Pith. sign in

REVIEW 5 major objections 4 minor 21 references

Update-Aware Robust Optimal Model Predictive Control for Nonlinear Systems

T0 review · 5 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Update-aware MPC provably widens the feasible set for nonlinear systems.

desk verdict Genuinely new update-aware MPC formulation with correct set-inclusion theorems, but the central algorithm is unproved and the GSIP-to-SIP reduction appears to drop universal quantifiers. read the letter →

arxiv 2506.01729 v2 pith:MELYU7YF submitted 2025-06-02 eess.SY cs.SYmath.OC

J. Wehbeh , E. C. Kerrigan This is my paper
classification eess.SYcs.SYmath.OC MSC 90C3493C10
keywords modelpredictivecontrolrobustoptimalmin-maxMPCnonlinearsystemssemi-infiniteprogrammingexistenceconstraintsdecreasinghorizondynamic
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

Robust (min-max) model predictive control normally recomputes the whole remaining input sequence at each step, even though the controller will re-solve later; that wastes information and can make solvable problems look infeasible. This paper proposes an update-aware variant for decreasing-horizon nonlinear systems that plans only the next input while requiring that, for every disturbance, some future continuation keeps the problem feasible and keeps the worst-case cost below a running bound. The paper proves that this formulation has a larger feasible set than the conventional one, so its optimal worst-case bound is never worse and is usually better, that the scheme is recursively feasible, and that the bound is non-increasing from one step to the next. It casts the computation as a chain of nested existence-constrained semi-infinite programs and solves them by local reduction with adaptively generated worst-case uncertainty scenarios. On a planar quadrotor benchmark the update-aware controller reaches a higher terminal height than the conventional robust controller and solves two scenarios the conventional controller cannot.

What carries the argument

The load-bearing object is the nested existence-constrained semi-infinite program. Starting from the dynamic programming principle of optimality, the paper introduces $U^\ast_k(z_k)$, the set of next inputs $v_k$ such that for all disturbances $\omega_k$ and all resulting states $s_k$ there exists a continuation input in $U^\ast_{k+1}$, and $J^\ast_k(z_k, \gamma_k)$, the set of $v_k$ for which such a continuation keeps the worst-case total cost no larger than $\gamma_k$. The optimization then becomes $\min \delta_k$ over $U^\ast_k(z_k) \cap J^\ast_k(z_k, \delta_k)$, a finite-dimensional problem whose constraints quantify over infinite uncertainty sets. To solve it, each stage is rewritten as a semi-infinite program, and the infinite quantifications are handled by local reduction: at each iteration one generates finitely many uncertainty scenarios that most violate the constraints, following [20] and the existence-constrained extension in [16]. Because the scenario-generation subproblem for the cost constraint has a decision-dependent uncertainty set, it is a generalized semi-infinite program; the paper converts it into a regular SIP through a logical decomposition plus a smoothing step [21], preserving the nested recursive structure.

What would settle it

Take a two-step problem with a small, finite disturbance set and a non-convex reachable set, evaluate the recursion (14) exactly by enumeration, and compare its value with the output of (17) solved by local reduction; if the value from (17) is smaller than the exact min-max value, or if applying $u^\ast_0$ produces a state from which no $u^\ast_1$ satisfying (17) exists, the central equivalence fails. A more targeted check is to set the smoothing parameter $\epsilon$ in (27) to zero and test whether the smoothed constraint ever admits a scenario that violates the original constraint (24b).

Watch

Extended reading notes

Core claim

The central claim is that accounting for the fact that the control trajectory will be re-optimized at future time steps changes the robust optimal control problem in a way that can be made precise and solved. At time $k$ the algorithm computes only the next control segment $u^\ast_k(z_k)$ and a worst-case bound $\gamma^\ast_k(z_k)$ by demanding, through sets $U^\ast_k$ and $J^\ast_k$, that for every disturbance $\omega_k$ and every resulting next state $s_k$ there exists a future continuation policy that keeps all remaining constraints satisfied and keeps the total cost at or below $\gamma_k$. This existence-constrained formulation is obtained from the recursive min-max problem by swapping a universal quantifier with an existential one; the paper proves the swapped feasible set is a superset of the no-update one (Theorem 1), giving $\gamma^\ast_k(z_k) \le \bar\gamma_k(z_k)$ (Theorem 2), recursive feasibility (Theorem 3), and $\gamma^\ast_{k+1}(z_{k+1}) \le \gamma^\ast_k(z_k)$ along closed-loop trajectories (Theorem 4). The paper claims this is the first min-max MPC with explicit dynamic programming that handles arbitrary nonlinear systems and that generates its own optimal uncertainty scenarios instead of relying on a fixed scenario tree. The planar quadrotor demonstration shows the update-aware controller achieving a better worst-case performance bound and solving two of three benchmark scenarios that the non-update-aware controller cannot solve.

Load-bearing premise

All the guarantees rest on the paper's unproved claim that the recursive min-max problem (14) is exactly equivalent to the existence-constrained problem (17), and on the asserted conversion of the generalized semi-infinite program (24) into the regular SIP (27); if either reduction is not exact, the algorithm can return a suboptimal or infeasible input.

Editorial extensions

If this is right

  • Problems that are infeasible for a non-update-aware robust MPC can become feasible, because the constraint is only that some future policy exists for each disturbance rather than that one open-loop plan works for all disturbances.
  • The closed-loop worst-case performance bound is never worse than the non-update-aware bound, and it is guaranteed not to increase between successive re-optimizations.
  • The uncertainty space is discretized adaptively by worst-case constraint-violating scenarios rather than by a fixed scenario tree, so the scenario grid is chosen by the optimization itself.
  • The computational cost is substantial: the number of semi-infinite programs to solve scales linearly with the horizon in the best case and exponentially in the worst case, in line with earlier dynamic-programming-based MPC approaches.
  • On the paper's planar quadrotor benchmark, update-aware MPC reaches a terminal height of 50.91 versus 42.73 for the non-update-aware controller in the solvable scenario, and solves the two scenarios the latter cannot.

Reading between the lines

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

  • The quantifier swap is the conceptual core: update-aware robust MPC replaces open-loop plans with the existence of a closed-loop continuation, and the same idea could plausibly extend to receding-horizon MPC if terminal ingredients are added, though the paper only treats decreasing horizons.
  • The guarantees are proven for exact solutions of the nested SIPs; an implementation using local or multistart solvers may return a suboptimal input, so a certified version would need global optimization or validated bounds on the constraint violations.
  • The monotone decrease of the performance bound provides a natural online warm-starting scheme: the previous stage's bound is a valid upper bound for the next stage and could be used as a cut to accelerate the nested solves.
  • The smoothing parameter in the generalized-SIP conversion is said to be the smallest positive constant; if it is instead chosen numerically, the smoothed feasible set differs from the true one, so the reported improvements may be slightly optimistic relative to the exact formulation.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 4 minor

Summary. The paper proposes an update-aware robust optimal MPC scheme for decreasing-horizon nonlinear systems. The controller is supposed to account for the fact that future inputs will be re-optimized, by formulating the trajectory generation problem as a nested sequence of existence-constrained semi-infinite programs (SIPs). The authors prove set-containment and worst-case cost results (Theorems 1 and 2), recursive feasibility (Theorem 3), and monotone improvement of the performance bound (Theorem 4). The numerical section applies the proposed algorithm to a planar quadrotor example and reports improved performance over a non-update-aware robust MPC baseline.

Significance. The conceptual idea of encoding future re-optimization through quantifier alternation is interesting and, if made rigorous, would be a useful contribution to robust MPC for nonlinear systems. Theorems 1 and 2 are elementary quantifier arguments and appear correct as stated. However, the algorithmic core of the paper is not established: the equivalence between the recursive min-max problem (14) and the existence-constrained formulation (17) is explicitly left unproved, and the conversion of the generalized SIP (24) into the regular SIP (27) is asserted without a derivation and appears to change the quantifier structure of the problem. The reported experiments do not compensate for these gaps because they do not verify that the implemented solver follows the stated reduction. As it stands, the paper does not support its central claim that Algorithm 1 provably returns the true optimal solution to the update-aware min-max problem.

major comments (5)
  1. [§III.A, Eqs. (14)–(17)] The paper states that the equivalence between the recursive min-max problem (14) and the existence-constrained formulation (17) 'relies on (15) and (16) describing the constraints of (14) exactly, and is left out of this paper.' This equivalence is load-bearing: Algorithm 1 solves (17), and Theorems 3 and 4, as well as the claim of returning the true optimal solution, depend on (17) being exactly equivalent to the intended optimal control problem. Without a proof, the central algorithmic claim is unsupported. This is not a routine detail, because (14) is a single optimization over v_k with an embedded future optimal value, whereas (17) introduces an auxiliary scalar δ_k and intersects two separately defined sets; whether these formulations coincide is precisely the question.
  2. [§IV, Eqs. (24)–(27)] The conversion of the generalized SIP (24) into the regular SIP (27) is asserted without derivation. The text moves from a universal condition over δ_{k+1} and v_{k+1} in (24b) and (25) to the single inequality (27), which contains no explicit quantifier over δ_{k+1}; the minimization over λ and ω_{k+1} in (27) does not by itself enforce the original universal statement. A concrete terminal instance with P=2 and γ_k=0 illustrates the problem: the true violation condition from (24b) is σ_k ≤ 2, whereas (27) with δ_{k+1}=1 and λ=(0,1,0) accepts σ_k=3 as feasible. Thus, as written, the reduction changes the problem, and the scenarios generated by the described procedure need not certify constraint (21d). A rigorous derivation and an explicit statement of the quantifiers retained in (27) are required before the algorithm can be said to solve (17).
  3. [§IV, final paragraph] The contributions in §I-C and the abstract claim that the method 'returns the true optimal solution to the min-max problem,' but the last paragraph of §IV concedes that the problems (21), (22), and (23) are 'usually non-convex in practice' and that the implementation uses 'easily parallelizable multistart methods.' For nonconvex SIPs, local reduction with multistart heuristics does not guarantee global optimality; the paper even notes that global optimization methods would be needed if guaranteed optimality is required. This contradiction means that the reported numerical implementation cannot substantiate the global-optimality claim, and the claim should either be removed or supported by a global optimization argument.
  4. [§V, Table I and Figure 2] The numerical study compares objective values and computation times between the two controllers, but it does not report constraint-violation checks, scenario counts, or any verification that the implemented solver follows the reduction (25)–(27). The statement that UARO-MPC 'successfully solves all 3 problems' is therefore not backed by the data shown. The experiments cannot validate the correctness of the reduction from (24) to (27), which is the main unresolved technical point of the paper.
  5. [§III.B, Theorem 4] Theorem 4's proof relies on the claim that u*_k(z_k) belongs to U*_k(z_k) ∩ J*_k(z_k, γ*_k) under (17a) and on the non-emptiness of the sets in (16). These conclusions are valid only if (17) is equivalent to (14) and if the numerical solver actually solves (17). Since both points are unproved, Theorem 4 does not guarantee the monotone decrease of the performance bound for the implemented algorithm.
minor comments (4)
  1. [§IV, Eqs. (21c) and (22c)] The constraints (21c) and (22c) use the symbols x_k, u_k, w_k, whereas the surrounding expressions use the optimization variables s_k, v_k, ω_k; this notational inconsistency should be fixed for clarity.
  2. [§IV, Eq. (26)] The notation 'P i+2 k' in (26) is confusing; it should presumably be P^{k+2}_k or similar, consistent with (22d). Please clarify the index convention.
  3. [§IV, Eq. (27)] In (27), δ_{k+1} appears as a free parameter, but the surrounding text does not explain how δ_{k+1} is chosen during scenario generation or whether it is part of the upper-level decision variables. This should be stated explicitly.
  4. [§IV] There is a typographical double period at the end of the paragraph on multistart methods ('significant computational cost..').

Circularity Check

2 steps flagged · score 4.0 of 10

No fitting-to-data circularity: the update-aware feasibility/performance theorems are genuinely quantifier-based. The load-bearing circularity is algorithmic: the solver's correctness is delegated to the authors' own [16] and [21], with the central equivalence (14)-(17) left unproved.

  1. self citation load bearing [Section III-A after Eq. (17); Section IV, Eqs. (21) and (27)]
    "“The proof for this equivalence relies on (15) and (16) describing the constraints of (14) exactly, and is left out of this paper. … Then, from [16], (17) can be reformulated into the sequence of problems (21). … We address this using the procedure in [21], transforming the constraint of (24b) into the requirement that … (25) … which, using the smoothing procedure of [21], allows us to write (25) as (27).”"

    The advertised guarantee that Algorithm 1 returns the true min-max solution is made computable by two transformations that are not derived in this paper: (17)->(21) is attributed to [16], and (24)->(27) is attributed to [21]. Both references are by the same authors, and the paper explicitly states that the proof of the key equivalence (14)<->(17) is left out. The solver's correctness therefore rests on an unverified self-citation chain rather than on a derivation contained in, or independently checkable from, this manuscript. If the cited transformations are accepted as given, the algorithm's optimality is adopted by construction from those prior claims.

  2. ansatz smuggled in via citation [Section IV, Eqs. (24)-(27)]
    "“Unfortunately, due to the dependence of its uncertainty set on a decision variable, (24) is a Generalized SIP. We address this using the procedure in [21], transforming the constraint of (24b) into … (25) … which, using the smoothing procedure of [21], allows us to write (25) as (27).”"

    The conversion of the universal constraint (24b) into the single min-over-(omega,lambda) inequality (27) is the step that lets Algorithm 1 certify the nested constraint (21d). It is justified only by citation to [21], the authors' own work, and no derivation or independent numerical check appears in the paper. As written, (27) does not carry the universal quantifiers over delta_{k+1} and v_{k+1} that appear in (24b), so the regular SIP is not shown to be equivalent to the GSIP. The claim that solving (27) solves (24) is thus exactly the cited 'procedure,' smuggled in as a black box.

full rationale

The theoretical results Theorems 1-4 are not circular: they follow from quantifier-order arguments and the definitions of the update-aware sets (15)-(17), and they would stand independently of any numerical solver. There is no fitted parameter renamed as a prediction; the quadrotor results are simulations of the two controllers, not fitted outputs. The circularity concern is confined to the algorithmic layer. The paper's core claim that the method 'returns the true optimal solution to the min-max problem' relies on (i) an omitted proof of the equivalence (14)<->(17), and (ii) two transformations delegated to the authors' own prior work: the existence-constrained SIP reformulation of [16] and the GSIP-to-SIP smoothing of [21]. The latter is particularly load-bearing because, as written in (27), the universal quantifiers of (24b) are absent, so the equivalence is not self-evident and is not established in this manuscript. These are not fitting-to-data or definitional circularities, but they make the solver's correctness dependent on an unverified self-citation chain, so the paper is not fully self-contained. Score 4 reflects that the central update-aware insight and its feasibility/performance theorems have independent content, while the claimed optimality of Algorithm 1 is imported rather than derived.

Assumptions & free parameters 0 free parameters · 7 assumptions · 0 invented entities

The central algorithmic result inherits its solution machinery from the authors' prior work [16] and [21]; the assumptions are standard compactness and continuity conditions. No new physical entities are introduced, and no free parameters are fitted to data.

assumptions (7)
  • domain assumption The sets U and W are compact (Assumption 1).
    Invoked in Section II to ensure the semi-infinite programs are well-defined and the worst-case maxima are attained.
  • domain assumption X(u, w) is compact for all u, w (Assumption 2).
    Invoked in Section II to guarantee the feasible state trajectory set is compact for each control and disturbance.
  • domain assumption The cost function J is bounded for all feasible arguments (Assumption 3).
    Invoked in Section II to ensure J* and the value functions are bounded.
  • domain assumption The cost function J and constraints g are continuous (Assumption 4).
    Invoked in Section II to justify the use of local reduction methods for SIPs.
  • domain assumption Bellman's principle of optimality applies to the min-max robust control problem.
    Invoked in Section III-A to separate the current decision from the future continuation, forming the recursion (14).
  • standard math The Blankenship-Falk local reduction method solves the arising SIPs (from [20]).
    Invoked in Section IV as the foundation for replacing infinite uncertainty sets with finite scenario sets.
  • ad hoc to paper The generalized-SIP smoothing procedure of [21] correctly converts the existence-constrained constraints into a regular SIP.
    Invoked in Section IV, equation (27), using a self-cited method that is not independently verified and whose logical transformation is not derived in this paper.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Update-Aware Robust Optimal Model Predictive Control for Nonlinear Systems." pith.science (2026). https://pith.science/paper/MELYU7YF

@misc{pith2026250601729,
  author       = {Pith},
  title        = {Pith review of: Update-Aware Robust Optimal Model Predictive Control for Nonlinear Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MELYU7YF}},
  note         = {Machine review of arXiv:2506.01729}
}
read the original abstract

Robust optimal or min-max model predictive control (MPC) approaches aim to guarantee constraint satisfaction over a known, bounded uncertainty set while minimizing a worst-case performance bound. Traditionally, these methods compute a trajectory that meets the desired properties over a fixed prediction horizon, apply a portion of the resulting input, and then re-solve the MPC problem using newly obtained measurements at the next time step. However, this approach fails to account for the fact that the control trajectory will be updated in the future, potentially leading to conservative designs. In this paper, we present a novel update-aware robust optimal MPC algorithm for decreasing horizon problems on nonlinear systems that explicitly accounts for future control trajectory updates. This additional insight allows our method to provably expand the feasible solution set and guarantee improved worst-case performance bounds compared to existing techniques. Our approach formulates the trajectory generation problem as a sequence of nested existence-constrained semi-infinite programs (SIPs), which can be efficiently solved using local reduction techniques. To demonstrate its effectiveness, we evaluate our approach on a planar quadrotor problem, where it clearly outperforms an equivalent method that does not account for future updates at the cost of increased computation time.

Figures

Figures reproduced from arXiv: 2506.01729 by the authors.

Figure 1
Figure 1. Illustration of the quadrotor’s horizontal position ( [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Average γ values computed at each time step for Scenario 1. and the known disturbance set is W = {w |−wmax ≤ wk ≤ wmax ∀k ∈ {0, . . . , 4} } . (32) We compare the two controllers for the scenarios where c = 1 and wmax = 0.001 (Scenario 1), c = 0.1 and wmax = 0.001 (Scenario 2), and c = 1 and wmax = 0.01 (Scenario 3) across 500 simulated runs. The controller of (12a) (RO-MPC) fails to deal with Scenarios 2 and 3, whi… view at source ↗

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

21 extracted references · 19 canonical work pages

  1. [16]

    Semi-infinite programs for robust con- trol and optimization: Efficient solutions and extensions to existence constraints,

    J. Wehbeh and E. C. Kerrigan, “Semi-infinite programs for robust con- trol and optimization: Efficient solutions and extensions to existence constraints,” in 8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024 . IFAC, 2024, pp. 317–322

    2024

  2. [21]

    State-Dependent Uncertainty Modeling in Robust Optimal Control Problems through Generalized Semi-Infinite Programming

    J. Wehbeh and E. C. Kerrigan, “State-dependent uncertainty modeling in robust optimal control problems through generalized semi-infinite programming,” 2025. [Online]. Available: https://arxiv.org/abs/2503.10389

    work page Pith review arXiv 2025

  3. [1]

    J. B. Rawlings, D. Q. Mayne, M. Diehl et al., Model predictive control: theory, computation, and design . Nob Hill Publishing Madison, WI, 2017, vol. 2

    work page 2017

  4. [2]

    Au- tomatic scenario generation for efficient solution of robust optimal control problems,

    M. Zagorowska, P. Falugi, E. O’Dwyer, and E. C. Kerrigan, “Au- tomatic scenario generation for efficient solution of robust optimal control problems,” International Journal of Robust and Nonlinear Control, vol. 34, no. 2, pp. 1370–1396, 2024

    work page 2024

  5. [3]

    Min-max feedback model predictive control for constrained linear systems,

    P. O. Scokaert and D. Q. Mayne, “Min-max feedback model predictive control for constrained linear systems,” IEEE Transactions on Auto- matic control, vol. 43, no. 8, pp. 1136–1142, 1998

    work page 1998

  6. [4]

    Adaptive dynamic programming for control: A survey and recent advances,

    D. Liu, S. Xue, B. Zhao, B. Luo, and Q. Wei, “Adaptive dynamic programming for control: A survey and recent advances,” IEEE Transactions on Systems, Man, and Cybernetics: Systems , vol. 51, no. 1, pp. 142–160, 2020

    work page 2020

  7. [5]

    Control of constrained dynamic systems,

    D. Q. Mayne, “Control of constrained dynamic systems,” European Journal of Control , vol. 7, no. 2-3, pp. 87–99, 2001

    work page 2001

  8. [6]

    Approximate robust dynamic program- ming and robustly stable MPC,

    J. Bj ¨ornberg and M. Diehl, “Approximate robust dynamic program- ming and robustly stable MPC,” Automatica, vol. 42, no. 5, pp. 777– 782, 2006

    work page 2006

Show all 21 references
  1. [7]

    Min-max control of constrained uncertain discrete-time linear systems,

    A. Bemporad, F. Borrelli, and M. Morari, “Min-max control of constrained uncertain discrete-time linear systems,” IEEE Transactions on automatic control , vol. 48, no. 9, pp. 1600–1606, 2003

    2003

  2. [8]

    Inf–sup control of discontinuous piecewise affine systems,

    J. Spjøtvold, E. Kerrigan, D. Mayne, and T. Johansen, “Inf–sup control of discontinuous piecewise affine systems,” International Journal of Robust and Nonlinear Control: IFAC-Affiliated Journal , vol. 19, no. 13, pp. 1471–1492, 2009

    2009

  3. [9]

    Feedback min-max model predictive control using a single linear program: robust stability and the explicit solution,

    E. C. Kerrigan and J. M. Maciejowski, “Feedback min-max model predictive control using a single linear program: robust stability and the explicit solution,” International Journal of Robust and Nonlinear Control: IFAC-Affiliated Journal, vol. 14, no. 4, pp. 395–413, 2004

    2004

  4. [10]

    Tube-based robust nonlinear model predictive control,

    D. Q. Mayne, E. C. Kerrigan, E. Van Wyk, and P. Falugi, “Tube-based robust nonlinear model predictive control,” International journal of robust and nonlinear control , vol. 21, no. 11, pp. 1341–1353, 2011

    2011

  5. [11]

    Interactive multi-modal motion planning with branch model predictive control,

    Y . Chen, U. Rosolia, W. Ubellacker, N. Csomay-Shanklin, and A. D. Ames, “Interactive multi-modal motion planning with branch model predictive control,” IEEE Robotics and Automation Letters , vol. 7, no. 2, pp. 5365–5372, 2022

    2022

  6. [12]

    Disturbance rejection MPC framework for input-affine nonlinear systems,

    H. Xie, L. Dai, Y . Lu, and Y . Xia, “Disturbance rejection MPC framework for input-affine nonlinear systems,” IEEE Transactions on Automatic Control, vol. 67, no. 12, pp. 6595–6610, 2021

    2021

  7. [13]

    An efficient min/max robust model predictive control for nonlinear discrete-time systems with dynamic disturbance,

    T. H. Nguyen, D. Q. Bui, P. N. Dao et al. , “An efficient min/max robust model predictive control for nonlinear discrete-time systems with dynamic disturbance,” Chaos, Solitons & Fractals , vol. 180, p. 114551, 2024

    2024

  8. [14]

    Robust MPC via min–max differential inequalities,

    M. E. Villanueva, R. Quirynen, M. Diehl, B. Chachuat, and B. Houska, “Robust MPC via min–max differential inequalities,” Automatica, vol. 77, pp. 311–321, 2017

    2017

  9. [15]

    Handling the constraints in min-max MPC,

    J. Hu, X. Lv, H. Pan, and M. Zhang, “Handling the constraints in min-max MPC,” IEEE Transactions on Automation Science and Engineering, vol. 21, no. 1, pp. 296–304, 2022

    2022

  10. [17]

    Robust dynamic optimization of batch processes under parametric uncertainty: Utilizing approaches from semi-infinite pro- grams,

    J. Puschke, H. Djelassi, J. Kleinekorte, R. Hannemann-Tam ´as, and A. Mitsos, “Robust dynamic optimization of batch processes under parametric uncertainty: Utilizing approaches from semi-infinite pro- grams,” Computers & Chemical Engineering , vol. 116, pp. 253–267, 2018

    2018

  11. [18]

    Robust output feedback of nonlin- ear systems through the efficient solution of min-max optimization problems,

    J. Wehbeh and E. C. Kerrigan, “Robust output feedback of nonlin- ear systems through the efficient solution of min-max optimization problems,” in 2024 IEEE 63rd Conference on Decision and Control (CDC). IEEE, 2024, pp. 8870–8875

    2024

  12. [19]

    Dynamic programming,

    R. Bellman, “Dynamic programming,” science, vol. 153, no. 3731, pp. 34–37, 1966

    1966

  13. [20]

    Infinitely constrained optimization problems,

    J. W. Blankenship and J. E. Falk, “Infinitely constrained optimization problems,” Journal of Optimization Theory and Applications , vol. 19, pp. 261–281, 1976

    1976

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.