Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents an innovative approach that integrates Integral Reinforcement Learning, the Multivariate Probabilistic Collocation Method, and Dynamic Event-Triggered Control for the optimal control of time-varying systems with random parameters and Asymmetric Input Constraints. The theoretical derivations are rigorous, and the Lyapunov-based stability analysis is thorough, demonstrating a solid theoretical foundation.

The introduction and related work sections do not adequately review recent advances. Furthermore, the experimental validation, while demonstrating feasibility, lacks comparative analysis with state-of-the-art methods, which limits the persuasiveness of the claimed contributions.

The authors are recommended to strengthen the literature review by incorporating recent work. Specifically, the following two references should be cited to better contextualize the work:

1.Compensator-Based Self-Learning: Optimal Operational Control for Two-Time-Scale Systems With Input Constraints, IEEE Transactions on Industrial Informatics, 2024, 20(7): 9465–9475.

Comparative studies with existing methods in the simulation section will further strengthen the contribution of this paper.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1. As the authors state, “This study explores a stochastic guarantee cost control (GCC) for time-varying systems with random parameters and asymmetric input constraints by employing integral reinforcement learning (IRL) method in the dynamic event-triggered (DET) mode”. It turns out that the objective of the article is the exploration of stochastic guarantee cost control (GCC) etc etc, but this phrase does not appear in the title, and does not appear a second time in the text. Therefore, it would be useful to actually emphasize in the text how this cost of control is guaranteed, both through mathematical relationships and through numerical simulation.
2. The authors were validated (so to speak) by publishing an article, Reference 29, in a top journal, in 2022. It would be useful for readers to mark in the text of the article the progress made towards that publication.
3. Why, in Fig. 5, for the square of the norm of ej, an entire space is marked in blue, and not a curve?
4. 6 would require a more detailed description
5. The Hamiltonian function and Bellman's optimality principle would require point descriptions before they could be used.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper is original, rigorous, and relevant. Only small refinements (as listed below) in explanation, simulation detail, and presentation are needed to make it stronger and more accessible.

• The background and references are strong, but you could add a short paragraph highlighting the practical importance of asymmetric input constraints (for example, in robotics, aerospace, or power systems).
• This would help non-specialist readers quickly see the motivation.
• The theoretical framework is rigorous. To improve readability, consider adding short explanatory notes after major derivations (for example, after Theorem 1, Line 148) to briefly explain the practical meaning.
• Flowcharts or step-by-step schematic diagrams for Algorithm 1 and Algorithm 2 would make the procedure clearer for practitioners.
• The simulation is useful for demonstrating feasibility. If possible, include a short table or graph comparing your proposed approach with a baseline (for example, ETC without DETC, or RL without MPCM). Even a simple comparison would highlight the performance gains more clearly.
• Adding metrics such as computational efficiency or communication savings would strengthen the case.
• The conclusion is aligned with the study goals. To improve impact, consider explicitly stating the main practical benefits (reduced computational burden, improved handling of AICs, resource-efficient communication).
• The manuscript is well-written. A light edit to shorten some long sentences would make it more accessible.
• Figures and tables could be slightly refined to improve readability.

Comments on the Quality of English Language

The quality of English in the manuscript is overall good and does not require major revisions. The technical content is clearly conveyed, and the grammar is generally accurate. However, some sentences are quite long and densely packed with information, which may make it difficult for readers to follow. Shortening these sentences and simplifying phrasing where possible would improve readability.  So, kindly check for such sentences. Minor edits for clarity and conciseness will help make the paper more accessible to a broader audience.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This study explores a stochastic guarantee cost control (GCC) for time-varying systems with random parameters and asymmetric input constraints by employing the integral reinforcement learning (IRL) method in the dynamic event-triggered (DET) mode. The following issues need to be resolved.

1. Some English expressions in the section of introduction need to be polished. For example, the sentence “...integrating reinforcement learning (IRL) ideas...” is better to change into “... integrating reinforcement learning (RL) ideas ...”.

2. The innovation of this article needs to be reorganized to highlight its contribution to the

section of introduction.

3. In the remark, what is the meaning of “this study focuses on solving the OC problem of AICs”? Please provide necessary explanations and restate the content of Remark 2. Additionally, the English expression in Theorem 1 needs to be reorganized.

4. Please check Theorems 2 and 3 to ensure their correctness.
5. Please check Formulas (72) and (73) to ensure their correctness.
6. There is an issue with the ‘icon‘ labeling in Figure 2. Please check it.
7. The conclusion needs to be reorganized to highlight the work of this article.
8. In the simulation section, the description of the graphics should be more comprehensive to highlight the superiority of the algorithm proposed in this paper.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf