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arxiv: 1906.08546 · v1 · pith:MJ2WFZMKnew · submitted 2019-06-20 · 📡 eess.SY · cs.SY· math.OC

Dual-control based approach to batch process operation under uncertainty based on optimality-conditions parameterization

Radoslav Paulen , Miroslav Fikar This is my paper

Pith reviewed 2026-05-25 19:28 UTC · model grok-4.3

classification 📡 eess.SY cs.SYmath.OC
keywords dual controlbatch processesparametric uncertaintyoptimality conditionsscenario-based approachadaptive predictive controlrobust controlmembrane filtration
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The pith

Parameterized optimality conditions enable dual robust control of batch processes under uncertainty.

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

The paper tackles the dual-control problem for batch processes with unknown parameters, where the controller must trade off immediate robust performance against actions that excite the plant enough to learn the parameters and improve future performance. It proposes embedding parameterized conditions of optimality into an adaptive predictive-control scheme. Dual features are handled by a scenario-based multi-stage formulation that models the adaptive robust decision problem and projects the resulting decisions into the controller predictions. This is presented as a way to increase computational efficiency while avoiding the conservativeness of prior methods, and the scheme is demonstrated on a batch membrane filtration example.

Core claim

The central claim is that dual robust control of batch processes under parametric uncertainty can be achieved by using parameterized conditions of optimality inside an adaptive predictive-control framework, with dual features incorporated via a scenario-based multi-stage approach that models the adaptive robust decision problem and projects this decision into the controller predictions.

What carries the argument

Parameterized conditions of optimality combined with a scenario-based multi-stage adaptive predictive controller that captures the performance-versus-excitation trade-off.

Load-bearing premise

A finite set of scenarios suffices to capture the adaptive robust decision problem and the parameterization of optimality conditions stays valid when placed inside the multi-stage predictions.

What would settle it

An experiment or simulation in which the closed-loop performance changes substantially when the number of scenarios is increased, or in which the embedded optimality-condition parameterization produces infeasible or inconsistent predictions across stages.

Figures

Figures reproduced from arXiv: 1906.08546 by Miroslav Fikar, Radoslav Paulen.

Figure 1
Figure 1. Figure 1: Illustration of the parameterization of the optimal control policy under uncertainty. [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Scenario tree representation of the uncertainty evolution for a multi-stage con [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Nanodiafiltration process scheme. final concentrations c1,f and c2,f must be met. The transmembrane pressure is controlled at a constant value. The temperature of the solution is maintained around a constant value using a heat exchanger. The manipulated variable u(t) is the ratio between fresh water inflow into the tank and the permeate outflow qp that is given by qp = γ1 ln  γ2 c1c γ3 2  = γ1 (ln(γ2) − … view at source ↗
Figure 4
Figure 4. Figure 4: Results obtained using the adaptive strategy. Set-membership estimates over time [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Results obtained using the dual-control strategy. Set-membership estimates over [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: A box plot with the statistical information (the median as solid horizontal line, [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
read the original abstract

This paper presents a scheme for dual robust control of batch processes under parametric uncertainty. The dual-control paradigm arises in the context of adaptive control. A trade-off should be decided between the control actions that (robustly) optimize the plant performance and between those that excite the plant such that unknown plant model parameters can be learned precisely enough to increase the robust performance of the plant. Some recently proposed approaches can be used to tackle this problem, however, this will be done at the price of conservativeness or significant computational burden. In order to increase computational efficiency, we propose a scheme that uses parameterized conditions of optimality in the adaptive predictive-control fashion. The dual features of the controller are incorporated through scenario-based (multi-stage) approach, which allows for modeling of the adaptive robust decision problem and for projecting this decision into predictions of the controller. The proposed approach is illustrated on a case study from batch membrane filtration.

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

0 major / 2 minor

Summary. The manuscript proposes a dual robust control scheme for batch processes under parametric uncertainty. It parameterizes the conditions of optimality from the nominal problem and embeds them in a scenario-based multi-stage predictive control formulation to capture the adaptive robust decision problem, allowing the controller predictions to incorporate both robust performance optimization and plant excitation for parameter learning. The approach is demonstrated on a batch membrane filtration case study showing the expected performance-excitation trade-off.

Significance. If the parameterization of optimality conditions remains valid inside the multi-stage scenario tree, the method offers a tractable route to dual control that avoids the conservativeness or high computational cost of prior approaches. The consistent derivation noted in the full manuscript and the concrete case-study illustration of the trade-off constitute a clear contribution to adaptive robust control of batch processes.

minor comments (2)
  1. [Abstract] Abstract, paragraph on the proposed scheme: the statement that the scenario-based approach 'allows for modeling of the adaptive robust decision problem' would be clearer if it explicitly referenced the stationarity conditions used for parameterization (as described in the derivation section).
  2. [Case study] Case study section: the number of scenarios and the branching structure of the multi-stage tree are not stated numerically; adding these values would allow readers to assess the claimed computational efficiency directly.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, recognition of the contribution, and recommendation of minor revision. The assessment accurately reflects the proposed parameterization of optimality conditions within the multi-stage scenario framework for dual control.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper derives a parameterization of optimality conditions from the stationarity conditions of the nominal problem and embeds it into a scenario-based multi-stage formulation for dual robust control. This construction is presented as an independent extension that projects adaptive decisions into controller predictions without reducing the claimed performance or dual features to re-expressions of the input scenarios or fitted parameters by construction. No load-bearing self-citations, self-definitional steps, or ansatzes smuggled via citation are identified. The case study on membrane filtration demonstrates the expected performance-excitation trade-off in a manner consistent with the stated assumptions. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard domain assumptions of robust and adaptive control plus the novel parameterization step; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Parametric uncertainty can be adequately represented by a finite collection of scenarios for the purpose of multi-stage decision making
    Invoked when the dual features are incorporated through the scenario-based approach.

pith-pipeline@v0.9.0 · 5690 in / 1177 out tokens · 22613 ms · 2026-05-25T19:28:59.139982+00:00 · methodology

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Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages

  1. [1]

    23 (4) Barton, P

    Problems without Path Constraints.Industrial & Engineering Chemistry Research1994, 33, 2111–2122. 23 (4) Barton, P. I.; Pantelides, C. C. gPROMS - a Combined Discrete/Continuous Modelling Environment for Chemical Processing Systems.Simulation Series 1993, 25, 25–34. (5) Process Systems Enterprise, gPROMS. 1997–2009. (6) Čižniar, M.; Fikar, M.; Latifi, M. A...

    work page 1993

  2. [2]

    InControl and Optimisation of Process Systems; Pushpa- vanam, S., Ed.; Advances in Chemical Engineering Supplement C; Academic Press, 2013; Vol

    (13) Francois, G.; Bonvin, D. InControl and Optimisation of Process Systems; Pushpa- vanam, S., Ed.; Advances in Chemical Engineering Supplement C; Academic Press, 2013; Vol. 43; pp 1 –

    work page 2013

  3. [3]

    (16) Jang, H.; Lee, J

    (15) Martí,R.; Lucia,S.; Sarabia,D.; Paulen,R.; Engell,S.; dePrada,C.Improvingscenario decomposition algorithms for robust nonlinear model predictive control.Computers & Chemical Engineering 2015, 79, 30–45. (16) Jang, H.; Lee, J. H.; Biegler, L. T. A robust NMPC scheme for semi-batch polymer- ization reactors. IFAC-PapersOnLine 2016, 49, 37 – 42, 11th IF...

    work page 2015

  4. [4]

    Extents of Reaction and Flow for Homogeneous Reaction Systems with Inlet and Outlet Streams.AIChE Journal 2010,

    (20) Amrhein, M.; Bhatt, N.; Srinivasan, B.; Bonvin, D. Extents of Reaction and Flow for Homogeneous Reaction Systems with Inlet and Outlet Streams.AIChE Journal 2010,

    work page 2010

  5. [5]

    Exact linearization and control of a continuous stirred tank reactor

    (21) Liou, C.; Hsiue, T. Exact linearization and control of a continuous stirred tank reactor. Journal of the Chinese Institute of Engineers1995, 18, 825–833. (22) Feldbaum, A. Dual control theory. I.Avtomatika i telemekhanika1995, 21, 1240–1249. (23) Filatov, N. M.; Unbehauen, H. Survey of adaptive dual control methods.IEE Proceed- ings - Control Theory ...

    work page 2000

  6. [6]

    C.; Potschka, A.; Schlöder, J

    (28) La, H. C.; Potschka, A.; Schlöder, J. P.; Bock, H. G. Dual Control and Online Optimal Experimental Design.SIAM Journal on Scientific Computing2017, 39, B640–B657. (29) Lorenzen, M.; Cannon, M.; AllgÃűwer, F. Robust MPC with recursive model update. Automatica 2019, 103, 461–471. (30) Lee, J. M.; Lee, J. H. An approximate dynamic programming based appro...

    work page 2019

  7. [7]

    Adaptive receding horizon control for constrained MIMO systems.Automatica 2014, 50, 3019 –

    (31) Tanaskovic, M.; Fagiano, L.; Smith, R.; Morari, M. Adaptive receding horizon control for constrained MIMO systems.Automatica 2014, 50, 3019 –

    work page 2014

  8. [8]

    Adaptive model predictive control for linear time varying MIMO systems.Automatica 2019, 105, 237 –

    (32) Tanaskovic, M.; Fagiano, L.; Gligorovski, V. Adaptive model predictive control for linear time varying MIMO systems.Automatica 2019, 105, 237 –

    work page 2019

  9. [9]

    (33) Heirung, T. A. N.; Ydstie, B. E.; Foss, B. Dual adaptive model predictive control. Automatica 2017, 80, 340 –

    work page 2017

  10. [10]

    Real-time algorithm for self-reflective model predictive control

    (34) Feng, X.; Houska, B. Real-time algorithm for self-reflective model predictive control. Journal of Process Control2018, 65, 68–77. 26 (35) Thangavel, S.; Lucia, S.; Paulen, R.; Engell, S. Towards dual robust nonlinear model predictive control: A multi-stage approach. Proc. Amer Contr Conf. 2015; pp 428–433. (36) Thangavel, S.; Lucia, S.; Paulen, R.; En...

    work page 2015

  11. [11]

    Recursive state estimation: Unknown but bounded errors and system inputs

    (38) Schweppe, F. Recursive state estimation: Unknown but bounded errors and system inputs. IEEE Transactions on Automatic Control1968, 13, 22–28. (39) Fogel, E.; Huang, Y. On the value of information in system identification – Bounded noise case.Automatica 1982, 18, 229 –

    work page 1982

  12. [12]

    Toward Fast Dynamic Optimization: An In- direct Algorithm That Uses Parsimonious Input Parameterization.Industrial & Engi- neering Chemistry Research2018, 57, 10038–10048

    (41) Aydin, E.; Bonvin, D.; Sundmacher, K. Toward Fast Dynamic Optimization: An In- direct Algorithm That Uses Parsimonious Input Parameterization.Industrial & Engi- neering Chemistry Research2018, 57, 10038–10048. (42) Rodrigues, D.; Bonvin, D. Dynamic Optimization of Reaction Systems via Exact Par- simonious Input Parameterization.Industrial & Engineeri...

    work page 2015

  13. [13]

    Worst-case formulations of model predictive control for systems with bounded parameters.Automatica 1997, 33, 763 –

    (45) Lee, J.; Yu, Z. Worst-case formulations of model predictive control for systems with bounded parameters.Automatica 1997, 33, 763 –

    work page 1997

  14. [14]

    Set-membership methodology for model- based prognosis.ISA Transactions 2017, 66, 216 –

    (46) Yousfi, B.; RaÃŕssi, T.; Amairi, M.; Aoun, M. Set-membership methodology for model- based prognosis.ISA Transactions 2017, 66, 216 –

    work page 2017

  15. [15]

    M.; Lee, J

    (48) Lee, J. M.; Lee, J. H. Approximate dynamic programming-based approaches for in- putâĂŞoutput data-driven control of nonlinear processes.Automatica 2005, 41, 1281–

    work page 2005

  16. [16]

    Optimal feeding strategy of diafiltration buffer in batch membrane processes.Journal of Membrane Science2012, 411-412, 160–172

    (49) Paulen, R.; Fikar, M.; Foley, G.; Kovács, Z.; Czermak, P. Optimal feeding strategy of diafiltration buffer in batch membrane processes.Journal of Membrane Science2012, 411-412, 160–172. (50) Söderström, T. Errors-in-variables methods in system identification.Automatica 2007, 43, 939 –

    work page 2007

  17. [17]

    R.; Paulen, R

    (51) Gottu Mukkula, A. R.; Paulen, R. Model-based design of optimal experiments for nonlinear systems in the context of guaranteed parameter estimation.Computers & Chemical Engineering 2017, 99, 198 –

    work page 2017

  18. [18]

    Dynamic optimization of batch processes: I

    (52) Srinivasan, B.; Palanki, S.; Bonvin, D. Dynamic optimization of batch processes: I. Characterization of the nominal solution.Computers & Chemical Engineering 2003, 27, 1–26. 28 (53) Jönsson, A.-S.; Trägårdh, G. Ultrafiltration applications.Desalination 1990, 77, 135 – 179, Proceedings of the Symposium on Membrane Technology. 29

    work page 2003