Trajectory Tracking of Unmanned Hovercraft: Event-Triggered NMPC Under Actuation Limits and Disturbances
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript proposes an event-based adaptive nonlinear model predictive control (EANMPC) strategy for trajectory tracking of unmanned hovercraft subject to actuator saturation, unknown time-varying disturbances, and model uncertainty. The authors introduce an event-triggered rolling-optimisation framework with an adaptive prediction horizon aimed at improving tracking accuracy while reducing computational burden. Stability under the adaptive horizon is discussed, and two simulation studies are presented to illustrate the effectiveness of the approach. The topic is timely and relevant, particularly for real-time control systems where computational resources are limited and conventional MPC becomes difficult to deploy in practice. The work aims to address the well-known challenge of achieving a balance between real-time feasibility and control accuracy in nonlinear under-actuated platforms. The manuscript has a number of vantage points. The event-based MPC design directly addresses limitations of standard NMPC implementations, and the adaptive horizon concept is promising for reducing computational load. The simulation studies are structured and suggest improvements in triggering frequency and cost function behaviour as tracking error decreases. Although I consider the manuscript as having valid contributions, I have some comments for thew authors. First, the abstract and conclusion lack clarity and cohesion; they read as disconnected statements rather than concise, well-structured summaries of motivation, methodology, results, and contributions. Second, the specific contributions of the work are not stated explicitly enough. I would recommend having list of contributions at the end of the introduction. Specifically, it was not clear to me what was novel relative to existing event-triggered MPC frameworks, adaptive horizon MPC techniques. Second, the stability analysis needs more detailed derivation and more rigorous justification. Important details are missing, such as assumptions on disturbance boundedness, feasibility of the receding horizon under adaptive updates, and conditions ensuring contraction or robustness. Third, the the validation is limited. Comparison with state-of-the-art MPCs that also use a level of event-triggered mechanisms are required. Also, it would be interesting to see he about of actuator time or actuator energy consumption save through the event triggered mechanism.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe manuscript is interesting and addresses current issues related to the control of small unmanned vehicles. The elements of novelty and achievements presented in the article, according to the authors, concern three aspects with which I agree:
- the EANMPC algorithm is applied to better handle actuator limitations and to significantly enhance trajectory-tracking performance,
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a novel proof of input-to-state stability for EANMPC without local linearization is provided,
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a decreasing prediction horizon is employed to improve control performance and to reduce the number of control triggers at high speeds.
The introduction contains appropriate information and refers to relevant literature.
In my opinion, section 2 leaves much to be desired regarding the modeling of the system. The hovercraft dynamics model is presented very briefly in lines 96–106. Moreover, no literature sources are referenced in this section. I consider this a significant imperfection.
The applied method is presented in much greater detail, along with a stability analysis.
Section 4 documents the conducted simulations and presents the verification of the method. I have the most comments regarding this section.
Two trajectories were selected for the tests: a circle and a sinusoidal trajectory. I am curious how the controlled system would behave on trajectories that are not described by simple harmonic functions. In particular, how would it perform on a piecewise-linear (polyline) trajectory? This is usually how motion for this type of vehicle is planned.
The range of motion for trajectory no. 1 (the circle) is only about ten times the length of the tested vehicle, and the range of motion along the y-axis for trajectory no. 2 is even smaller. For this reason, I consider the obtained results to be insufficiently representative.
Time plots for the sideslip are not presented.
The descriptions of the figures showing the "cost function" and "time interval" are very brief and superficial. Sentences such as "Figure 14 shows the cost function changes under different methods. Figure 15 shows the triggering time intervals under different methods, respectively." do not explain anything to the reader beyond what is already stated in the figure captions.
The conclusion is too general and does not refer to a quantitative analysis of the obtained results. The results are poorly described and explained. I recommend expanding the conclusion with such an analysis or adding a section containing a critical evaluation of the results.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsThank you for your responses and consideration of my suggestions and comments. Please only improve the reference to literature on line 116.
