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arxiv: 2604.21030 · v1 · submitted 2026-04-22 · 📡 eess.SY · cs.AI· cs.RO· cs.SY· math.OC

Recognition: unknown

A Systematic Review and Taxonomy of Reinforcement Learning-Model Predictive Control Integration for Linear Systems

Mohsen Jalaeian Farimani , Roya Khalili Amirabadi , Davoud Nikkhouy , Malihe Abdolbaghi , Mahshad Rastegarmoghaddam , Shima Samadzadeh
Authors on Pith no claims yet

Pith reviewed 2026-05-09 23:19 UTC · model grok-4.3

classification 📡 eess.SY cs.AIcs.ROcs.SYmath.OC
keywords reinforcement learningmodel predictive controllinear systemssystematic literature reviewtaxonomyintegration strategieshybrid controladaptive control
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The pith

This review organizes RL-MPC integrations for linear systems into a five-dimensional taxonomy and synthesizes recurring design patterns from the literature.

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

The paper conducts a systematic literature review of how reinforcement learning is combined with model predictive control in linear or linearized systems. It classifies published studies across RL functional roles, algorithm classes, MPC formulations, cost-function structures, and application domains. A cross-dimensional synthesis identifies common pairings and trends while noting persistent issues such as computational cost, sample efficiency, robustness, and stability guarantees. The resulting structure supplies a reference that researchers can use to position new work or select components for hybrid controllers. By mapping the fragmented literature, the review aims to support more systematic development of adaptive constrained control.

Core claim

The literature on RL-MPC integrations for linear systems can be organized through a taxonomy based on RL functional roles, RL algorithm classes, MPC formulations, cost-function structures, and application domains, with cross-synthesis revealing recurring design patterns, methodological trends, and challenges including computational burden, sample efficiency, robustness, and closed-loop guarantees.

What carries the argument

A multi-dimensional taxonomy covering RL functional roles, RL algorithm classes, MPC formulations, cost-function structures, and application domains that structures the reviewed studies and enables identification of design patterns through cross-dimensional synthesis.

If this is right

  • New RL-MPC proposals can be located in the taxonomy to show their relation to existing combinations.
  • Observed associations between RL algorithm classes and MPC formulations can guide component selection for specific domains.
  • Documented challenges such as computational burden direct attention to efficiency improvements in future designs.
  • The synthesis supports evaluation of closed-loop stability and robustness when RL augments linear MPC.
  • Patterns in cost-function structures and application domains can inform tailored controller development.

Where Pith is reading between the lines

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

  • The same taxonomy approach could later be applied to nonlinear systems to compare how integration strategies differ.
  • Controlled experiments could test whether the most frequent pattern combinations actually deliver the reported performance benefits.
  • The reference structure may help avoid redundant exploration of already-covered RL-MPC pairings.
  • The organization highlights opportunities to incorporate additional guarantees from safe RL or distributed control into the hybrid setting.

Load-bearing premise

The five chosen taxonomy dimensions are sufficient to capture all major integration strategies without omissions, and the database search through 2025 captured a representative set of relevant peer-reviewed studies.

What would settle it

Discovery of multiple significant peer-reviewed papers on RL-MPC for linear systems that cannot be placed in any of the five taxonomy categories or were missed by the systematic search would show the review is incomplete.

Figures

Figures reproduced from arXiv: 2604.21030 by Davoud Nikkhouy, Mahshad Rastegarmoghaddam, Malihe Abdolbaghi, Mohsen Jalaeian Farimani, Roya Khalili Amirabadi, Shima Samadzadeh.

Figure 1
Figure 1. Figure 1: This figure illustrates the systematic review protocol employed in this study. Developed in accordance with [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Taxonomy of Reinforcement Learning roles in MPC–RL integrations. [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The co-occurrence between categories based on RL roles in MPC–RL integrations. [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Temporal distribution of RL roles applied in MPC–RL integrations. [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Taxonomy of Reinforcement Learning algorithms implemented in MPC–RL frameworks. [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Temporal evolution of RL algorithm types adopted in MPC–RL literature. [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Taxonomy of Cost Functions in MPC–RL Linear Control [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Taxonomy of MPC Formulations 21 [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Taxonomy of MPC–RL application fields in linear control [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Application fields of MPC–RL integration during years [PITH_FULL_IMAGE:figures/full_fig_p023_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: MPC type vs. RL algorithms in the integration of MPC–RL for linear control [PITH_FULL_IMAGE:figures/full_fig_p024_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: MPC type vs. RL roles in the integration of MPC–RL for linear control [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: RL algorithms vs. RL roles in the integration of MPC–RL for linear control [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Application fields vs. RL roles in the integration of MPC–RL for linear control [PITH_FULL_IMAGE:figures/full_fig_p025_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: MPC type vs. application fields in the integration of MPC–RL for linear control [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: MPC cost functions vs. application fields in the integration of MPC–RL for linear control [PITH_FULL_IMAGE:figures/full_fig_p026_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: MPC cost functions vs. MPC type in the integration of MPC–RL for linear control [PITH_FULL_IMAGE:figures/full_fig_p026_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: MPC cost functions vs. RL algorithms in the integration of MPC–RL for linear control [PITH_FULL_IMAGE:figures/full_fig_p027_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: MPC cost functions vs. RL roles in the integration of MPC–RL for linear control [PITH_FULL_IMAGE:figures/full_fig_p027_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: RL algorithms vs. application fields in the integration of MPC–RL for linear control [PITH_FULL_IMAGE:figures/full_fig_p028_20.png] view at source ↗
read the original abstract

The integration of Model Predictive Control (MPC) and Reinforcement Learning (RL) has emerged as a promising paradigm for constrained decision-making and adaptive control. MPC offers structured optimization, explicit constraint handling, and established stability tools, whereas RL provides data-driven adaptation and performance improvement in the presence of uncertainty and model mismatch. Despite the rapid growth of research on RL--MPC integration, the literature remains fragmented, particularly for control architectures built on linear or linearized predictive models. This paper presents a comprehensive Systematic Literature Review (SLR) of RL--MPC integrations for linear and linearized systems, covering peer-reviewed and formally indexed studies published until 2025. The reviewed studies are organized through a multi-dimensional taxonomy covering RL functional roles, RL algorithm classes, MPC formulations, cost-function structures, and application domains. In addition, a cross-dimensional synthesis is conducted to identify recurring design patterns and reported associations among these dimensions within the reviewed corpus. The review highlights methodological trends, commonly adopted integration strategies, and recurring practical challenges, including computational burden, sample efficiency, robustness, and closed-loop guarantees. The resulting synthesis provides a structured reference for researchers and practitioners seeking to design or analyze RL--MPC architectures based on linear or linearized predictive control formulations.

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

1 major / 0 minor

Summary. The paper presents a comprehensive systematic literature review (SLR) of RL-MPC integrations for linear and linearized systems. It organizes the reviewed studies via a multi-dimensional taxonomy covering RL functional roles, RL algorithm classes, MPC formulations, cost-function structures, and application domains; conducts a cross-dimensional synthesis to identify recurring design patterns and associations; and highlights methodological trends, integration strategies, and practical challenges including computational burden, sample efficiency, robustness, and closed-loop guarantees. The result is positioned as a structured reference for researchers and practitioners.

Significance. If the underlying SLR methodology proves complete and the taxonomy exhaustive, the work would provide a useful organizing framework for the fragmented literature on RL-MPC hybrids in linear systems, potentially guiding design choices and identifying open challenges. The cross-dimensional synthesis is a constructive element that could help the community move beyond ad-hoc integrations.

major comments (1)
  1. [Abstract / Methods] Abstract and (presumed) Methods section: the manuscript asserts a 'comprehensive' SLR covering peer-reviewed studies until 2025 but supplies no concrete details on search strings, databases queried, inclusion/exclusion criteria, number of papers screened or included, quality assessment, or PRISMA flow. Without these elements the representativeness of the corpus and the validity of the taxonomy and cross-synthesis cannot be verified, directly undercutting the central claim of comprehensiveness.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive and detailed review. We agree that the systematic literature review methodology must be documented with greater transparency to support the claim of comprehensiveness. We address the single major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract / Methods] Abstract and (presumed) Methods section: the manuscript asserts a 'comprehensive' SLR covering peer-reviewed studies until 2025 but supplies no concrete details on search strings, databases queried, inclusion/exclusion criteria, number of papers screened or included, quality assessment, or PRISMA flow. Without these elements the representativeness of the corpus and the validity of the taxonomy and cross-synthesis cannot be verified, directly undercutting the central claim of comprehensiveness.

    Authors: We acknowledge the validity of this observation. The submitted manuscript does not contain a dedicated Methods section or PRISMA flow diagram describing the SLR protocol. In the revised version we will insert a new Methods section that explicitly reports: the databases searched (IEEE Xplore, Scopus, Web of Science, ScienceDirect, and SpringerLink), the precise search strings and Boolean combinations employed, the inclusion and exclusion criteria (peer-reviewed English-language studies on RL-MPC for linear or linearized systems published through 2025, with clear focus on integration architectures), the screening process, the number of records identified, screened, and finally included, any quality-assessment steps applied, and a PRISMA flow diagram. These additions will enable independent verification of corpus representativeness and will not alter the taxonomy or cross-dimensional synthesis already presented. revision: yes

Circularity Check

0 steps flagged

No circularity in literature review synthesis

full rationale

This paper is a systematic literature review synthesizing external peer-reviewed studies on RL-MPC integrations. It contains no original derivations, equations, predictions, fitted parameters, or self-referential definitions that could reduce to inputs by construction. The taxonomy dimensions and cross-dimensional synthesis draw directly from the reviewed corpus without any load-bearing self-citation chains or ansatz smuggling. The central claims rest on the external literature rather than internal tautologies, making the work self-contained against the circularity criteria.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the assumption that the literature corpus is comprehensively and representatively captured by standard academic indexing up to 2025 and that the selected taxonomy dimensions adequately partition the design space.

axioms (1)
  • domain assumption The body of peer-reviewed and formally indexed studies on RL-MPC for linear systems published until 2025 can be exhaustively identified through standard academic databases and search procedures.
    The review's claim of comprehensive coverage depends on this premise.

pith-pipeline@v0.9.0 · 5565 in / 1423 out tokens · 55615 ms · 2026-05-09T23:19:06.068217+00:00 · methodology

discussion (0)

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Reference graph

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