Adaptive Sliding Mode Control for Unmanned Surface Vehicles with Predefined-Time Tracking Performances
Round 1
Reviewer 1 Report
1) Provide a list of contributions and give sufficient evidences to support your claim.
2) Is Eq. (1) from a specific source? If not, the authors need to provide more details on how to derive this equation.
3) Remark 1: It has been mentioned that all actuators can have loss of effectiveness and bias faults simultaneously. Assume that kappa_i is very small, and corresponding tau_b is non-zero. This case can be seen as loss of actuator. Can the proposed method address this cases?
4) Lyapunov function given in (40) is quadratic. As shown in [R1] and [R2], using non-quadratic Lyapunov functions in adaptive schemes can lead to a better performance. The authors need to discuss this very important point as a remark. Consider using the suggested articles to conduct the discussion in the remark:
[R1]. "Performance enhanced model reference adaptive control through switching non-quadratic Lyapunov functions", 2015. [https://doi.org/10.1016/j.sysconle.2014.12.001]
[R2]. "Model reference adaptive control with L^{1+α} tracking", 1996. [https://doi.org/10.1080/00207179608921661]
5) The authors need to compare their method with a state-of-the-art method. This would help the readers to understand the advantages and disadvantages of the proposed method.
Acceptable.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper deals with the issue of trajectory tracking for a fully actuated class USV object. Theoretically, the work is well written and the reasoning is correct. The algorithm presented is derived from known methods that have been used to meet certain qualitative and quantitative criteria.
1. Although the literature review is done correctly, there is a lack of explanation as to what is the actual novelty of this work. It can be inferred that it is the design of a control algorithm that takes into account multiple qualitative criteria and provides robustness to selected classes of disturbance.
2. The authors do not convincingly state why the proposed algorithm is applied to USV control. The whole problem is that since the USV is assumed to be a fully actuated system, as implied by model (1) and (8), the presented controller can be used for an entire class of mechanical systems with similar characteristics. However, if a particular model of the USV is considered, e.g. in simulation, the assumption of sliding control at the force/torque \tau level without considering the actuator properties may not be appropriate. First of all, generating an input with a high switching frequency, which is characteristic of the SMC strategy, should be avoided for a real system. It would be more realistic to assume that such a signal is the control voltage of the actuator. However, even in such a case, a maximum switching frequency and signal saturation would have to be assumed. If this is not done, it is difficult to assess the system properties for a realistic USV model. I think that the authors should perform a nominal analysis (without the constraints imposed on the actuator dynamics) and a more realistic analysis that takes into account potential implementation constraints. This is important, as the authors take into account hysteresis effects, but on the other hand do not show the operation of the system at the limited sampling rate of the control loop.
3. There is a lack of commentary on the need for velocity measurement and the influence of measurement noise. How is the signal \dot\theta determined in equation (29)? Has the estimation of this component in the presence of noise been considered in the simulations? Please note that An Imprecise estimation of \dot\theta can lead to unacceptable closed-loop control performance.
4. Relationship (17) is unclear. How to interpret the "+" after the d/dt differentiation operator?
5. The norm | | in (18) should be explained. I believe that since x is a scalar function the norm | | is used to define the absolute value.
Other comments.
6. In the first sentence of the paper, instead of USV, it is better to use the plural form or to write that USV refers to a class of planar vessels. Without this, the sentence sounds rather odd, as USV is not about one particular system.
7. Line 20: "the inherent complex dynamics of USV, such as model uncertainties". This sentence should be corrected as model and modelling uncertainties are different concepts. Of course, a complex model can foster the appearance of uncertainties.
8. Line 26: The word "gain" does not fully reflect the issue. Rather, it is a design parameter whose selection is driven by the upper bound of the lumped disturbance.
9. Literature references in Definiotion 1, 2, Assumption 1, Lemma 1: a space is missing after the designation "([])".
10. Punctuation marks are missing from the equations. This is a mistake because equations should be parts of a sentence to which the rules of punctuation apply.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
No further comment.
Acceptable.
Reviewer 2 Report
The paper has been revised and some of my doubts have been properly clarified by the authors.
I maintain that the main drawback of the proposed solution seems to be the necessity to measure velocities of the object and the possible sensitivity of the algorithm to measurement uncertainties. This can be problematic in implementation.
It may also be troublesome to assume that the object is a fully-actuated system, as implied by the form of equation (1). I think it would be valuable to consider an underactuated system subject to second order nonholonomic consraints.
In a theoretical sense, however, the paper is correct and the mathematical reasoning is clear. Regarding Remark 4, it is worth showing explicitly that: k_j sign(\sigma_j) is a continuous function.
