadratic programming and orthogonal collocation, Comput. Chem. Eng., 8, 243-248, (1984)
[15] Bock, H.; Eich, E.; Schlöder, J.; Strehmel, K. (ed.), Numerical solution of constrained least squares boundary value problems in differential-algebraic equations, (1988), Leipzig · Zbl 0682.65047
[16] Bock, H., Plitt, K.: A multiple shooting algorithm for direct solution of optimal control problems. In: IFAC World Congress, pp. 242-247. Pergamon Press (1984)
[17] Boiroux, D., Hagdrup, M., Mahmoudi, Z., Madsen, H., Bagterp, J., et al.: An ensemble nonlinear model predictive control algorithm in an artificial pancreas for people with type 1 diabetes. In: European Control Conference (ECC), pp. 2115-2120 (2016)
[18] Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004) · Zbl 1058.90049
[19] Bremer, J.; Rätze, KH; Sundmacher, K., Co\(_{2}\) methanation: optimal start-up control of a fixed-bed reactor for power-to-gas applications, AIChE J., 63, 23-31, (2017)
[20] Büskens, C., Wassel, D.: Modeling and Optimization in Space Engineering, Chapter. The ESA NLP Solver WORHP. Springer, Berlin (2012) · Zbl 1365.90007
[21] Byrd, RH; Nocedal, J.; Waltz, RA; Pillo, G. (ed.); Roma, M. (ed.), KNITRO: an integrated package for nonlinear optimization, 35-59, (2006), Berlin · Zbl 1108.90004
[22] casiopeia. https://github.com/adbuerger/casiopeia. Accessed 19 May 2017
[23] Clp. https://projects.coin-or.org/Clp. Accessed 1 Feb 2017
[24] CppAD. http://www.coin-or.org/CppAD. Accessed 11 May 2012
[25] Cabianca, L.: Advanced techniques for robust dynamic optimization of chemical reactors. Master’s thesis, Politecnico Milano (2014)
[26] Codas, A.; Jahanshahi, E.; Foss, B., A two-layer structure for stabilization and optimization of an oil gathering network, IFAC-PapersOnLine, 49, 931-936, (2016)
[27] Cuthrell, J.; Biegler, L., Simultaneous optimization and solution methods for batch reactor profiles, Comput. Chem. Eng., 13, 49-62, (1989)
[28] Davis, T.: Direct Methods for Sparse Linear Systems. SIAM, Philadelphia (2006) · Zbl 1119.65021
[29] Coninck, R.; Helsen, L., Practical implementation and evaluation of model predictive control for an office building in Brussels, Energy Build., 111, 290-298, (2016)
[30] Coninck, R.; Helsen, L., Quantification of flexibility in buildings by cost curves—methodology and application, Appl. Energy, 162, 653-665, (2016)
[31] Coninck, R.; Magnusson, F.; Åkesson, J.; Helsen, L., Toolbox for development and validation of grey-box building models for forecasting and control, J. Build. Perform. Simul., 9, 288-303, (2016)
[32] Debrouwere, F., Loock, W.V., Pipeleers, G., Diehl, M., Schutter, J.D.: Time-optimal path following for robots with object collision avoidance using Lagrangian duality. In: 2012 Benelux Meeting on Systems and Control (2013)
[33] Debrouwere, F., Van Loock, W., Pipeleers, G., Swevers, J.: Time-optimal tube following for robotic manipulators. In: 2014 IEEE 13th International Workshop on Advanced Motion Control (AMC), pp. 392-397 (2014)
[34] Domahidi, A., Zgraggen, A., Zeilinger, M., Morari, M., Jones, C.: Efficient interior point methods for multistage problems arising in receding horizon control. In: IEEE Conference on Decision and Control (CDC), pp. 668 - 674. Maui (2012)
[35] Dunning, I., Huchette, J., Lubin, M.: JuMP: a modeling language for mathematical optimization. arXiv:1508.01982 [math.OC] (2015) · Zbl 1368.90002
[36] Durand, H.; Ellis, M.; Christofides, PD, Economic model predictive control designs for input rate-of-change constraint handling and guaranteed economic performance, Comput. Chem. Eng., 92, 18-36, (2016)
[37] Ellis, M., Christofides, P.D.: On closed-loop economic performance under Lyapunov-based economic model predictive control. In: American Control Conference (ACC), pp. 1778-1783 (2016)
[38] Erhard, M.; Horn, G.; Diehl, M., A quaternion-based model for optimal control of an airborne wind energy system, ZAMM J. Appl. Math. Mech. Z. Angew. Math. Mech., 97, 7-24, (2017)
[39] Ersdal, AM; Fabozzi, D.; Imsland, L.; Thornhill, NF, Model predictive control for power system frequency control taking into account imbalance uncertainty, IFAC Proc. Vol., 47, 981-986, (2014)
[40] Ersdal, AM; Imsland, L.; Uhlen, K., Model predictive load-frequency control, IEEE Trans. Power Syst., 31, 777-785, (2016)
[41] Feng, X., Houska, B.: Real-time algorithm for self-reflective model predictive control. arXiv:1611.02408 (2016)
[42] Ferreau, H.: qpOASES—an open-source implementation of the online active set strategy for fast model predictive control. In: Workshop on Nonlinear Model Based Control—Software and Applications, pp. 29-30 (2007)
[43] Fiacco, AV; Ishizuka, Y., Sensitivity and stability analysis for nonlinear programming, Ann. Oper. Res., 27, 215-235, (1990) · Zbl 0718.90086
[44] Fouquet, M., Guéguen, H., Faille, D., Dumur, D.: Hybrid dynamic optimization of power plants using sum-up rounding and adaptive mesh refinement. In: IEEE Conference on Control Applications, pp. 316-321 (2014)
[45] Fourer, R., Gay, D.M., Kernighan, B.W.: AMPL: a modeling language for mathematical programming, 2nd edn. Thomson, Stamford (2003) · Zbl 0701.90062
[46] Frasch, J.V., Vukov, M., Ferreau, H., Diehl, M.: A dual Newton strategy for the efficient solution of sparse quadratic programs arising in SQP-based nonlinear MPC (2013). Optimization Online 3972
[47] Frasch, JV; Wirsching, L.; Sager, S.; Bock, HG, Mixed-level iteration schemes for nonlinear model predictive control, IFAC Proc. Vol., 45, 138-144, (2012)
[48] Frison, G., Sorensen, H., Dammann, B., Jorgensen, J.: High-performance small-scale solvers for linear model predictive control. In: European Control Conference (ECC), pp. 128-133 (2014)
[49] Gabiccini, M., Artoni, A., Pannocchia, G., Gillis, J.: A computational framework for environment-aware robotic manipulation planning. In: Bicchi, A., Burgard, W. (eds.) Robotics Research. Proceedings in Advanced Robotics, vol 3. Springer, Cham (2018)
[50] Gebremedhin, AH; Manne, F.; Pothen, A., What color is your Jacobian? Graph coloring for computing derivatives, SIAM Rev., 47, 629-705, (2005) · Zbl 1076.05034
[51] Geebelen, K., Wagner, A., Gros, S., Swevers, J., Diehl, M.: Moving horizon estimation with a huber penalty function for robust pose estimation of tethered airplanes. In: American Control Conference (ACC), pp. 6169-6174 (2013)
[52] Gertz, E.; Wright, S., Object-oriented software for quadratic programming, ACM Trans. Math. Softw., 29, 58-81, (2003) · Zbl 1068.90586
[53] Gesenhues, J., Hein, M., Habigt, M., Mechelinck, M., Albin, T., Abel, D.: Nonlinear object-oriented modeling based optimal control of the heart. In: European Control Conference (ECC), pp. 2108-2114 (2016)
[54] Giering, R., Kaminski, T.: Automatic sparsity detection implemented as a source-to-source transformation. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) Lecture Notes in Computer Science, vol. 3994, pp. 591-598. Springer, Berlin, Heidelberg (2006)
[55] Giles, M.: Collected matrix derivative results for forward and reverse mode algorithmic differentiation. In: Bischof, C.H., Bücker, H.M., Hovland, P., Naumann, U., Utke, J. (eds.) Advances in Automatic Differentiation, pp. 35-44. Springer, Berlin (2008) · Zbl 1154.65308
[56] Gill, P.; Murray, W.; Saunders, M., SNOPT: an SQP algorithm for large-scale constrained optimization, SIAM Rev., 47, 99-131, (2005) · Zbl 1210.90176
[57] Gillis, J.: Practical methods for approximate robust periodic optimal control of nonlinear mechanical systems. Ph.D. thesis, Arenberg Doctoral School, KU Leuven (2015)
[58] Griewank, A., Juedes, D., Mitev, H., Utke, J., Vogel, O., Walther, A.: ADOL-C: a package for the automatic differentiation of algorithms written in C, C++. Tech. rep., Technical University of Dresden, Institute of Scientific Computing and Institute of Geometry (1999). Updated version of the paper published in ACM Transactions on Mathematical Software, vol. 22, pp. 131-167 (1996) · Zbl 0884.65015
[59] Griewank, A.; Mitev, C., Detecting Jacobian sparsity patterns by Bayesian probing, Math. Program., 93, 1-25, (2002) · Zbl 1012.65040
[60] Griewank, A., Walther, A.: Evaluating Derivatives, 2nd edn. SIAM, Philadelphia (2008) · Zbl 1159.65026
[61] Gros, S.: A distributed algorithm for NMPC-based wind farm control. In: IEEE Conference on Decision and Control (CDC), pp. 4844-4849 (2014)
[62] Gros, S., Diehl, M.: Modeling of airborne wind energy systems in natural coordinates. In: Ahrens, U., Diehl, M., Schmehl, R. (eds.) Airborne Wind Energy. Springer, Berlin (2013)
[63] Gros, S., Zanon, M., Diehl, M.: Baumgarte stabilisation over the SO (3) rotation group for control. In: IEEE Conference on Decision and Control (CDC), pp. 620-625 (2015)
[64] Gurobi Optimizer Reference Manual Version 7.0. https://www.gurobi.com. Accessed 2 June 2018
[65] HSL. A collection of Fortran codes for large scale scientific computation. http://www.hsl.rl.ac.uk. Accessed 2 June 2018
[66] Hanssen, KG; Foss, B., Scenario based implicit dual model predictive control, IFAC-PapersOnLine, 48, 416-421, (2015)
[67] Hart, W.; Watson, JP; Woodruff, D., Pyomo: modeling and solving mathematical programs in Python, Math. Program. Comput., 3, 1-42, (2011)
[68] Haugen, J.; Imsland, L., Monitoring moving objects using aerial mobile sensors, IEEE Trans. Control Syst. Technol., 24, 475-486, (2016)
[69] Herrmann, S., Utschick, W.: Availability and interpretability of optimal control for criticality estimation in vehicle active safety. In: Design, Automation & Test in Europe Conference & Exhibition (DATE), pp. 415-420 (2016)
[70] Hindmarsh, A.; etal., SUNDIALS: suite of nonlinear and differential/algebraic equation solvers, ACM Trans. Math. Softw., 31, 363-396, (2005) · Zbl 1136.65329
[71] Holmqvist, A.; Magnusson, F., Open-loop optimal control of batch chromatographic separation processes using direct collocation, J. Process Control, 46, 55-74, (2016)
[72] Holmqvist, A.; etal., Dynamic parameter estimation of atomic layer deposition kinetics applied to in situ quartz crystal microbalance diagnostics, Chem. Eng. Sci., 111, 15-33, (2014)
[73] Horn, G., Diehl, M.: Numerical trajectory optimization for airborne wind energy systems described by high fidelity aircraft models. In: Ahrens, U., Diehl, M., Schmehl, R. (eds.) Airborne Wind Energy, pp. 205-218. Springer, Berlin, Heidelberg (2013)
[74] IBM Corp.: IBM ILOG CPLEX V12.1, User’s Manual for CPLEX (2009)
[75] Janka, D.; Kirches, C.; Sager, S.; Wchter, A., An SR1/BFGS SQP algorithm for nonconvex nonlinear programs with block-diagonal Hessian matrix, Math. Program. Comput., 8, 435-459, (2016) · Zbl 1391.90575
[76] Kirches, C.: Fast numerical methods for mixed-integer nonlinear model-predictive control. Ph.D. thesis, Ruprecht-Karls-Universität Heidelberg (2010) · Zbl 1312.65101
[77] Krishnamoorthy, D.; Foss, B.; Skogestad, S., Real-time optimization under uncertainty applied to a gas lifted well network, Processes, 4, 52, (2016)
[78] Larsson, P.O., Casella, F., Magnusson, F., Andersson, J., Diehl, M., Akesson, J.: A framework for nonlinear model-predictive control using object-oriented modeling with a case study in power plant start-up. In: IEEE Conference on Computer Aided Control System Design (CACSD), pp. 346-351 (2013)
[79] Lattner, C., Adve, V.: LLVM: a compilation framework for lifelong program analysis & transformation. In: International Symposium on Code Generation and Optimization (2004)
[80] Le, T.T., Truong, B.D., Jost, F., Le, C.P., Halvorsen, E., Sager, S.: Synthesis of optimal controls and numerical optimization for the vibration-based energy harvesters. arXiv:1608.08885 (2016)
[81] Leek, V.: An Optimal Control Toolbox for MATLAB Based on CasADi. Master’s thesis, Linköping University (2016)
[82] Leineweber, D.: Efficient reduced SQP methods for the optimization of chemical processes described by large sparse DAE models, Fortschritt-Berichte VDI Reihe 3, Verfahrenstechnik, vol. 613. VDI Verlag, Düsseldorf (1999)
[83] Licitra, G., Sieberling, S., Engelen, S., Williams, P., Ruiterkamp, R., Diehl, M.: Optimal control for minimizing power consumption during holding patterns for airborne wind energy pumping system. In: European Control Conference (ECC), pp. 1574-1579 (2016)
[84] Liu, M.; Tan, Y.; Padois, V., Generalized hierarchical control, Auton. Robots, 40, 17-31, (2016)
[85] Lopes, V.V., et al.: On the use of markov chain models for the analysis of wind power time-series. In: Conference on Environment and Electrical Engineering (EEEIC), pp. 770-775 (2012)
[86] Lucia, S.; Andersson, JA; Brandt, H.; Bouaswaig, A.; Diehl, M.; Engell, S., Efficient robust economic nonlinear model predictive control of an industrial batch reactor, IFAC Proc. Vol., 47, 11093-11098, (2014)
[87] Lucia, S., Engell, S.: Control of towing kites under uncertainty using robust economic nonlinear model predictive control. In: European Control Conference (ECC), pp. 1158-1163 (2014)
[88] Lucia, S.; Paulen, R., Robust nonlinear model predictive control with reduction of uncertainty via robust optimal experiment design, IFAC Proc. Vol., 47, 1904-1909, (2014)
[89] Lucia, S., Paulen, R., Engell, S.: Multi-stage nonlinear model predictive control with verified robust constraint satisfaction. In: IEEE Conference on Decision and Control (CDC), pp. 2816-2821 (2014)
[90] Lucia, S.; Schliemann-Bullinger, M.; Findeisen, R.; Bullinger, E., A set-based optimal control approach for pharmacokinetic/pharmacodynamic drug dosage design, IFAC-PapersOnLine, 49, 797-802, (2016)
[91] Lucia, S., Tătulea-Codrean, A., Schoppmeyer, C., Engell, S.: An environment for the efficient testing and implementation of robust nmpc. In: IEEE Conference on Control Applications, pp. 1843-1848 (2014)
[92] Lucia, S.; Tătulea-Codrean, A.; Schoppmeyer, C.; Engell, S., Rapid development of modular and sustainable nonlinear model predictive control solutions, Control Eng. Pract., 60, 51-62, (2017)
[93] Lundahl, K., Lee, C.F., Frisk, E., Nielsen, L.: Path-dependent rollover prevention for critical truck maneuvers. In: Symposium of the International Association for Vehicle System Dynamics (IAVSD 2015), p. 317. CRC Press (2016)
[94] Lynn, LL; Parkin, ES; Zahradnik, RL, Near-optimal control by trajectory approximations, I&EC Fundam., 9, 58-63, (1970)
[95] Lynn, LL; Zahradnik, RL, The use of orthogonal polynomials in the near-optimal control of distributed systems by trajectory approximation, Int. J. Control, 12, 1079-1087, (1970) · Zbl 0203.46804
[96] mpc-tools-casadi. https://bitbucket.org/rawlings-group/mpc-tools-casadi. Accessed 19 May 2017
[97] Magnusson, F.; Åkesson, J., Dynamic optimization in jmodelica.org, Processes, 3, 471-496, (2015)
[98] Marcucci, T.; Gabiccini, M.; Artoni, A., A two-stage trajectory optimization strategy for articulated bodies with unscheduled contact sequences, IEEE Robot. Autom. Lett., 2, 104-111, (2017)
[99] Maree, J., Imsland, L.: Multi-objective predictive control for non steady-state operation. In: European Control Conference (ECC), pp. 1541-1546 (2013)
[100] Maree, J.; Imsland, L., On multi-objective economic predictive control for cyclic process operation, J. Process Control, 24, 1328-1336, (2014)
[101] Maree, J.P., Imsland, L.: Optimal control strategies for oil production under gas coning conditions. In: IEEE Conference on Control Applications, pp. 572-578 (2014)
[102] Martí, R., et al.: An efficient distributed algorithm for multi-stage robust nonlinear predictive control. In: European Control Conference (ECC), pp. 2664-2669 (2015)
[103] Merz, M., Johansen, T.A.: Feasibility study of a circularly towed cable-body system for uav applications. In: Conference on Unmanned Aircraft Systems (ICUAS), pp. 1182-1191 (2016)
[104] Minko, T., Wisniewski, R., Bendtsen, J.D., Izadi-Zamanabadi, R.: Non-linear model predictive supervisory controller for building, air handling unit with recuperator and refrigeration system with heat waste recovery. In: IEEE Conference on Control Applications, pp. 1274-1281 (2016)
[105] Mukkula, ARG; Paulen, R., Model-based design of optimal experiments for nonlinear systems in the context of guaranteed parameter estimation, Comput. Chem. Eng., 99, 198-213, (2017)
[106] Naumann, U.: The Art of Differentiating Computer Programs: An Introduction to Algorithmic Differentiation. No. 24 in Software, Environments, and Tools. SIAM, Philadelphia (2012) · Zbl 1275.65015
[107] Nezhadali, V.; Eriksson, L., A framework for modeling and optimal control of automatic transmission systems, IFAC-PapersOnLine, 48, 285-291, (2015)
[108] Nezhadali, V.; Eriksson, L., Optimal control of engine controlled gearshift for a diesel-electric powertrain with backlash, IFAC-PapersOnLine, 49, 762-768, (2016)
[109] Nimmegeers, P., Telen, D., Beetens, M., Logist, F., Van Impe, J.: Parametric uncertainty propagation for robust dynamic optimization of biological networks. In: American Control Conference (ACC), pp. 6929-6934 (2016)
[110] Nimmegeers, P.; Telen, D.; Logist, F.; Impe, J., Dynamic optimization of biological networks under parametric uncertainty, BMC Syst. Biol., 10, 86, (2016)
[111] Pannocchia, G.; Gabiccini, M.; Artoni, A., Offset-free MPC explained: novelties, subtleties, and applications, IFAC-PapersOnLine, 48, 342-351, (2015)
[112] Patil, S., Kahn, G., Laskey, M., Schulman, J., Goldberg, K., Abbeel, P.: Scaling up gaussian belief space planning through covariance-free trajectory optimization and automatic differentiation. In: Algorithmic Foundations of Robotics XI, pp. 515-533. Springer, Berlin (2015)
[113] Poland, J., Stadler, K.S.: Stochastic optimal planning of solar thermal power. In: Les Antibes J. (ed.) IEEE Conference on Control Applications, pp. 593-598 (2014)
[114] Reiter, A., Müller, A., Gattringer, H.: Inverse kinematics in minimum-time trajectory planning for kinematically redundant manipulators. In: Annual Conference of the IEEE Industrial Electronics Society (IECON), pp. 6873-6878 (2016)
[115] Rostampour, V.; Esfahani, PM; Keviczky, T., Stochastic nonlinear model predictive control of an uncertain batch polymerization reactor, IFAC-PapersOnLine, 48, 540-545, (2015)
[116] Scholz, T.; Raischel, F.; Lopes, VV; Lehle, B.; Wächter, M.; Peinke, J.; Lind, PG, Parameter-free resolution of the superposition of stochastic signals, Phys. Lett. A, 381, 194-206, (2017) · Zbl 1372.60055
[117] Scott, P., Thiébaux, S.: Distributed multi-period optimal power flow for demand response in microgrids. In: ACM Conference on Future Energy Systems, pp. 17-26 (2015)
[118] Sirmatel, I.I., Geroliminis, N.: Model predictive control of large-scale urban networks via perimeter control and route guidance actuation. In: IEEE Conference on Decision and Control (CDC), pp. 6765-6770 (2016)
[119] Sivertsson, M.; Eriksson, L., Optimal stationary control of diesel engines using periodic control, J. Automob. Eng., 231, 457-475, (2017)
[120] Skjong, E., et al.: Management of harmonic propagation in a marine vessel by use of optimization. In: IEEE Transportation Electrification Conference and Expo (ITEC), pp. 1-8 (2015)
[121] St John, PC; Doyle, FJ, Estimating confidence intervals in predicted responses for oscillatory biological models, BMC Syst. Biol., 7, 71, (2013)
[122] Thangavel, S., Lucia, S., Paulen, R., Engell, S.: Towards dual robust nonlinear model predictive control: A multi-stage approach. In: American Control Conference (ACC), pp. 428-433 (2015)
[123] Trägårdh, M.; etal., Input estimation for drug discovery using optimal control and markov chain Monte Carlo approaches, J. Pharmacokinet. Pharmacodyn., 43, 207-221, (2016)
[124] Utstumo, T., Berge, T.W., Gravdahl, J.T.: Non-linear model predictive control for constrained robot navigation in row crops. In: IEEE Conference on Industrial Technology (ICIT), pp. 357-362 (2015)
[125] Duijkeren, N.; Keviczky, T.; Nilsson, P.; Laine, L., Real-time NMPC for semi-automated highway driving of long heavy vehicle combinations, IFAC-PapersOnLine, 48, 39-46, (2015)
[126] Vallerio, M.; Vercammen, D.; Impe, J.; Logist, F., Interactive NBI and (E)NNC methods for the progressive exploration of the criteria space in multi-objective optimization and optimal control, Comput. Chem. Eng., 82, 186-201, (2015)
[127] Loock, W.; Pipeleers, G.; Swevers, J., B-spline parameterized optimal motion trajectories for robotic systems with guaranteed constraint satisfaction, Mech. Sci., 6, 163-171, (2015)
[128] Van Parys, R., Pipeleers, G.: Online distributed motion planning for multi-vehicle systems. In: European Control Conference (ECC), pp. 1580-1585 (2016)
[129] Venrooij, J., et al.: Comparison between filter-and optimization-based motion cueing in the Daimler driving simulator. In: Driving Simulation Conference (2016)
[130] Verheyleweghen, A., Jäschke, J.: Health-aware operation of a subsea gas compression system under uncertainty. In: Foundations of Computer Aided Process Operations/Chemical Process Control (2017)
[131] Verschueren, R., van Duijkeren, N., Quirynen, R., Diehl, M.: Exploiting convexity in direct optimal control: a sequential convex quadratic programming method. In: IEEE Conference on Decision and Control (CDC), pp. 1099-1104 (2016)
[132] Verschueren, R., van Duijkeren, N., Swevers, J., Diehl, M.: Time-optimal motion planning for n-dof robot manipulators using a path-parametric system reformulation. In: American Control Conference (ACC), pp. 2092-2097 (2016)
[133] Vochten, M., De Laet, T., De Schutter, J.: Generalizing demonstrated motions and adaptive motion generation using an invariant rigid body trajectory representation. In: IEEE Conference on Robotics and Automation (ICRA), pp. 234-241 (2016)
[134] Wächter, A.; Biegler, L., On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming, Math. Program., 106, 25-57, (2006) · Zbl 1134.90542
[135] Walraven, D.; etal., Optimum configuration of shell-and-tube heat exchangers for the use in low-temperature organic rankine cycles, Energy Convers. Manag., 83, 177-187, (2014)
[136] Welsh, DJA; Powell, MB, An upper bound for the chromatic number of a graph and its application to timetabling problems, Comput. J., 10, 85-86, (1967) · Zbl 0147.15206
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.