Uncertainty in vessel control direction poses significant challenges in maritime operations, particularly in dynamic positioning, towing, and offshore wind farm maintenance. Traditional control methods struggle to handle uncertainties in system states for maritime operations, unmodeled dynamics, and multibody interactions. This study introduces an adaptive zone barrier Lyapunov control approach to address these challenges by ensuring vessel stability within a predefined operational zone while allowing adaptive parameter adjustments to compensate for uncertainties. The zone barrier Lyapunov function is employed to enforce safe operational constraints, preventing excessive deviations, while an adaptive control law dynamically estimates and adjusts system parameters. The proposed approach is validated through simulations of unmanned surface vehicle station-keeping and trajectory tracking. Results demonstrate that adaptive zone barrier Lyapunov control maintains vessel stability and maneuverability even when control direction is uncertain, outperforming conventional Lyapunov-based methods in handling constraint and robust effects. This study highlights the effectiveness of integrating zone barrier Lyapunov control with adaptive mechanisms for vessel motion control, offering a robust framework for enhancing maritime safety and operational efficiency in offshore environments.

In this paper, we propose the dynamic high-gain scaling technique and solutions to input saturation for uncertain strict-feedback nonlinear systems. Although high gain affords fast response and high accuracy for the improvement of tracking performance, there are two inescapable potential risks: (i) excessive high gain would amplify the negative effects from non-vanishing mismatched uncertainties; (ii) high gain may conflict with the limited regulation capacity. Herein, two strategies based on invariance property are applied to high-gain control, aiming to address these two risks separately. On the one hand, by defining the function of performance robustness evaluation (PRE), the scaling gain grows to speed up the convergence rate and then maintains at an acceptable high level while guaranteeing the robustness to uncertainties in an invariant set. On the other hand, for handling the input saturation, the control barrier function (CBF)-based quadratic program (QP) describes the function of performance safety evaluation (PSE) that helps assess the system safety and decide whether the compensation for saturation is necessary, as such, the balance between performance and saturation gets achieved. Numerical simulations and a semi-physical experiment are performed to investigate the performance of our proposed methodology. Note to Practitioners—The motivation of this article is that stringent time response constraints are necessary for security or to increase productivity in practical applications, while control constraints exist widely in control systems. The lack of constraint satisfaction may inevitably result in safety defects, performance degradation. Based on these observations, a balanced safety-critical high-gain control scheme is proposed for input-constrained nonlinear uncertain strict-feedback systems. The contribution focuses on finding a balanced relationship between rapid response ability, robustness to mismatched uncertainties, and finite regulation capability in the high-gain control framework, since excessive control gain would potentially amplify the effect of non-vanishing mismatched uncertainty or lead to unexpected control saturation. Moreover, the theoretical derivation demonstrates that: only the system has the tolerance of matched uncertainties when the high gain grows to infinity, otherwise there must exit a maximum value for high gain to maintain the robustness and stability; the PSE function assesses the system safety under saturation conditions and decides whether to continue improving control performance or compensate for saturation for the maintenance of stability.

Ensuring the side-by-side configuration of the automated surface vessels under the effect of the uncertainties of the environment attracted continued efforts on this challenging issue. This paper investigates the learning-based safety-enhanced adaptive side-by-side control algorithm that suitably defines and uses the modified adaptive control barrier functions to tackle the constrained control satisfied under the uncertainty environment by ensuring the control barriers on state-variables constraints. In addition to the inherent adaptivity of the adaptive control barrier functions, the finite-time auxiliary system is enabled to modify the adaptive control barrier functions, which considers the unknown part of the nominal model to ensure the satisfaction of system constraints, especially under uncertain situations. For the formulated quadratic programs with adaptive control barrier functions and control Lyapunov functions, the operator splitting quadratic program is employed in problem-solving, which effectively enlarges the robustness of problem-solving, making it particularly efficient and reliable for real-time applications. The effectiveness of the proposed method is demonstrated via comparative simulations under uncertain cases to show the superior adaptive ability under the model uncertainties, which can be employed in marine industry applications, e.g., carbon emissions estimation modeling and optimization.Note to Practitioners—This paper was motivated by enlarging the adaptive ability of optimization-based safe operation for safety-critical automated surface vessels control under the side-by-side configuration under the effect of the uncertainty of the environment. The proposed learning-based safety-enhanced adaptive side-by-side control algorithm promotes adaptivity and control performance with the usage of the finite-time auxiliary system to the refined adaptive control barrier functions in the optimization problem formulation. The problem-solving is accelerated with the usage of the operator-splitting quadratic program. These implements effectively enlarge the robustness of the proposed method, making it particularly efficient and reliable for industrial real-time applications. The proposed method employed a complicated system design with the outcome of a simple algorithm implemented with promoted adaptivity and robustness, which can be employed in industrial applications in future research to promote current control system performance.

This paper focuses on the assessment of non-complete states in complex task networks and establishes an online capability boundary assessment model based on real-time feature parameters. By utilizing multivariate heterogeneous state features for data mining and pattern recognition, we delve into virtual sample generation technology using an overall diffusion trend approach. This starts by examining the validity of sample data and analyzing the relevance of data acquired within the feature space . Building on this foundation, the overall diffusion trend method is applied to generate virtual sample input that aligns with the sampling distribution characteristics of avionics system equipment. To address non-complete state evaluation in complex task networks, we design a comprehensive model. This model involves constructing a system signal flow block diagram and a structural diagram depicting the available capacity of subsystems and the overall system tasks. The establishment of unknown function relationships in signal connections is achieved through a fusion of neural network and fuzzy logic systems . Finally, an intelligent optimization algorithm is employed to determine system parameters. Utilizing this neuro-fuzzy system in simulation, we attain real-time system responses and evaluate the output regarding the available capacity of system tasks.

High-performance learning-based control for the typical safety-critical autonomous vehicles invariably requires that the full-state variables are constrained within the safety region even during the learning process. To solve this technically critical and challenging problem, this work proposes an adaptive safe reinforcement learning (RL) algorithm that invokes innovative safety-related RL methods with the consideration of constraining the full-state variables within the safety region with adaptation. These are developed toward assuring the attainment of the specified requirements on the full-state variables with two notable aspects. First, thus, an appropriately optimized backstepping technique and the asymmetric barrier Lyapunov function (BLF) methodology are used to establish the safe learning framework to ensure system full-state constraints requirements. More specifically, each subsystem's control and partial derivative of the value function are decomposed with asymmetric BLF-related items and an independent learning part. Then, the independent learning part is updated to solve the Hamilton-Jacobi-Bellman equation through an adaptive learning implementation to attain the desired performance in system control. Second, with further Lyapunov-based analysis, it is demonstrated that safety performance is effectively doubly assured via a methodology of a constrained adaptation algorithm during optimization (which incorporates the projection operator and can deal with the conflict between safety and optimization). Therefore, this algorithm optimizes system control and ensures that the full set of state variables involved is always constrained within the safety region during the whole learning process. Comparison simulations and ablation studies are carried out on motion control problems for autonomous vehicles, which have verified superior performance with smaller variance and better convergence performance under uncertain circumstances. The effectiveness of the safe performance of overall system control with the proposed method accordingly has been verified.

This paper studies synchronized optimization control for the cooperatively connected autonomous vehicle platoon formulation applicable in various driving scenarios and accommodates multiple vehicles dynamically entering or exiting the platoon. More specifically, the proposed algorithm consists of bi-layered synchronized optimization that enables the ultimate optimized control to attain the synchronized convergence property, and also importantly, ensures the satisfaction of safety performance requirements. The first layer of the proposed approach involves formulating the platoon dynamics and ensuring that the platoon operates within safe boundaries while optimizing its overall performance. To achieve this, the prescribed performance control is utilized to ensure that the state-variables remain within a predefined region throughout the synchronized optimization process. In the second layer, the control optimization takes into account the vehicle dynamics and actuators of either heterogeneous or homogeneous individual vehicles, improving performance and coordination within the platoon. In each optimization layer, the optimized backstepping is utilized, and the norm-normalized sign function is appropriately incorporated with the decomposition design to establish the learning framework with the outcome that attains the synchronized properties simultaneously. The adaptive dynamic programming and gradient-constrained method are utilized in the learning design to iteratively optimize system control while keeping the learning parts within the admissible policy region. Importantly, it is rigorously shown that this particular development and methodology attains the noteworthy time-synchronized stability property and outcome that all vehicle agents arrive at the desired relative position at the same time with synchronized convergence. Additionally, it is also shown that the methodology of our specific algorithmic strategy significantly also attains the desired outcomes of “string stability” (jointly with the above-mentioned desired outcomes of “time-synchronized stability”). To evaluate its effectiveness, comparative studies with different methods are carried out to showcase the significantly better desired outcomes attained with this methodology of synchronized optimization. Further evaluations in scenarios involving dynamic entry and exit of multiple vehicles demonstrate the corresponding capability and effectiveness in achieving the desired objectives.

Guaranteed safety and performance under various circumstances remain technically critical and practically challenging for the wide deployment of autonomous vehicles. Safety-critical systems in general, require safe performance even during the reinforcement learning (RL) period. To address this issue, a Barrier Lyapunov Function-based safe RL (BLF-SRL) algorithm is proposed here for the formulated nonlinear system in strict-feedback form. This approach appropriately arranges and incorporates the BLF items into the optimized backstepping control method to constrain the state-variables in the designed safety region during learning. Wherein, thus, the optimal virtual/actual control in every backstepping subsystem is decomposed with BLF items and also with an adaptive uncertain item to be learned, which achieves safe exploration during the learning process. Then, the principle of Bellman optimality of continuous-time Hamilton-Jacobi-Bellman equation in every backstepping subsystem is satisfied with independently approximated actor and critic under the framework of actor-critic through the designed iterative updating. Eventually, the overall system control is optimized with the proposed BLF-SRL method. It is furthermore noteworthy that the variance of the attained control performance under uncertainty is also reduced with the proposed method. The effectiveness of the proposed method is verified with two motion control problems for autonomous vehicles through appropriate comparison simulations.

This article investigates the control barrier performance function (CBPF)-based event-triggered cooperative formation control of underactuated unmanned surface vehicles (USVs) under the consideration of input saturation. Compared with the cooperative formation commonly studied in existing literature, three distinct features of the present work are: 1) the conflict between consensus performance-related constraint and the control capability limitation gets balanced based on CBPF-based control; 2) the CBPF-based path updating alleviates the negative cooperative coupling for performance constraint maintenance; and 3) the parallel dynamic event-triggering (PDET) mechanism under the nonrecursive design framework reduces the update frequency of the controllers by adjusting the triggering threshold and gain in parallel. Numerical simulations are provided to verify the validity of the obtained theoretical results.

This article proposes an adaptive neural trajectory tracking control scheme forn-DOF robotic manipulators subjected to parameter variations, unknown functions, and time-varying external disturbances. First, the computed torque control (CTC) method is designed to reduce the system's nonlinearity. Second, radial basis function neural networks (RBFNNs) are constructed to approximate the uncertainties due to parameter variations and unknown functions. It is also important to note that the RBFNN's centers and widths are defined by state constraints. As a result of the nonlinear disturbance observer (NDO), the RBFNNs' approximation errors and disturbances are estimated to further improve tracking performance. The barrier Lyapunov function (BLF) ensures the closed-loop system's stability, guaranteeing tracking performance while preventing state constraint violation. Furthermore, sensitivity analysis provides a ranking of the importance of design parameters in influencing dynamic responses. Finally, simulations on a seven-degrees of freedom robotic manipulator are performed to validate the effectiveness of the proposed method.