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arxiv: 2503.24031 · v2 · submitted 2025-03-31 · 📡 eess.SY · cs.SY· math.OC

An ANN-Enhanced Approach for Flatness-Based Constrained Control of Nonlinear Systems

Huu-Thinh Do , Ionela Prodan , Florin Stoican This is my paper

Pith reviewed 2026-05-22 22:25 UTC · model grok-4.3

classification 📡 eess.SY cs.SYmath.OC
keywords differentially flat systemsrectified linear unit networksconstrained controlmixed-integer programmingmodel predictive controlcontrol Lyapunov functionsnonlinear systems
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The pith

ReLU neural networks represent geometrically distorted constraints from flatness linearization as unions of polytopes for mixed-integer control.

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

The paper shows how rectified linear unit neural networks can address the constraint distortion that occurs when differentially flat nonlinear systems are linearized through a change of variables. Flat systems allow feedback linearization, but the original input and state constraints become non-convex and geometrically warped in the new coordinates. The networks are trained to express these warped sets as unions of polytopes. This polytope-union form then permits standard mixed-integer programming solvers to enforce the constraints exactly inside control Lyapunov function designs and model predictive control. The same representation further yields an explicit closed-form solution for the MPC problem applied to the original nonlinear dynamics.

Core claim

By using rectified linear unit neural networks, the geometrically distorted constraints arising from the flatness transformation can be represented as a union of polytopes. This enables the use of mixed-integer programming tools to guarantee constraint satisfaction when integrated into control Lyapunov function-based designs and model predictive control for nonlinear flat systems, including explicit solutions to the MPC problem.

What carries the argument

ReLU neural network that maps the flat-system constraint set to a union of polytopes, which carries the argument by converting the non-convex problem into one solvable by MIP solvers while preserving the original constraint guarantees.

If this is right

  • Constraint satisfaction guarantees become available for flat systems via off-the-shelf MIP solvers inside both CLF and MPC formulations.
  • The explicit MPC solution can be computed directly for the nonlinear system without online optimization.
  • The same polytope-union description extends to any control method that operates in the linearized flat coordinates.
  • Real-time implementation becomes feasible once the neural network has been trained offline.

Where Pith is reading between the lines

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

  • The method may reduce online computation time compared with direct nonlinear optimization, because the heavy lifting is moved to the offline training and the MIP solver operates on linear constraints.
  • Similar neural-network representations could be applied to other coordinate transformations that distort constraints, such as those arising in feedback linearization of non-flat systems.
  • The approach invites testing on higher-dimensional flat systems where manual polytope enumeration becomes intractable.

Load-bearing premise

A ReLU neural network can approximate the geometrically distorted constraints closely enough that any input satisfying the polytope union also satisfies the true original constraints.

What would settle it

A closed-loop simulation or hardware test on a flat system in which an input chosen by the MIP solver satisfies the neural-network polytope union but violates one of the original nonlinear state or input constraints.

read the original abstract

Neural networks have proven practical for a synergistic combination of advanced control techniques. This work analyzes the implementation of rectified linear unit neural networks to achieve constrained control in differentially flat systems. Specifically, the class of flat systems enjoys the benefit of feedback linearizability, i.e., the systems can be linearized by means of a proper variable transformation. However, the price for linearizing the dynamics is that the constraint descriptions are distorted geometrically. Our results show that, by using neural networks, these constraints can be represented as a union of polytopes, enabling the use of mixed-integer programming tools to guarantee constraint satisfaction. We further analyze the integration of the characterization into efficient settings such as control Lyapunov function-based and model predictive control (MPC). Interestingly, this description also allows us to explicitly compute the solution of the MPC problem for the nonlinear system. Several examples are provided to illustrate the effectiveness of our framework.

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 claims that rectified linear unit (ReLU) neural networks can represent the geometrically distorted input/state constraints arising from the flatness transformation in differentially flat nonlinear systems as a union of polytopes. This enables direct use of mixed-integer programming (MIP) solvers to enforce the original constraints, with further integration into control-Lyapunov-function and model-predictive-control (MPC) designs; the latter is claimed to admit an explicit closed-form solution. Several numerical examples are said to illustrate the framework.

Significance. If the approximation can be shown to preserve exact or rigorously conservative guarantees, the method would provide a practical bridge between flatness-based linearization and off-the-shelf MIP/MPC solvers for constrained nonlinear control. The explicit-MPC claim, if substantiated, would be a notable technical contribution.

major comments (2)
  1. [Abstract] Abstract / central claim: the statement that the ReLU network 'enables the use of mixed-integer programming tools to guarantee constraint satisfaction' is load-bearing yet unsupported by any description of how the inevitable approximation error is handled. Because the flatness map generally produces nonlinear constraint boundaries, a learned piecewise-linear representation is an approximation; without an outer-approximation encoding, interval bounds on the network output, or a robust counterpart inside the MIP, feasible points of the encoded problem can violate the true constraints.
  2. [Abstract] Abstract / § (approach): no information is given on network training, approximation-error bounds, validation that the learned union of polytopes is a faithful (or conservative) representation of the transformed constraints, or numerical verification that the MIP/MPC solutions satisfy the original nonlinear constraints to within a stated tolerance.
minor comments (1)
  1. [Abstract] The abstract refers to 'several examples' without naming the systems, the dimension of the flat outputs, or the quantitative metrics (e.g., constraint violation rates, closed-loop performance) used to demonstrate effectiveness.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight areas where additional rigor and detail will strengthen the manuscript. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract / central claim: the statement that the ReLU network 'enables the use of mixed-integer programming tools to guarantee constraint satisfaction' is load-bearing yet unsupported by any description of how the inevitable approximation error is handled. Because the flatness map generally produces nonlinear constraint boundaries, a learned piecewise-linear representation is an approximation; without an outer-approximation encoding, interval bounds on the network output, or a robust counterpart inside the MIP, feasible points of the encoded problem can violate the true constraints.

    Authors: We agree that the abstract claim requires supporting detail on error handling, which is not explicitly provided in the current manuscript. The work treats the ReLU representation as enabling MIP-based enforcement but does not describe a conservative encoding or robust formulation. In revision we will qualify the abstract claim to refer to guarantees with respect to the learned set and add a section on conservative over-approximation together with error-bound incorporation into the MIP. revision: yes

  2. Referee: [Abstract] Abstract / § (approach): no information is given on network training, approximation-error bounds, validation that the learned union of polytopes is a faithful (or conservative) representation of the transformed constraints, or numerical verification that the MIP/MPC solutions satisfy the original nonlinear constraints to within a stated tolerance.

    Authors: The referee correctly notes the absence of these implementation and validation details. The manuscript emphasizes the overall framework and illustrative examples but omits training procedures, error analysis, and explicit verification. We will revise by adding a dedicated subsection (or appendix) covering network training, error-bound computation, representation validation, and numerical checks in the examples that report satisfaction of the original constraints to a stated tolerance. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation relies on standard flatness and ReLU properties

full rationale

The paper claims that ReLU networks can represent flatness-induced distorted constraints as unions of polytopes for MIP/MPC use. This rests on known differential flatness (feedback linearizability) and the piecewise-linear nature of ReLU networks, without any quoted reduction of a prediction to a fitted input, self-definitional mapping, or load-bearing self-citation chain. No equations or sections in the provided text exhibit a result forced by construction from the same fitted quantities or prior author work invoked as uniqueness. The approach is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper rests on the domain assumption of differential flatness and the universal approximation capability of ReLU networks for the specific geometric distortion; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Differentially flat systems can be feedback linearized by a suitable variable transformation.
    Explicitly stated in the abstract as the benefit of the flat systems class.

pith-pipeline@v0.9.0 · 5691 in / 1197 out tokens · 48407 ms · 2026-05-22T22:25:05.835595+00:00 · methodology

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Reference graph

Works this paper leans on

61 extracted references · 61 canonical work pages · 1 internal anchor

  1. [1]

    Control Handbook, 909–917 (1996)

    Isidori, A., Benedetto, M.: Feedback linearization of nonlinear systems. Control Handbook, 909–917 (1996)

    work page 1996

  2. [2]

    NONLINEAR DYNAMICS70(2), 907–939 (2012) https: //doi.org/10.1007/s11071-012-0529-5

    Taha, H.E., Hajj, M.R., Nayfeh, A.H.: Flight dynamics and control of flapping- wing mavs: a review. NONLINEAR DYNAMICS70(2), 907–939 (2012) https: //doi.org/10.1007/s11071-012-0529-5

    work page doi:10.1007/s11071-012-0529-5 2012

  3. [3]

    In: 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp

    Li, S., Chen, H., Zhang, W., Wensing, P.M.: Quadruped robot hopping on two legs. In: 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 7448–7455 (2021). IEEE 30 −1.5 −1 −0.5 0 0.5 1 −10 0 10 20 z1 (rad) v (rad/s2) C 2 Z {ζ : Θ 2 ζ ≤θ 2 + M } Fig. C1While the constraint is active (i.e.,β= 0in (C9)), the resulting inequali...

    work page 2021

  4. [4]

    In: 2016 IEEE 55th Conference on Decision and Control (CDC), pp

    Farahani, S.S., Papusha, I., McGhan, C., Murray, R.M.: Constrained autonomous satellite docking via differential flatness and model predictive control. In: 2016 IEEE 55th Conference on Decision and Control (CDC), pp. 3306–3311 (2016). IEEE

    work page 2016

  5. [5]

    Acta Astronau- tica167, 391–403 (2020)

    Sanchez, J.C., Gavilan, F., Vazquez, R., Louembet, C.: A flatness-based predic- tive controller for six-degrees of freedom spacecraft rendezvous. Acta Astronau- tica167, 391–403 (2020)

    work page 2020

  6. [6]

    PAMM12(1), 731–732 (2012)

    Utz, T., Kugi, A.: Flatness-based feedforward control design of a system of parabolic pdes based on finite difference semi-discretization. PAMM12(1), 731–732 (2012)

    work page 2012

  7. [7]

    Mounier, H., Rudolph, J.: Flatness-based control of nonlinear delay systems: A chemicalreactorexample.InternationalJournalofControl71(5),871–890(1998)

    work page 1998

  8. [8]

    NONLINEAR DYNAMICS109(1, SI), 57–75 (2022) https://doi.org/10.1007/s11071-022-07267-z

    Hametner, C., Boehler, L., Kozek, M., Bartlechner, J., Ecker, O., Du, Z.P., Koelbl, R., Bergmann, M., Bachleitner-Hofmann, T., Jakubek, S.: Intensive care unit occupancy predictions in the covid-19 pandemic based on age-structured modelling and differential flatness. NONLINEAR DYNAMICS109(1, SI), 57–75 (2022) https://doi.org/10.1007/s11071-022-07267-z

    work page doi:10.1007/s11071-022-07267-z 2022

  9. [9]

    IFAC-PapersOnLine55(16), 406– 411 (2022)

    Do, H.T., Nicolau, F., Stoican, F., Prodan, I.: Tracking control for a flat system under disturbances: a fixed-wing uav example. IFAC-PapersOnLine55(16), 406– 411 (2022)

    work page 2022

  10. [10]

    Springer, (2009) 31

    Levine, J.: Analysis and Control of Nonlinear Systems: A Flatness-based Approach. Springer, (2009) 31

    work page 2009

  11. [11]

    NONLINEAR DYNAMICS87(3), 1749– 1761 (2017) https://doi.org/10.1007/s11071-016-3149-7

    Zhang, Z., Wu, Y., Huang, J.: Differential-flatness-based finite-time anti-swing control of underactuated crane systems. NONLINEAR DYNAMICS87(3), 1749– 1761 (2017) https://doi.org/10.1007/s11071-016-3149-7

    work page doi:10.1007/s11071-016-3149-7 2017

  12. [12]

    In: 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp

    Greeff, M., Schoellig, A.P.: Flatness-based model predictive control for quadrotor trajectory tracking. In: 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 6740–6745 (2018). IEEE

    work page 2018

  13. [13]

    Energy268, 126658 (2023)

    Kong, X., Abdelbaky, M.A., Liu, X., Lee, K.Y.: Stable feedback linearization- based economic mpc scheme for thermal power plant. Energy268, 126658 (2023)

    work page 2023

  14. [14]

    IEEE Transactions on Automatic Control68(11), 7014–7021 (2023)

    Alsalti, M., Lopez, V.G., Berberich, J., Allgöwer, F., Müller, M.A.: Data- based control of feedback linearizable systems. IEEE Transactions on Automatic Control68(11), 7014–7021 (2023)

    work page 2023

  15. [15]

    In: 2023 62nd IEEE Conference on Decision and Control (CDC), pp

    De Persis, C., Gadginmath, D., Pasqualetti, F., Tesi, P.: Data-driven feedback lin- earization with complete dictionaries. In: 2023 62nd IEEE Conference on Decision and Control (CDC), pp. 3037–3042 (2023). IEEE

    work page 2023

  16. [16]

    IEEE Transactions on Industrial Electronics 64(5), 4076–4090 (2016)

    Hou, Z., Chi, R., Gao, H.: An overview of dynamic-linearization-based data- driven control and applications. IEEE Transactions on Industrial Electronics 64(5), 4076–4090 (2016)

    work page 2016

  17. [17]

    Systems & Control Letters54(4), 325–329 (2005)

    Willems, J.C., Rapisarda, P., Markovsky, I., De Moor, B.L.: A note on persistency of excitation. Systems & Control Letters54(4), 325–329 (2005)

    work page 2005

  18. [18]

    Automatica144, 110484 (2022)

    Greco, L., Mounier, H., Bekcheva, M.: An approximate characterisation of the set of feasible trajectories for constrained flat systems. Automatica144, 110484 (2022)

    work page 2022

  19. [19]

    Journal of process Control122, 113–133 (2023)

    Skogestad, S., Zotică, C., Alsop, N.: Transformed inputs for linearization, decoupling and feedforward control. Journal of process Control122, 113–133 (2023)

    work page 2023

  20. [20]

    Nonlinear Dynamics53, 273–280 (2008)

    Ibanez,C.A.,Frias,O.G.:Controllingtheinvertedpendulumbymeansofanested saturation function. Nonlinear Dynamics53, 273–280 (2008)

    work page 2008

  21. [21]

    International Journal of Control 93(6), 1266–1279 (2020)

    Nguyen, N.T., Prodan, I., Lefèvre, L.: Flat trajectory design and tracking with saturation guarantees: a nano-drone application. International Journal of Control 93(6), 1266–1279 (2020)

    work page 2020

  22. [22]

    IEEE Control Systems Letters7, 2347–2352 (2023)

    Tiriolo, C., Lucia, W.: A set-theoretic control approach to the trajectory track- ing problem for input–output linearized wheeled mobile robots. IEEE Control Systems Letters7, 2347–2352 (2023)

    work page 2023

  23. [23]

    In: Proceedings of 1994 American 32 Control Conference-ACC’94, vol

    Nevistic, V., Del Re, L.: Feasible suboptimal model predictive control for lin- ear plants with state dependent constraints. In: Proceedings of 1994 American 32 Control Conference-ACC’94, vol. 3, pp. 2862–2866 (1994). IEEE

    work page 1994

  24. [24]

    International Journal of Control70(4), 603–616 (1998)

    Kurtz, M.J., Henson, M.A.: Feedback linearizing control of discrete-time non- linear systems with input constraints. International Journal of Control70(4), 603–616 (1998)

    work page 1998

  25. [25]

    IEEE Control Systems Letters7, 2191–2196 (2023)

    Hall, A.W., Greeff, M., Schoellig, A.P.: Differentially flat learning-based model predictive control using a stability, state, and input constraining safety filter. IEEE Control Systems Letters7, 2191–2196 (2023)

    work page 2023

  26. [26]

    In: 2021 60th IEEE Conference on Decision and Control (CDC), pp

    Greeff, M., Hall, A.W., Schoellig, A.P.: Learning a stability filter for uncertain dif- ferentially flat systems using gaussian processes. In: 2021 60th IEEE Conference on Decision and Control (CDC), pp. 789–794 (2021). IEEE

    work page 2021

  27. [27]

    IEEE Control Systems Letters (2024)

    Do, H.-T., Prodan, I.: On the constrained feedback linearization control based on the milp representation of a relu-ann. IEEE Control Systems Letters (2024)

    work page 2024

  28. [28]

    In: Hybrid Systems: Computation and Control: 7th International Work- shop, HSCC 2004, Philadelphia, PA, USA, March 25-27, 2004

    Kvasnica, M., Grieder, P., Baotić, M., Morari, M.: Multi-parametric toolbox (mpt). In: Hybrid Systems: Computation and Control: 7th International Work- shop, HSCC 2004, Philadelphia, PA, USA, March 25-27, 2004. Proceedings 7, pp. 448–462 (2004). Springer

    work page 2004

  29. [29]

    Provable Certificates for Adversarial Examples: Fitting a Ball in the Union of Polytopes

    Jordan, M., Lewis, J., Dimakis, A.G.: Provable certificates for adversarial examples: Fitting a ball in the union of polytopes. arXiv preprint arXiv: arXiv:1903.08778 (2019)

    work page internal anchor Pith review Pith/arXiv arXiv 1903

  30. [30]

    IEEE transactions on neural networks and learning systems33(2), 644–653 (2020)

    Hu, Q., Zhang, H., Gao, F., Xing, C., An, J.: Analysis on the number of linear regions of piecewise linear neural networks. IEEE transactions on neural networks and learning systems33(2), 644–653 (2020)

    work page 2020

  31. [31]

    IEEE Transactions on Automatic Control69(1), 202–213 (2023)

    Samanipour, P., Poonawala, H.A.: Stability analysis and controller synthesis using single-hidden-layer relu neural networks. IEEE Transactions on Automatic Control69(1), 202–213 (2023)

    work page 2023

  32. [32]

    Journal of Computational and Applied Mathematics441, 115667 (2024)

    Goujon, A., Etemadi, A., Unser, M.: On the number of regions of piecewise linear neural networks. Journal of Computational and Applied Mathematics441, 115667 (2024)

    work page 2024

  33. [33]

    IEEE transactions on cybernetics50(9), 3866–3878 (2020)

    Karg, B., Lucia, S.: Efficient representation and approximation of model pre- dictive control laws via deep learning. IEEE transactions on cybernetics50(9), 3866–3878 (2020)

    work page 2020

  34. [34]

    Advances in neural information processing systems27 (2014)

    Montúfar, G., Pascanu, R., Cho, K., Bengio, Y.: On the number of linear regions of deep neural networks. Advances in neural information processing systems27 (2014)

    work page 2014

  35. [35]

    IEEE Transactions on Automatic Control68(9), 5201–5215 (2022)

    Fabiani, F., Goulart, P.J.: Reliably-stabilizing piecewise-affine neural network 33 controllers. IEEE Transactions on Automatic Control68(9), 5201–5215 (2022)

    work page 2022

  36. [36]

    Automatica43(1), 31–43 (2007)

    Ge, S.S., Tee, K.P.: Approximation-based control of nonlinear mimo time-delay systems. Automatica43(1), 31–43 (2007)

    work page 2007

  37. [37]

    In: Proceedings of the 28th ACM International Conference on Hybrid Systems: Computation and Control, pp

    Sivaramakrishnan, V., Kalagarla, K.C., Devonport, R., Pilipovsky, J., Tsiotras, P., Oishi, M.: Saver: A toolbox for sampling-based, probabilistic verification of neural networks. In: Proceedings of the 28th ACM International Conference on Hybrid Systems: Computation and Control, pp. 1–7 (2025)

    work page 2025

  38. [38]

    In: International Symposium on Automated Technology for Verification and Analysis, pp

    Ehlers, R.: Formal verification of piece-wise linear feed-forward neural networks. In: International Symposium on Automated Technology for Verification and Analysis, pp. 269–286 (2017). Springer

    work page 2017

  39. [39]

    arXiv preprint arXiv:2505.11546 (2025)

    Li, X., Wei, T., Liu, C., Girard, A., Kolmanovsky, I.: Control invariant sets for neural network dynamical systems and recursive feasibility in model predictive control. arXiv preprint arXiv:2505.11546 (2025)

    work page arXiv 2025

  40. [40]

    Journal of Global Optimization81(1), 109–152 (2021)

    Rössig, A., Petkovic, M.: Advances in verification of relu neural networks. Journal of Global Optimization81(1), 109–152 (2021)

    work page 2021

  41. [41]

    Springer, (2015)

    Prodan, I., Stoican, F., Olaru, S., Niculescu, S.-I.: Mixed-integer Representa- tions in Control Design: Mathematical Foundations and Applications. Springer, (2015)

    work page 2015

  42. [42]

    IEEE Transactions on Information Theory67(5), 2581– 2623 (2021)

    Elbrächter, D., Perekrestenko, D., Grohs, P., Bölcskei, H.: Deep neural network approximation theory. IEEE Transactions on Information Theory67(5), 2581– 2623 (2021)

    work page 2021

  43. [43]

    Liang, S., Srikant, R.: Why deep neural networks for function approximation? In: International Conference on Learning Representations (2022)

    work page 2022

  44. [44]

    Neural Networks161, 129– 141 (2023)

    Franco, N.R., Fresca, S., Manzoni, A., Zunino, P.: Approximation bounds for convolutional neural networks in operator learning. Neural Networks161, 129– 141 (2023)

    work page 2023

  45. [45]

    Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis vol. 317. Springer, (2009)

    work page 2009

  46. [46]

    International Journal of Robust and Nonlinear Control (2024)

    Fabiani, F., Goulart, P.J.: Robust stabilization of polytopic systems via fast and reliable neural network-based approximations. International Journal of Robust and Nonlinear Control (2024)

    work page 2024

  47. [47]

    The American Mathe- matical Monthly97(3), 233–235 (1990)

    Folland, G.B.: Remainder estimates in taylor’s theorem. The American Mathe- matical Monthly97(3), 233–235 (1990)

    work page 1990

  48. [48]

    IFAC-PapersOnLine53(2), 5499–5504 (2020) 34

    Romagnoli, R., Couto, L.D., Garone, E.: A new reference governor strategy for union of linear constraints. IFAC-PapersOnLine53(2), 5499–5504 (2020) 34

    work page 2020

  49. [49]

    IEEE/CAA Journal of Automatica Sinica10(3), 584–602 (2023)

    Li, B., Wen, S., Yan, Z., Wen, G., Huang, T.: A survey on the control lya- punov function and control barrier function for nonlinear-affine control systems. IEEE/CAA Journal of Automatica Sinica10(3), 584–602 (2023)

    work page 2023

  50. [50]

    Blanchini, F., Miani, S.: Set-theoretic Methods in Control vol. 78. Springer, (2008)

    work page 2008

  51. [51]

    https: //www.gurobi.com

    Gurobi Optimization, LLC: Gurobi Optimizer Reference Manual (2024). https: //www.gurobi.com

    work page 2024

  52. [52]

    In: 2021 60th IEEE Conference on Decision and Control (CDC), pp

    Quirynen, R., Di Cairano, S.: Sequential quadratic programming algorithm for real-time mixed-integer nonlinear mpc. In: 2021 60th IEEE Conference on Decision and Control (CDC), pp. 993–999 (2021). IEEE

    work page 2021

  53. [53]

    In: 2012 IEEE International Conference on Control Applications, pp

    Kandler, C., Ding, S.X., Koenings, T., Weinhold, N., Schultalbers, M.: A differen- tial flatness based model predictive control approach. In: 2012 IEEE International Conference on Control Applications, pp. 1411–1416 (2012). IEEE

    work page 2012

  54. [54]

    Automatica34(10), 1205–1217 (1998)

    Chen,H.,Allgöwer,F.:Aquasi-infinitehorizonnonlinearmodelpredictivecontrol scheme with guaranteed stability. Automatica34(10), 1205–1217 (1998)

    work page 1998

  55. [55]

    IEEE Transac- tions on automatic control26(2), 346–358 (1981)

    Sontag, E.: Nonlinear regulation: The piecewise linear approach. IEEE Transac- tions on automatic control26(2), 346–358 (1981)

    work page 1981

  56. [56]

    Christophersen, F.J.: Piecewise Affine Systems, pp. 39–42. Springer, Berlin, Heidelberg (2007)

    work page 2007

  57. [57]

    International Journal of Robust and Nonlinear Control: IFAC-Affiliated Journal13(3-4), 261–279 (2003)

    Mayne, D.Q., Raković, S.: Model predictive control of constrained piecewise affine discrete-time systems. International Journal of Robust and Nonlinear Control: IFAC-Affiliated Journal13(3-4), 261–279 (2003)

    work page 2003

  58. [58]

    IEEE Control Systems Magazine38(4), 89–107 (2018)

    Nicotra, M.M., Garone, E.: The explicit reference governor: A general frame- work for the closed-form control of constrained nonlinear systems. IEEE Control Systems Magazine38(4), 89–107 (2018)

    work page 2018

  59. [59]

    In: 2017 25th Mediterranean Conference on Control and Automation (MED), pp

    Stoican, F., Prodan, I., Popescu, D., Ichim, L.: Constrained trajectory generation for uav systems using a b-spline parametrization. In: 2017 25th Mediterranean Conference on Control and Automation (MED), pp. 613–618 (2017). IEEE

    work page 2017

  60. [60]

    In: 2023 European Control Conference (ECC), pp

    Vu, N., Pham, T., Prodan, I., Lefevre, L.: Port-hamiltonian observer for state- feedback control design. In: 2023 European Control Conference (ECC), pp. 1–6 (2023). IEEE

    work page 2023

  61. [61]

    Annual Reviews in Control51, 65–87 (2021) 35

    Ioan, D., Prodan, I., Olaru, S., Stoican, F., Niculescu, S.-I.: Mixed-integer programming in motion planning. Annual Reviews in Control51, 65–87 (2021) 35

    work page 2021