Event-Triggered Control Breaks New Ground for Asymmetrical Underactuated Surface Vessels

Marine robotics has long grappled with the challenge of stabilizing underactuated surface vessels (USVs)—vessels lacking lateral control forces and bound by second-order nonholonomic constraints—especially when accounting for the real-world asymmetry of such craft, a detail often overlooked in traditional control design. A team of researchers from the Chinese Academy of Sciences has developed a groundbreaking event-triggered global asymptotic stabilization control strategy that addresses this gap, enabling stable, resource-efficient operation of asymmetrical USVs while maintaining high control performance. This innovative approach not only solves the longstanding problem of global asymptotic stabilization for asymmetrical USVs but also drastically reduces actuator manipulation and system resource consumption by updating control signals only when predefined trigger conditions are met, marking a significant leap forward in marine control theory and practical engineering applications.

USVs have become indispensable across military and civilian marine operations, from coastal patrol and autonomous navigation to search-and-rescue and underwater salvage missions. Their underactuated nature, however, poses unique control challenges: the origin of the USV system fails to satisfy Brockett’s condition, meaning time-invariant smooth state feedback control laws cannot achieve asymptotic stability. For decades, researchers have focused on designing smooth time-varying or discontinuous control laws to overcome this limitation, but most work has assumed symmetric USV models—an oversimplification that does not align with real-world vessel design and operation. Even as event-triggered control (ETC) has emerged as a solution to the tradeoff between control signal sampling frequency, resource use, and actuator wear in marine systems, existing ETC research for USVs has been limited to trajectory and path tracking, with no viable global asymptotic stabilization solutions for either symmetric or asymmetrical USVs. Trajectory and path tracking, while challenging, do not impose the same strict constraints as stabilization control, which requires confining both the position and heading of a USV to a fixed reference point—an essential capability for dynamic positioning and autonomous berthing, two critical USV operations. Prior attempts at ETC for USV stabilization relied on T-S fuzzy rules, which restrict the state variation range of the vessel and thus fail to achieve global stability, leaving a critical research gap in marine control engineering.

To address these challenges, Rui Wang, Changlong Si, Hui Ma, and Chengpeng Hao from the Key Laboratory of Information Technology for Autonomous Underwater Vehicles at the Institute of Acoustics, Chinese Academy of Sciences, and the University of Chinese Academy of Sciences, set out to design an ETC strategy that would enable global asymptotic stabilization for asymmetrical USVs, a first in the field. Their work centers on a two-step coordinate transformation approach that redefines the global asymptotic stabilization problem of the original asymmetrical USV system as a stabilization problem for an underactuated subsystem of a transformed model— a key simplification that leverages cascade system theory and builds on foundational work in USV control design. By converting the original system’s state and input variables, the researchers eliminated the off-diagonal terms and asymmetry-induced complexities that had stymied previous stabilization efforts, creating a more tractable subsystem that could be targeted with tailored control laws.

A core innovation of the research is the design of a time-varying continuous stabilization control law using periodic time functions to construct auxiliary variables. Recognizing that the underactuated subsystem still required a time-varying approach to satisfy Brockett’s condition, the team introduced smooth periodic time functions with bounded magnitudes and derivatives (and non-vanishing time derivatives as time approaches infinity) to build two auxiliary variables. These variables were used to design the control thrust for the USV and an ideal heading angular velocity, with a second control law for the control moment that enables the vessel to asymptotically track this ideal angular velocity. This dual auxiliary variable design ensures that the underactuated subsystem’s states converge to the origin, a prerequisite for the global stabilization of the original asymmetrical USV system.

Complementing the time-varying control law is a novel switching threshold event-triggering mechanism (ETM) that lies at the heart of the resource efficiency of the proposed strategy. Unlike traditional time-triggered control systems that update control signals at fixed sampling intervals— a practice that either wastes resources with high sampling frequencies or degrades control performance with low frequencies—the ETM designed by the team updates the controller only when predefined trigger conditions are satisfied. The mechanism features a dual threshold strategy: for large control signal amplitudes, a fixed threshold triggers updates to avoid abrupt signal changes and system oscillations; for small amplitudes, a proportional threshold with a constant offset triggers updates to ensure precise control near the stabilization reference point. This switching design balances stability and precision, a critical consideration for USV operation where both large transient movements and fine-tuned positioning are required. The researchers also defined sampling errors between the ideal control signal and the event-triggered control input, proving that these errors remain bounded and do not compromise the system’s stability.

The team’s ETC design is further optimized to compensate for sampling errors and enhance control accuracy, particularly as the USV’s states approach the stabilization origin. The control thrust and moment laws incorporate a class-K function and a time-varying positive function that converges to zero as time approaches infinity— a design choice that leverages a key inequality from control theory to bound the impact of sampling errors. When the vessel’s states are far from the origin, the control law prioritizes rapid state convergence; as the vessel nears the reference point, the law shifts to compensate for sampling errors, ensuring that the system converges to the origin without steady-state error. This adaptive behavior is a critical improvement over existing ETC strategies, which often sacrifice precision for resource efficiency or vice versa.

A rigorous stability analysis underpins the proposed control strategy, with the researchers proving two key theorems that validate its performance and practicality. First, they demonstrate that the closed-loop system of the asymmetrical USV with the designed ETC is globally uniformly bounded (GUB), meaning all system states remain within finite bounds for all time, and the system origin is globally asymptotically stable (GAS), meaning all states converge to the origin as time approaches infinity. This proof relies on the construction of two Lyapunov functions— a standard tool in nonlinear control analysis— and a case-by-case examination of the switching threshold ETM (fixed and proportional threshold cases). The team leverages Barbălat’s lemma to prove asymptotic convergence, showing that the auxiliary variables, subsystem states, and ultimately the original USV system states all converge to zero. Second, they prove that the ETC has a positive lower bound on the minimum trigger interval, meaning the system cannot exhibit Zeno behavior— a pathological phenomenon in event-triggered systems where an infinite number of trigger events occur in a finite time interval, rendering the controller impractical. By showing that the rate of change of the sampling error is bounded, the researchers confirm that trigger events are spaced by a positive minimum time, and the controller is causally realizable (i.e., control signals depend only on past and present system states, not future states).

To validate the effectiveness of their proposed strategy, the researchers conducted a series of numerical simulations using a well-characterized asymmetrical USV model with real-world physical parameters, targeting an autonomous berthing mission with an initial state far from the stabilization origin (a lateral position of 2 meters, longitudinal position of -2 meters, and initial heading angle of -π/2 radians). They compared the performance of their ETC strategy with a state-of-the-art time-varying stabilization control law for USVs, a widely cited method in the field with a fixed sampling period of 0.05 seconds. The simulation results revealed significant performance advantages for the event-triggered approach: the ETC strategy exhibited smaller oscillations and overshoot in all USV states (position, heading angle, longitudinal velocity, lateral velocity, and heading angular velocity) compared to the traditional time-varying control law. This reduction in transients is attributed to the ETM’s ability to avoid the large initial control input amplitudes and zero-order hold effects that plague fixed-sampling control systems, which can cause violent state changes in underactuated systems.

Equally important are the resource and actuator efficiency gains of the proposed ETC. The traditional time-varying control law required 600 control signal updates in the first 30 seconds of simulation due to its fixed 0.05-second sampling period. In contrast, the event-triggered control thrust was updated only 62 times, and the control moment just 90 times, over the same 30-second window— a drastic reduction in actuator manipulation that directly extends the lifespan of USV actuation systems, a critical consideration for unmanned marine vehicles operating in remote or harsh environments. The ETC strategy also consumed significantly less energy than the traditional method, as measured by an energy consumption index based on the integral of the squared control signals over time. The lower energy consumption is a result of the ETM’s selective update mechanism, which avoids the constant control signal adjustments of fixed-sampling systems, and the control law’s adaptive compensation for sampling errors, which eliminates the need for overly large control amplitudes to maintain stability. Notably, the ETC strategy also avoided the physically unrealizable large heading angular velocities produced by the traditional control law, a key practical advantage for real-world USV operation where actuation systems have inherent performance limits (e.g., torque saturation for the heading control moment).

The simulation results also confirm the global stability of the proposed strategy, with all USV states converging to the origin without steady-state error, even with the actuator saturation constraint imposed on the control moment (a maximum of 5 N·m). This is a critical result for practical engineering, as all real-world actuation systems are subject to saturation limits, and control laws must account for these constraints to avoid instability or performance degradation. The switching threshold ETM’s ability to balance stability and precision is further validated by the trigger interval results, which show that the ETC updates the control signals more frequently when the USV is far from the origin (to enable rapid convergence) and less frequently as the vessel nears the reference point (to save resources), a behavior that aligns with the operational needs of USV stabilization and berthing.

The research represents a paradigm shift in USV control design, with three key contributions to marine control theory and engineering. First, it is the first to propose an event-triggered global asymptotic stabilization control strategy for asymmetrical USVs, filling a longstanding research gap and addressing the real-world asymmetry of USV models that had been ignored in previous ETC work. Second, it combines coordinate transformation, time-varying feedback control, and a switching threshold ETM into a unified control framework that achieves both global asymptotic stability and resource efficiency— a balance that had eluded previous researchers working on USV stabilization. Third, it provides a rigorous theoretical proof of the strategy’s stability and practicality, including the absence of Zeno behavior and causal realizability, laying a solid foundation for real-world implementation on physical USVs.

Beyond its direct application to asymmetrical USVs, the research has broader implications for marine robotics and nonlinear control systems. The coordinate transformation approach and switching threshold ETM can be extended to other underactuated nonlinear systems, including autonomous underwater vehicles (AUVs), unmanned aerial vehicles (UAVs), and mobile robots, all of which face similar challenges of stabilization with limited actuation and resource constraints. The strategy’s ability to account for system asymmetry also makes it applicable to a wide range of real-world marine vessels, from small unmanned surface craft to larger autonomous ships, where asymmetry is an inherent design feature due to hull geometry, propeller placement, and payload distribution.

In practical terms, the proposed ETC strategy enables the development of more efficient, reliable, and durable USVs for military and civilian applications. For dynamic positioning— a critical capability for offshore operations such as oil and gas exploration, marine research, and offshore wind farm maintenance— the strategy ensures that USVs can maintain a fixed position with high precision while minimizing energy use and actuator wear, extending mission duration and reducing maintenance costs. For autonomous berthing, the strategy’s small overshoot and oscillation characteristics enable smooth, safe docking of USVs in confined harbors or coastal areas, a key requirement for unmanned marine operations where human intervention is limited or unavailable. The resource efficiency of the ETC also makes it ideal for small USVs with limited on-board power and computing resources, a common constraint in low-cost marine robotics systems.

Looking ahead, the research opens several promising avenues for further investigation. The team notes that future work could extend the strategy to account for unknown model parameters and external disturbances— such as ocean currents, wind, and waves— which are pervasive in real-world marine environments and can degrade control performance. Adaptive and robust control techniques could be integrated with the event-triggered framework to create a self-tuning control law that compensates for parameter uncertainty and external disturbances in real time. Another area of future research is the implementation of the ETC strategy on a physical USV platform, which would validate its performance in real-world conditions and identify practical engineering challenges (e.g., sensor noise, communication delays, and actuator dynamics) that need to be addressed in the control law design. The team also suggests that the switching threshold ETM could be optimized for specific USV missions, with adaptive threshold parameters that adjust based on mission requirements (e.g., high precision for berthing, high speed for patrol).

The development of this event-triggered global asymptotic stabilization control strategy for asymmetrical USVs is a significant milestone in marine robotics, bridging the gap between theoretical control design and real-world engineering application. By addressing the longstanding challenge of stabilizing asymmetrical underactuated surface vessels with a resource-efficient, high-performance control law, the research from the Chinese Academy of Sciences paves the way for the next generation of autonomous marine vehicles— vehicles that are more efficient, reliable, and capable of operating autonomously in the complex, unstructured marine environment for extended periods. As unmanned surface vessels continue to grow in importance across military and civilian sectors, this innovative control strategy will play a pivotal role in unlocking their full potential, enabling a new era of autonomous marine operations.

Author Affiliations: Rui Wang¹², Changlong Si¹, Hui Ma¹, Chengpeng Hao¹; ¹Key Laboratory of Information Technology for Autonomous Underwater Vehicles, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China; ²University of Chinese Academy of Sciences, Beijing 100049, China Journal: Control Theory & Applications, Volume 38, Issue 6, June 2021 DOI: 10.7641/CTA.2020.00487 Word count: 3892