Transverse Function Control for Underactuated MSV With Stochastic Disturbances Under Output Error Constraints

SummaryThis paper studies the problem of stabilizing reference trajectories (also called as the trajectory tracking problem) for underactuated marine vehicles under predefined tracking error constraints. The boundary functions of the predefined constraints are asymmetric and time‐varying. The time‐varying boundary functions allow us to quantify prescribed performance of tracking errors on both transient and steady‐state stages. To overcome difficulties raised by underactuation and nonzero off‐diagonal terms in the system matrices, we develop a novel transverse function control approach to introduce an additional control input in backstepping procedure. This approach provides practical stabilization of any smooth reference trajectory, whether this trajectory is feasible or not. By practical stabilization, we mean that the tracking errors of vehicle position and orientation converge to a small neighborhood of zero. With the introduction of an error transformation function, we construct an inverse‐hyperbolic‐tangent‐like barrier Lyapunov function to show practical stability of the closed‐loop systems with prescribed transient and steady‐state performances. To deal with unmodeled dynamic uncertainties and external disturbances, we employ neural network (NN) approximators to estimate uncertain dynamics and present disturbance observers to estimate unknown disturbances. Subsequently, we develop adaptive control, based on NN approximators and disturbance estimates, that guarantees the prescribed performance of tracking errors during the transient stage of on‐line NN weight adaptations and disturbance estimates. Simulation results show the performance of the proposed tracking control.

An adaptive controller is constructed for a class of stochastic manipulator nonlinear systems in this paper. The states are constrained in the compact set. A tan-type Barrier Lyapunov Function (BLF) is employed to deal with state constraints. The proposed control scheme guarantees the output error convergence to a small neighbourhood of zero. All the signals in the closed-loop system are bounded. The simulation results illustrate the validity of the proposed method.

This study presents the development of a robust second‐order sliding mode controller (SOSMC) that incorporates position error constraints into the control design. To achieve this, a barrier Lyapunov function (BLF) is employed, enabling the enforcement of predefined bounds on tracking errors throughout the system's evolution. This approach ensures that errors remain within previously known limits, thereby improving safety and reliability in practical applications, particularly robotic systems. The proposed control scheme guarantees the existence of a sliding mode and achieves exponential convergence of the tracking errors, even in the presence of bounded disturbances and model uncertainties. Hence, the main contribution of this study is the integration of the BLF into the SOSMC framework, which not only maintains robustness but also addresses the critical issue of constraint satisfaction. This is often overlooked in traditional sliding mode designs. The effectiveness and improved performance of the proposed controller are validated through simulation studies conducted on a three‐degree‐of‐freedom robotic manipulator and through experiments on a six‐degree‐of‐freedom robotic manipulator. Comparative results demonstrate that, unlike a conventional SOSMC without error constraints, the proposed controller successfully maintains position errors within the specified limits while preserving fast convergence and robustness. These findings highlight the significant benefits of incorporating barrier Lyapunov functions in sliding mode control strategies for systems with strict performance and safety requirements.

PurposeThis paper aims to design a fixed-time disturbance observer (FTDO)-based adaptive neural fixed-time control strategy for the uncertain medium-scale unmanned autonomous helicopter (UAH) with full-state constraints and external disturbances.Design/methodology/approachFirst, the tan-type barrier Lyapunov function (BLF) and neural network (NN) are constructed to deal with the full-state constraints and system uncertainties, respectively. Subsequently, the compound disturbances are estimated by FTDOs. Simultaneously, the FTDOs and fixed-time control strategy guarantees that the errors of disturbances and states converge to the desired region in fixed-time, and the upper bound on the convergence time of the FTDOs and the designed controller can be estimated through the devised parameters. In addition, Lyapunov stability theory proves that all states of the UAH system are semiglobally uniform ultimately bounded.FindingsThe designed controller combines the fixed-time stability theory with tan-type BLF, which proves that all states of the UAH can be constrained in a predefined region. Furthermore, the state and the disturbance errors converge to a desired region in fixed time, which improves the performance of the controller.Practical implicationsThe designed controller keeps the UAH within the safe range, reduces the accident rate and improves the operation efficiency.Originality/valueThere are few research studies on the constraints and convergence time of UAH. In this paper, based on the FTDO, an adaptive NN control strategy with tan-type BLF is proposed to ensure that the state errors can be constrained to a safety region and deal with the system uncertainties and the influence of external disturbances.

This work investigates the adaptive finite-time tracking problem for a class of strict-feedback nonlinear systems with parametric uncertainties and symmetric constant output constraint. A tan-type Barrier Lyapunov Function (BLF) is proposed to ensure the boundedness of the output tracking error, and a new tuning function is given to eliminate the effect of uncertainties. It is theoretically shown that the control scheme not only can assure the finite-time convergence of system output tracking error into a small set around zero but also can guarantee that the output constraint is not overstepped. The effectiveness of the proposed finite-time control scheme is further verified with a numerical example.

This paper addresses the fixed-time trajectory tracking control problem of a fully actuated marine surface vehicle with full state constraints and system uncertainties. A continuous fixed-time convergence tracking controller is proposed based on fixed-time control and adding a power integrator methods, which achieves system stabilization within a finite time independent of system initial conditions. Moreover, a novel barrier Lyapunov function with a power integrator is designed to ensure the full state tracking error within the constraints. To accurately estimate the lumped disturbances of the vehicle system, a fixed-time disturbance observer is designed to guarantee the settling time of the disturbance observer bounded by a time constant independent of initial estimation errors. Finally, the proposed control scheme is proved to be fixed-time stable via fixed-time Lyapunov stability theorem and the full state constraints can never be violated. A numerical simulation is provided to illustrate the effectiveness and superiority of the proposed control scheme.

A new robust tracking control approach is proposed for strict-feedback nonlinear systems with state and input constraints. The constraints are tackled by extending the control input as an extended state and introducing an integral barrier Lyapunov function (IBLF) to each step in a backstepping procedure. This extends current research on barrier Lyapunov functions(BLFs)-based control for nonlinear systems with state constraints to IBLF-based control for strict-feedback nonlinear systems with state and input constraints. Since the IBLF allows the original constraints to be mixed with the error terms, the use of IBLF decreases conservatism in barrier Lyapunov functions-based control. In the backstepping procedure, neural networks (NNs) with projection modifications are applied to estimate system uncertainties, due to their ability in guaranteeing estimators in a given bounded area. To facilitate the use of the once-differentiable NNs estimators in the backstepping procedure, the virtual controllers are passed through command filters. Finally, simulation results are presented to illustrate the feasibility and effectiveness of the proposed control.

Predefined-time stabilization of stochastic nonlinear systems with application to UAVs

This brief is devoted to the predesigned motion trajectory-based finite time dynamic positioning (DP) control for a marine surface vehicle (MSV) with unknown external disturbances. Firstly, a preset motion trajectory is presented through establishing the relationship function among position tracking errors and heading tracking error, facilitating the MSV to arrive in the equilibrium point along the pre-designed trajectory. Furthermore, a novel nonsingular and fast terminal sliding mode control (NTSMC) approach is investigated, which ensures faster convergence rate and better stability performance of the close-loop system than the conventional backstepping control approach. What’s more, by incorporating the adaptive technique with the NTSMC approach, an adaptive nonsingular and fast terminal sliding mode control (ANTSMC) strategy is addressed. Compared to the NTSMC approach, it strengthens robustness to disturbances and guarantees system states to converge to a closer neighborhood of the equilibrium point. Finally, simulation results illustrate the remarkable effectiveness of proposed control schemes.

In this paper, a novel iterative learning control (ILC) algorithm is presented for a class of joint position constrained robot manipulator systems. Unlike the traditional ILC probelms, where the reference trajectory is iteration invariant, the reference trajectory in this work can be non-repetitive over the iteration domain. A tan-type time-varying Barrier Lyapunov Function (BLF) is proposed to deal with the constraint requirements which can be both time and iteration varying. We show that under the proposed ILC scheme, uniform convergence of the full state tracking error beyond a small time interval in each iteration can be guaranteed over the iteration domain, while the constraints on the joint position vector will not be violated during operation. An illustrative example is presented in the end to demonstrate the effectiveness of the proposed control scheme.

Asymmetric error-constrained path-following control of a stratospheric airship with disturbances and actuator saturation

A stochastic model predictive control (SMPC) method is proposed for trajectory tracking of quadrotor helicopters with stochastic disturbances. The stochastic disturbances are assumed to be Gaussian white noises. The existing robust control methods generally guarantee that the tracking performances under the worst-case disturbances satisfying given conditions. However, the worst-case disturbances may have a vanishingly small probability of occurrence in practice, so these methods show great conservative. In this paper, the tracking errors caused by the disturbances are limited in the acceptable range with the given probability. The hierarchical control structure is used. In the outer loop, the position loop, SMPC controllers are designed for position tracking. In the inner loop, the attitude loop, the nonlinear dynamics are linearized by the feedback linearization strategy, and an SMPC controller is designed for attitude tracking. Finally, simulation results verify the effectiveness of the proposed method.

The use of manipulators can improve sustainable energy utilization efficiency and increase sustainable manufacturing practices for solar tracking systems and manufactures, and thus it is significant to guarantee a high tracking accuracy for manipulators. In this paper, an error-tracking adaptive iterative learning control (AILC) method is proposed for a constrained flexible-joint manipulator (FJM) with initial errors. Due to the existence of the repeated positioning drift, the accuracy of the actual manipulator and the sustainable energy utilization efficiency are affected, which motivates the error-tracking approach proposed in this paper to deal with the repeat positioning problem. The desired error trajectory is constructed, such that the tracking error can follow the desired error trajectory without arbitrary initial values and iteration-varying tasks. Then, the system uncertainties are approximated by the capability of fuzzy logic systems (FLSs), and the combined adaptive laws are designed to update the weight and the approximating error of FLSs. Considering the safety operation of the flexible-joint manipulator, both input and output constraints are considered, a quadratic-fractional barrier Lyapunov function (QFBLF) is constructed, such that the system output is always within the constrained region. Therefore, the proposed method can guarantee the output tracking accuracy of manipulators under arbitrary initial values and iteration-varying tasks and keep the system output within the constraints to improve the transient performance, such that the energy utilization and accessory manufacturing efficiency can be improved. Through the Lyapunov synthesis, it is proved that the tracking error can converge to zero as the number of iterations goes to infinity. Finally, comparative simulations are carried out to verify the effectiveness of the proposed method.

This article puts forward an event‐triggered adaptive neural tracking control strategy for a class of uncertain fractional‐order nonstrict‐feedback nonlinear systems with full‐state constraints and dead‐zone inputs. The proposed control strategy is capable of surmounting an inherent shortcoming in most traditional backstepping control approaches which results from the repeated differentiation of virtual control functions, and enhancing the transmission efficiency of control signals by introducing an event‐triggered mechanism with a dynamic threshold condition. Furthermore, by constructing a novel barrier Lyapunov function in each step of the backstepping procedure, the design difficulty arising from the system state constraints issue under fractional‐order cases is resolved. It is strictly proved that the tracking error can converge into a desired small neighborhood of the origin and all signals in the closed‐loop system are bounded. Finally, a simulation example is given to verify the effectiveness of our proposed control strategy.

In this paper, we present adaptive tracking control designs for a class of constrained nonlinear systems with completely unknown constants. A Barrier Lyapunov Function (BLF) is adopted to protect this limit from being destroyed. By guaranteeing negative semi-definite of the BLF during the design process, we keep the constraint is not transgressed. Adaptive control is used to address the unknown constants of the systems. It is shown that the tracking error is asymptotic stable without breaking a desired boundary value, and all the closed-loop signals are bounded when a flexible initial condition is satisfied. At last, two numerical examples are provided to see if the method would be effective.