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REVIEW 3 major objections 4 minor 48 references

Reference-Free Iterative Learning Model Predictive Control with Neural Certificates

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A neural certificate learned from past runs can serve as an iterative MPC's terminal cost and terminal set, keeping the online problem a nonlinear program with feasibility, stability, and non-increasing cost.

desk verdict The idea of replacing MIP with a learned neural CLBF in reference-free iterative LMPC is worth attention, but the advertised guarantees rest on assumptions that the verification procedure does not actually certify. read the letter →

arxiv 2507.14025 v1 pith:67TS2WVK submitted 2025-07-18 eess.SY cs.SY

Wataru Hashimoto , Kazumune Hashimoto , Masako Kishida , Shigemasa Takai This is my paper
classification eess.SYcs.SY
keywords modelpredictivecontroliterativelearningneuralcertificatefunctionLyapunovbarrierterminalcostandsetrecursivefeasibilityasymptoticstabilitydata-driven
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper proposes a way for model predictive control to improve at a task across repeated trials without a reference trajectory. In each trial, a neural network is trained from earlier trials' data to be a Control Lyapunov-Barrier Function (CLBF), and this function is used as both the terminal cost and the terminal constraint of the MPC. The central claim is that, when the learned function meets a set of certificate conditions, the optimization is feasible at every step, the closed loop is asymptotically stable about the goal state, and the total cost does not increase from one trial to the next except for explicit error terms. Because the terminal set is a smooth level-set inequality rather than a stored list of past states, the online problem is a standard nonlinear program, which the simulations show is much faster to solve than the mixed-integer formulation of earlier reference-free iterative learning MPC.

What carries the argument

The central object is the neural certificate function $V^j$, a discrete-time Control Lyapunov-Barrier Function whose sublevel set $\{x: V^{j-1}(x)\le c\}$ defines the terminal set and whose value defines the terminal cost in (5). The argument is carried by the certificate conditions (9a)–(9g): condition (9e), $\inf_{u\in U} V^j(f(x,u))-V^j(x)\le 0$ on the safe region, provides the forward-invariant tail control needed for recursive feasibility; condition (9f), $\inf_{u\in U}\gamma V^j(f(x,u))-V^j(x)+\ell(x,u)\le 0$, makes the MPC value function a Lyapunov function; and condition (9g), applied to past trajectories, gives the cross-iteration cost comparison in Theorem 3. A policy network $\pi_\phi$ is learned alongside $V^j$, and the loss (10) encodes these conditions with counterexample resampling during validation.

What would settle it

On the paper's Dubins car example, evaluate condition (9e) on a dense grid of states just inside the boundary of $\{x: V^j(x)\le c\}$ using the learned policy $\pi_\phi$; any grid point with $V^j(f(x,\pi_\phi(x)))>V^j(x)$ would falsify the forward-invariance assumption that Theorem 1 requires.

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Extended reading notes

Core claim

For the discrete-time nonlinear system (1) with a continuous stage cost satisfying Assumption 1, the paper studies the receding-horizon problem (5) whose terminal set is $\{x: V^{j-1}(x)\le c\}$ and whose terminal cost is $V^{j-1}$, with $V^j$ a neural network trained on data from previous iterations. The paper claims that if $V^j$ satisfies the CLBF-style conditions (9a)–(9g) — positivity, separation from the unsafe set, forward invariance, discounted decrease, and a data-side inequality — then the MPC is recursively feasible (Theorem 1), the equilibrium $x_F$ is asymptotically stable under the applied feedback (Theorem 2), and the infinite-horizon cost obeys $J^{j-1}_{0\to\infty}(x_s)\ge J^j_{0\to\infty}(x_s)-\gamma^N(\delta_1^{\max}+\delta_2)/(1-\gamma)$ (Theorem 3), becoming non-increasing when the violation terms vanish. The proposal is that these terminal components are learned offline from collected trajectory data, with the loss (10) and periodic validation, so that the online optimization stays a standard nonlinear program rather than a mixed-integer one.

Load-bearing premise

Everything rests on the learned safety-and-stability function satisfying its required inequalities everywhere in the state space, while the paper's verification checks only finitely many sampled points.

Editorial extensions

If this is right

  • Each online MPC step is a standard nonlinear program, so trial-by-trial control can be executed with far less computation than the mixed-integer approach used by earlier reference-free iterative learning MPC.
  • The certified region $\{x: V^j(x)\le c\}$ grows with each iteration, so the controller reaches states not visited before and the measured total cost falls from one trial to the next.
  • When the learned certificate satisfies the decrease conditions exactly, the total cost $J^j_{0\to\infty}(x_s)$ is guaranteed non-increasing in the iteration index, meaning every trial is at least as good as the one before.
  • Under the assumptions, every trial remains feasible at every time step and the closed-loop state converges to $x_F$ while avoiding the unsafe set, giving standard MPC guarantees without a tracking reference.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A quantitative progress metric that the authors do not define is the volume of the certified region $\{x: V^j(x)\le c\}$; tracking it across iterations would let a user decide when further trials are no longer expanding the safe set.
  • The error terms in Theorem 3 suggest a practical stopping rule: stop iterating once the observed cost decreases are comparable to $\gamma^N(\delta_1^{\max}+\delta_2)/(1-\gamma)$, since further improvement is then within the certificate's violation margin.
  • The same offline terminal-certificate loop could be transferred to stochastic or unknown dynamics by replacing the deterministic decrease conditions (9e)–(9f) with robust or probabilistic counterparts, an extension the paper leaves for future work.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes a reference-free iterative learning MPC scheme in which a neural-network certificate, trained on trajectory data from previous iterations, defines both the terminal cost and the terminal set of a finite-horizon nonlinear MPC problem. The certificate is constructed to approximate Control Lyapunov-Barrier Function (CLBF) conditions, and training is interleaved with verification over finite sample sets. The authors claim recursive feasibility, asymptotic stability of the target state, and a non-increasing performance cost over iterations under Assumptions 1-8. The method is evaluated on a Dubins car reach-avoid problem in a nominal setting and in a PyBullet TurtleBot simulation, with a comparison against the mixed-integer LMPC baseline of Rosolia and Borrelli.

Significance. If the stated guarantees were established, the paper would offer a practically appealing alternative to MIP-based iterative learning MPC: the online problem is a standard NLP, and the simulations show comparable control performance with substantially lower online computation. The core idea of using a learned neural CLBF as both terminal cost and terminal constraint is timely and the experiments are informative. The main limitation is that the key guarantees are delegated to Assumptions 5-8, which are not certified by the proposed finite-sample verification; in particular, the proof of recursive feasibility relies on a policy-specific forward invariance property that does not follow from the stated assumptions. As a rigorous contribution, the paper currently overstates what is established, though the conditional proof structure is a reasonable starting point for a revision.

major comments (3)
  1. The claim that the set {x | V^{j-1}(x) ≤ c} is forward invariant under the control policy pi_phi^{j-1} 'due to the conditions (9e)' is not a consequence of the stated assumptions. Condition (9e) is an infimum over u in U, so it does not imply the pointwise inequality V^{j-1}(f(x, pi_phi^{j-1}(x))) ≤ V^{j-1}(x), nor does it guarantee that pi_phi^{j-1}(x) lies in U or that f(x, pi_phi^{j-1}(x)) lies in X\A. Assumption 5 verifies only conditions (9a)-(9d), and Assumption 8 explicitly permits nonzero violations of (9e)-(9f); with a nonzero delta1 in (11), the terminal state can leave the level set even when V^{j-1}(x) ≤ c. Therefore the tail candidate in the proof may violate the terminal constraint (5e) and possibly the state/input constraints (5c)-(5d), so recursive feasibility is not established. A revision should either assume an exact, policy-specific invariance condition with state/input constraints, or prove the tail stays feasible using a strengthened version of Assumption 8 with explicit boundary slack that is actually verified.
  2. The verification procedure in Algorithm 2 is a finite-sample check: Ntest points are sampled, violating points are added, and training is repeated. Such a procedure cannot certify the global conditions (9a)-(9g), including the forward invariance of the c-level set and the discounted decrease condition (9f), over the entire continuous state space. Moreover, the paragraph after Assumption 8 states that 'the systematic way for imposing the conditions is out of the scope of this paper and will be considered in future work.' Since Theorems 1-3 all rest on these global conditions, the main guarantees are conditional on assumptions that the proposed algorithm does not deliver. In particular, there is no computational method to bound delta1 and delta2 or to check the condition delta1(x_{t+N|t}^*) < gamma^{-N} ell(x_{t|t}^*, u_{t|t}^*) required by Theorem 2. The abstract's unconditional statements about recursive feasibility, stability, and non-increasing cost are therefore stronger than what the manuscript actually supports.
  3. The non-increasing cost bound is essentially a restatement of the learned condition (12), not a consequence of the iterative improvement mechanism. Condition (12) is the epsilon-relaxed version of the training target (9g), which appears as the a5 term in the loss (10) and is evaluated on the very past trajectories whose costs are being compared in Theorem 3. The proof applies (12) with V^{j-1} to the iteration j-1 trajectory to lower-bound J^{j-1}, and then compares it with J^j. Thus, if delta2 and delta1^{j,max} are not certified independently of the training data, the theorem does not establish a meaningful performance-improvement property; it only says that the cost decrease is bounded by the training residuals. The paper claims in the abstract that the cost is non-increasing when the violation terms vanish, but the vanishing of these terms is neither certified nor implied by the training procedure.
minor comments (4)
  1. The last term of the loss has a mismatched parenthesis and a sign convention that is difficult to parse; as printed, the expression a5[-gamma V_theta(f(x_j_k, u_j_k) + V_theta(x_j_k) - ell(x_j_k, u_j_k)]+ appears to be missing a closing parenthesis after u_j_k, and the sign inside the bracket should be checked against condition (9g).
  2. The construction of Xsafe and Xunsafe via the alpha-shape boundary Balpha is underspecified: it is not stated whether 'x in Balpha' means inside the enclosed region, on the boundary, or outside, which directly affects the meaning of conditions (9c) and (9d) and the sampling of Dsafe and Dunsafe.
  3. The statement that 'the certified region is progressively enlarged' is supported only by a heatmap of the learned V^j; since Assumption 6 is not actually verified for the trained networks, the figure illustrates the learned level sets but does not certify monotonic enlargement of the safe set.
  4. The stage cost in the experiments is ell(x,u) = 0.001 ||x - x_F||^2, which is independent of u; this is compatible with Assumption 1 as written, but the paper should note explicitly that the theory permits control-independent stage costs, since some readers may expect a positive definite cost in both state and input.

Circularity Check

1 steps flagged · score 5.0 of 10

Partial circularity: Theorem 3's non-increasing cost conclusion is the training target (9g)/(12) telescoped on the very trajectory used in the loss, though feasibility and stability have independent content.

  1. fitted input called prediction [Section IV-C, Theorem 3 proof (Eqs. (16)-(21)); Assumption 8 Eq. (12); loss Eq. (10) in Section III-B]
    "Assumption 8: γV j(xj k+1) − V j(xj k) + ℓ(xj k, uj k) ≥ −δ2, ∀k ∈ N≥0. (12) ... Proof of Theorem 3: By recursively applying the condition (12) in Assumption (8), ... V j−1(xj−1 0 ) ≤ γN V j−1(xj−1 N ) + ... + δ2 ..."

    The a5 term in loss (10) is the positive part of −[γVθj(f(xj k, uj k)) − Vθj(xj k) + ℓ(xj k, uj k)], so minimizing it on the collected trajectory enforces exactly the inequality later stated as (9g). Assumption 8 then converts that trained objective into the standing bound (12) with slack δ2. Theorem 3's proof begins by telescoping (12) along the previous iteration's trajectory, yielding (16) and hence a lower bound on J^{j-1}; combined with (13) this gives (15). In the zero-error case the monotone-improvement claim is therefore the training target (9g) restated on the compared data, not an independent prediction of the MPC framework. The result is partially circular, though not fully, because the stability and recursive-feasibility theorems rely on separate arguments.

full rationale

The derivation chain is mostly a standard MPC argument: Theorems 1 and 2 take the terminal set/cost properties as premises and prove feasibility and stability from them, which is not circular. However, Theorem 1's proof invokes exact forward invariance under the learned policy via condition (9e), while Assumption 5 verifies only (9a)-(9d) and Assumption 8 permits violations; this is a missing-support/correctness gap, not a self-referential prediction, so I do not count it as circularity. The clearest circular step is Theorem 3: the loss function (10) contains a5[-(γV(f(x,u))-V(x)+ℓ)]_+, which trains V to satisfy condition (9g)/(12) on the previous trajectory; Assumption 8 asserts that inequality; and the proof obtains monotonicity by summing exactly that inequality along the same trajectory. Thus the non-increasing-cost claim is largely the fitted inequality restated. Since the feasibility and stability parts retain independent mathematical content and no load-bearing self-citations appear, the overall circularity score is 5 rather than higher.

Assumptions & free parameters 2 free parameters · 9 assumptions · 0 invented entities

No new physical entities are introduced. The central claims rest on a long list of assumptions, of which Assumptions 5-8 are the heaviest: they upgrade finite-sample neural training and sampled verification into global continuous-state certificates. Assumption 6 is especially fragile because no training mechanism enforces monotonic enlargement.

free parameters (2)
  • c (terminal level-set threshold) = 7 (experiments)
    Defines the terminal set {x | V <= c}; the safety and stability arguments depend on this choice, and it is selected by hand with no sensitivity analysis.
  • a1-a5 (loss weights) = all set to 1 (experiments)
    Relative weights between the CLBF conditions in loss (10); chosen by hand, no ablation or sensitivity study is reported.
assumptions (9)
  • domain assumption Assumption 1: the stage cost is continuous, positive definite with respect to xF, and xF is an equilibrium.
    Standard optimal-control assumption stated in Section II-B and used throughout the proofs.
  • domain assumption Assumption 2: a local optimal solution to problem (2) exists.
    Standard existence assumption used to justify the iterative optimal-control framing.
  • domain assumption Assumption 3: the initial state is fixed across iterations.
    This is the iterative-learning setting from [10],[11]; it is needed for the performance-cost comparison across iterations.
  • domain assumption Assumption 4: an initial dataset D0 and initial terminal function V0 are given, with feasibility at time 0.
    The iteration cannot start without an initial certificate and a feasible initialization; the paper does not specify how to construct D0 in general.
  • ad hoc to paper Assumption 5: the learned V^j satisfies conditions (9a)-(9d) for all j, verified over the state space.
    This transfers finite-sample training to a global property; only sampled verification is described in Section III-B1.
  • ad hoc to paper Assumption 6: the certified regions monotonically enlarge across iterations.
    Algorithm 2 does not enforce any monotonicity constraint; the only evidence is the empirical heatmap in Fig. 2.
  • ad hoc to paper Assumption 7: all states in the trajectory dataset Dj are contained in the certified region {V^j <= c}.
    This is required for the induction argument in Theorem 1 but is not guaranteed by the alpha-shape sampling scheme.
  • ad hoc to paper Assumption 8: violations of conditions (9e) and (9f) are bounded by delta1(x) and delta2.
    The bounds delta1 and delta2 are not estimated or bounded by training; Theorem 3's monotonicity result only holds in the zero-violation limit.
  • domain assumption The alpha-shape construction correctly separates a safe subset Xsafe from an unsafe superset Xunsafe.
    The alpha shape of Dj is treated as a faithful boundary of the safe region, which is an approximation that becomes unreliable with sparse data.

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Cite this review

Pith. "Pith review of Reference-Free Iterative Learning Model Predictive Control with Neural Certificates." pith.science (2026). https://pith.science/paper/67TS2WVK

@misc{pith2026250714025,
  author       = {Pith},
  title        = {Pith review of: Reference-Free Iterative Learning Model Predictive Control with Neural Certificates},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/67TS2WVK}},
  note         = {Machine review of arXiv:2507.14025}
}
read the original abstract

In this paper, we propose a novel reference-free iterative learning model predictive control (MPC). In the proposed method, a certificate function based on the concept of Control Lyapunov Barrier Function (CLBF) is learned using data collected from past control executions and used to define the terminal set and cost in the MPC optimization problem at the current iteration. This scheme enables the progressive refinement of the MPC's terminal components over successive iterations. Unlike existing methods that rely on mixed-integer programming and suffer from numerical difficulties, the proposed approach formulates the MPC optimization problem as a standard nonlinear program, enabling more efficient online computation. The proposed method satisfies key MPC properties, including recursive feasibility and asymptotic stability. Additionally, we demonstrate that the performance cost is non-increasing with respect to the number of iterations, under certain assumptions. Numerical experiments including the simulation with PyBullet confirm that our control scheme iteratively enhances control performance and significantly improves online computational efficiency compared to the existing methods.

Figures

Figures reproduced from arXiv: 2507.14025 by the authors.

Figure 1
Figure 1. The illustrative explanation of the proposed MPC [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The 2D heat map of the function V j after each iteration when the heading angle is fixed to θ = −π/4. The white line shows the c level set and light blue region shows the obstacle. From Theorem 2, xF is asymptotically stable for the closed￾loop system (1) and (8). Thus, by continuity of the function ℓ and Assumption 1, we have limt→∞ J LMPC,j t→t+N (x j t ) = 0. (19) From (18) and (19), we obtain J LMPC,j 0→N (x j t… view at source ↗
Figure 3
Figure 3. The actual trajectories of the vehicle position (nominal [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: The actual trajectories of the vehicle position (TurtleBot [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

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Works this paper leans on

48 extracted references · 42 canonical work pages

  1. [2]

    A novel iterative learning control formulation of generalized predictive control,

    G. M. Bone, “A novel iterative learning control formulation of generalized predictive control,” Automatica, vol. 31, no. 10, pp. 1483–1487, 1995. [Online]. Available: https://www.sciencedirect.com/ science/article/pii/000510989500051W

    arXiv 1995

  2. [3]

    Model predictive control technique combined with iterative learning for batch processes,

    K. S. Lee, I.-S. Chin, H. J. Lee, and J. H. Lee, “Model predictive control technique combined with iterative learning for batch processes,” AIChE Journal, vol. 45, no. 10, pp. 2175–2187, 1999. [Online]. Available: https://aiche.onlinelibrary.wiley.com/doi/abs/10.1002/aic.690451016 9

    work page doi:10.1002/aic.690451016 1999

  3. [4]

    Convergence of constrained model-based predictive control for batch processes,

    K. Lee and J. Lee, “Convergence of constrained model-based predictive control for batch processes,” IEEE Transactions on Automatic Control , vol. 45, no. 10, pp. 1928–1932, 2000

    work page 1928

  4. [5]

    Combined iterative learning and model predictive control scheme for nonlinear systems,

    Y . Zhou, X. Tang, D. Li, X. Lai, and F. Gao, “Combined iterative learning and model predictive control scheme for nonlinear systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems , vol. 54, no. 6, pp. 3558–3567, 2024

    work page 2024

  5. [6]

    Synthesis of ilc–mpc controller with data-driven approach for constrained batch processes,

    D. Li, S. He, Y . Xi, T. Liu, F. Gao, Y . Wang, and J. Lu, “Synthesis of ilc–mpc controller with data-driven approach for constrained batch processes,” IEEE Transactions on Industrial Electronics , vol. 67, no. 4, pp. 3116–3125, 2020

    work page 2020

  6. [7]

    Robust model predictive it- erative learning control for iteration-varying-reference batch processes,

    X. Liu, L. Ma, X. Kong, and K. Y . Lee, “Robust model predictive it- erative learning control for iteration-varying-reference batch processes,” IEEE Transactions on Systems, Man, and Cybernetics: Systems , vol. 51, no. 7, pp. 4238–4250, 2021

    work page 2021

  7. [8]

    A survey of iterative learning control,

    D. Bristow, M. Tharayil, and A. Alleyne, “A survey of iterative learning control,” IEEE Control Systems Magazine , vol. 26, no. 3, pp. 96–114, 2006

    work page 2006

  8. [9]

    Iterative learning control applied to batch processes: An overview,

    J. H. Lee and K. S. Lee, “Iterative learning control applied to batch processes: An overview,” Control Engineering Practice , vol. 15, no. 10, pp. 1306–1318, 2007, special Issue - International Symposium on Advanced Control of Chemical Processes (ADCHEM). [Online]. Available: https://www.sciencedirect.com/science/article/pii/ S0967066106002279

    work page 2007

Show all 48 references
  1. [10]

    Learning model predictive control for iterative tasks. a data-driven control framework,

    U. Rosolia and F. Borrelli, “Learning model predictive control for iterative tasks. a data-driven control framework,” IEEE Transactions on Automatic Control, vol. 63, no. 7, pp. 1883–1896, 2018

    2018

  2. [11]

    Learning model predictive control for iterative tasks: A computationally efficient approach for linear system,

    ——, “Learning model predictive control for iterative tasks: A computationally efficient approach for linear system,” IFAC- PapersOnLine, vol. 50, no. 1, pp. 3142–3147, 2017, 20th IFAC World Congress. [Online]. Available: https://www.sciencedirect.com/science/ article/pii/S2405...

    2017

  3. [12]

    Minimum time learning model predictive control,

    ——, “Minimum time learning model predictive control,” International Journal of Robust and Nonlinear Control , vol. 31, no. 18, pp. 8830–8854, 2021. [Online]. Available: https://onlinelibrary.wiley.com/ doi/abs/10.1002/rnc.5284

    2021 doi

  4. [13]

    Stabilization with guaranteed safety using control lyapunov–barrier function,

    M. Z. Romdlony and B. Jayawardhana, “Stabilization with guaranteed safety using control lyapunov–barrier function,” Automatica, vol. 66, pp. 39–47, 2016. [Online]. Available: https://www.sciencedirect.com/ science/article/pii/S0005109815005439

    2016

  5. [14]

    Safe nonlinear control using robust neural lyapunov-barrier functions,

    C. Dawson, Z. Qin, S. Gao, and C. Fan, “Safe nonlinear control using robust neural lyapunov-barrier functions,” in Proceedings of the 5th Conference on Robot Learning , ser. Proceedings of Machine Learning Research, A. Faust, D. Hsu, and G. Neumann, Eds., vol

  6. [15]

    On the optimality and convergence properties of the iterative learning model predictive controller,

    U. Rosolia, Y . Lian, E. T. Maddalena, G. Ferrari-Trecate, and C. N. Jones, “On the optimality and convergence properties of the iterative learning model predictive controller,” IEEE Transactions on Automatic Control, vol. 68, no. 1, pp. 556–563, 2023

    2023

  7. [16]

    Robust learning model predictive control for iterative tasks: Learning from experience,

    U. Rosolia, X. Zhang, and F. Borrelli, “Robust learning model predictive control for iterative tasks: Learning from experience,” in2017 IEEE 56th Annual Conference on Decision and Control (CDC) , 2017, pp. 1157– 1162

    2017

  8. [17]

    Abc-lmpc: Safe sample-based learning mpc for stochastic nonlinear dynamical systems with adjustable boundary con- ditions,

    B. Thananjeyan, A. Balakrishna, U. Rosolia, J. E. Gonzalez, A. Ames, and K. Goldberg, “Abc-lmpc: Safe sample-based learning mpc for stochastic nonlinear dynamical systems with adjustable boundary con- ditions,” in Algorithmic Foundations of Robotics XIV , S. M. LaValle, M. Lin...

    2021

  9. [18]

    Robust learning-based iterative model predictive control for unknown non- linear systems,

    W. Hashimoto, K. Hashimoto, M. Kishida, and S. Takai, “Robust learning-based iterative model predictive control for unknown non- linear systems,” IET Control Theory & Applications , vol. n/a, no. n/a. [Online]. Available: https://ietresearch.onlinelibrary.wiley.com/doi/ abs/10...

    doi

  10. [19]

    Distributed learning model predictive control for linear systems,

    Y . R. St ¨urz, E. L. Zhu, U. Rosolia, K. H. Johansson, and F. Borrelli, “Distributed learning model predictive control for linear systems,” in 2020 59th IEEE Conference on Decision and Control (CDC) , 2020, pp. 4366–4373

    2020

  11. [20]

    Learning how to autonomously race a car: A predictive control approach,

    U. Rosolia and F. Borrelli, “Learning how to autonomously race a car: A predictive control approach,” IEEE Transactions on Control Systems Technology, vol. 28, no. 6, pp. 2713–2719, 2020

    2020

  12. [21]

    Safety augmented value estimation from demonstrations (saved): Safe deep model-based rl for sparse cost robotic tasks,

    B. Thananjeyan, A. Balakrishna, U. Rosolia, F. Li, R. McAllister, J. E. Gonzalez, S. Levine, F. Borrelli, and K. Goldberg, “Safety augmented value estimation from demonstrations (saved): Safe deep model-based rl for sparse cost robotic tasks,” IEEE Robotics and Automation Lett...

    2020

  13. [22]

    A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability,

    H. CHEN and F. ALLG ¨oWER, “A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability,” Automatica, vol. 34, no. 10, pp. 1205–1217, 1998. [Online]. Available: https: //www.sciencedirect.com/science/article/pii/S0005109898000739

    1998

  14. [23]

    Constrained model predictive control: Stability and optimality,

    D. Mayne, J. Rawlings, C. Rao, and P. Scokaert, “Constrained model predictive control: Stability and optimality,” Automatica, vol. 36, no. 6, pp. 789–814, 2000. [Online]. Available: https: //www.sciencedirect.com/science/article/pii/S0005109899002149

    2000

  15. [24]

    Safe reinforcement learning using robust mpc,

    M. Zanon and S. Gros, “Safe reinforcement learning using robust mpc,” IEEE Transactions on Automatic Control, vol. 66, no. 8, pp. 3638–3652, 2021

    2021

  16. [25]

    Reinforcement learning-based model predictive control for discrete-time systems,

    M. Lin, Z. Sun, Y . Xia, and J. Zhang, “Reinforcement learning-based model predictive control for discrete-time systems,” IEEE Transactions on Neural Networks and Learning Systems , vol. 35, no. 3, pp. 3312– 3324, 2024

    2024

  17. [26]

    Ac4mpc: Actor-critic reinforcement learning for nonlinear model predictive control,

    R. Reiter, A. Ghezzi, K. Baumg ¨artner, J. Hoffmann, R. D. McAllister, and M. Diehl, “Ac4mpc: Actor-critic reinforcement learning for nonlinear model predictive control,” 2024. [Online]. Available: https://arxiv.org/abs/2406.03995

    2024 arXiv

  18. [27]

    Predictive control with learning-based terminal costs using approximate value iteration,

    F. Moreno-Mora, L. Beckenbach, and S. Streif, “Predictive control with learning-based terminal costs using approximate value iteration,” IFAC-PapersOnLine, vol. 56, no. 2, pp. 3874–3879, 2023, 22nd IFAC World Congress. [Online]. Available: https://www.sciencedirect.com/ scienc...

    2023

  19. [28]

    Value approximator-based learning model predictive control for iterative tasks,

    H. Bao, Q. Kang, X. Shi, M. Zhou, J. An, and Y . Al-Turki, “Value approximator-based learning model predictive control for iterative tasks,” IEEE Transactions on Automatic Control , vol. 69, no. 10, pp. 7020– 7027, 2024

    2024

  20. [29]

    Safe reinforcement learning using model predictive control with probabilistic control barrier function,

    X. Shen, A. Wachi, W. Hashimoto, K. Hashimoto, and S. Takai, “Safe reinforcement learning using model predictive control with probabilistic control barrier function,” in 2024 American Control Conference (ACC) , 2024, pp. 74–79

    2024

  21. [30]

    Actor-critic model predictive control,

    A. Romero, Y . Song, and D. Scaramuzza, “Actor-critic model predictive control,” in 2024 IEEE International Conference on Robotics and Automation (ICRA), 2024, pp. 14 777–14 784

    2024

  22. [31]

    Synthesis of model predictive control and reinforcement learning: Survey and classification,

    R. Reiter, J. Hoffmann, D. Reinhardt, F. Messerer, K. Baumg ¨artner, S. Sawant, J. Boedecker, M. Diehl, and S. Gros, “Synthesis of model predictive control and reinforcement learning: Survey and classification,”

  23. [32]

    Control barrier functions: Theory and applications,

    A. D. Ames, S. Coogan, M. Egerstedt, G. Notomista, K. Sreenath, and P. Tabuada, “Control barrier functions: Theory and applications,” in2019 18th European Control Conference (ECC) , 2019, pp. 3420–3431

    2019

  24. [33]

    Neural certificates for safe control policies,

    W. Jin, Z. Wang, Z. Yang, and S. Mou, “Neural certificates for safe control policies,” 2020. [Online]. Available: https://arxiv.org/abs/2006. 08465

    2020

  25. [34]

    Neural lyapunov control,

    Y .-C. Chang, N. Roohi, and S. Gao, “Neural lyapunov control,” in Advances in Neural Information Processing Systems, vol. 32. Curran Associates, Inc., 2019. [On- line]. Available: https://proceedings.neurips.cc/paper files/paper/2019/ file/2647c1dba23bc0e0f9cdf75339e120d2-Paper.pdf

    2019

  26. [35]

    Lyapunov- stable neural-network control,

    H. Dai, B. Landry, L. Yang, M. Pavone, and R. Tedrake, “Lyapunov- stable neural-network control,” arXiv preprint arXiv:2109.14152 , 2021

    2021 arXiv

  27. [36]

    The lyapunov neural network: Adaptive stability certification for safe learning of dynamical systems,

    S. M. Richards, F. Berkenkamp, and A. Krause, “The lyapunov neural network: Adaptive stability certification for safe learning of dynamical systems,” in Proceedings of The 2nd Conference on Robot Learning , ser. Proceedings of Machine Learning Research, vol. 87. PMLR, 29–31 Oc...

    2018

  28. [37]

    Learning control barrier functions from expert demon- strations,

    A. Robey, H. Hu, L. Lindemann, H. Zhang, D. V . Dimarogonas, S. Tu, and N. Matni, “Learning control barrier functions from expert demon- strations,” in 2020 59th IEEE Conference on Decision and Control (CDC), 2020, pp. 3717–3724

    2020

  29. [38]

    Neural lyapunov control for discrete-time systems,

    J. Wu, A. Clark, Y . Kantaros, and Y . V orobeychik, “Neural lyapunov control for discrete-time systems,” in Advances in Neural Information Processing Systems , A. Oh, T. Naumann, A. Globerson, K. Saenko, M. Hardt, and S. Levine, Eds., vol. 36. Curran Associates, Inc., 2023, p...

    2023

  30. [39]

    Lyapunov-stable neural control for state and output feedback: A novel formulation,

    L. Yang, H. Dai, Z. Shi, C.-J. Hsieh, R. Tedrake, and H. Zhang, “Lyapunov-stable neural control for state and output feedback: A novel formulation,” in Forty-first International Conference on Machine Learning, 2024. [Online]. Available: https://openreview.net/forum?id= 3xPMW9JURD

    2024

  31. [40]

    Learning robust output control barrier functions from safe expert 10 demonstrations,

    L. Lindemann, A. Robey, L. Jiang, S. Das, S. Tu, and N. Matni, “Learning robust output control barrier functions from safe expert 10 demonstrations,” IEEE Open Journal of Control Systems , vol. 3, pp. 158–172, 2024

    2024

  32. [41]

    Data-efficient safe learning and control with on-board sensors: Bayesian meta-learning and barrier function based approach,

    W. Hashimoto, K. Hashimoto, A. Wachi, X. Shen, M. Kishida, and S. Takai, “Data-efficient safe learning and control with on-board sensors: Bayesian meta-learning and barrier function based approach,” Advanced Robotics , vol. 0, no. 0, pp. 1–14, 2024. [Online]. Available: https:...

    2024

  33. [42]

    PyBullet,

    “PyBullet,” https://pybullet.org/wordpress/

  34. [43]

    Safe control with learned certificates: A survey of neural lyapunov, barrier, and contraction methods for robotics and control,

    C. Dawson, S. Gao, and C. Fan, “Safe control with learned certificates: A survey of neural lyapunov, barrier, and contraction methods for robotics and control,” IEEE Transactions on Robotics , vol. 39, no. 3, pp. 1749– 1767, 2023

    2023

  35. [44]

    Introduction to alpha shapes,

    K. Fischer, “Introduction to alpha shapes,” ETH Zurich, Tech. Rep., 2000, available online: http://www.stanford.edu/ ∼wluh/cs448b/ alphashapes.html

    2000

  36. [45]

    “CasADi,” https://web.casadi.org/

  37. [46]

    LMPC code,

    “LMPC code,” https://github.com/urosolia/LMPC

  38. [47]

    Turlebot for PyBullet,

    “Turlebot for PyBullet,” https://github.com/erwincoumans/pybullet robots

  39. [164]

    1724–1735

    PMLR, 08–11 Nov 2022, pp. 1724–1735. [Online]. Available: https://proceedings.mlr.press/v164/dawson22a.html

    2022

  40. [2025]

    Available: https://arxiv.org/abs/2502.02133

    [Online]. Available: https://arxiv.org/abs/2502.02133

    arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.