Tan-type Barrier Lyapunov Function Research Articles

Finite-time stability of a class of nonlinear cascaded systems with time-varying output constraints

The finite-time stabilization problem of a class of cascaded systems with time-varying output constraints is investigated in this paper. The system consists of input-to-state stable inverse dynamics and a nonholonomic system. The technology of changing the supply rate eliminates dynamic uncertainty. A new tan-type barrier Lyapunov function is utilized to handle time-varying output constraints. Under the unified framework of constrained and unconstrained systems, combined with the addition of power integrator technology and switch control strategy, a state feedback control strategy is proposed to ensure that the state of the closed-loop system converges to zero in a finite-time and always satisfies time-varying output constraints. Finally, simulation results verify the proposed control scheme’s effectiveness.

Adaptive output feedback stabilisation control for cascaded systems with output constraints and disturbance

The system under consideration is a cascaded system composed of integral input-to-state stable inverse dynamics and a non-holonomic system. An adaptive output feedback stabilisation control is proposed for the system with disturbance and output constraints. The dynamic uncertainty is eliminated using the technique that changes the supply rate. An extended state observer is proposed by defining the non-vanishing disturbance as a new state variable of the system. The asymmetric time-varying output constraint is solved by utilising the tan-type barrier Lyapunov function. The result shows that the adaptive output feedback controller guarantees the stability of the closed-loop system without violating the asymmetric time-varying output constraints under the backstepping technique. Simulation results are given to verify the effectiveness of the control method.

Adaptive Neural Control for a Class of Random Fractional-Order Multi-Agent Systems with Markov Jump Parameters and Full State Constraints

Based on an adaptive neural control scheme, this paper investigates the consensus problem of random Markov jump multi-agent systems with full state constraints. Each agent is described by the fractional-order random nonlinear uncertain system driven by random differential equations, where the random noise is the second-order stationary stochastic process. First, in order to deal with the unknown functions with Markov jump parameters, a radial basis function neural network (RBFNN) structure is introduced to achieve approximation. Second, for the purpose of keeping the agents’ states from violating the constraint boundary, the tan-type barrier Lyapunov function is employed. By using the stochastic stability theory and adopting the backstepping technique, a novel adaptive neural control design method is presented. Furthermore, to cope with the differential explosion problem in the design course, the extended state observer (ESO) is developed instead of neural network (NN) approximation or command filtering techniques. Finally, the exponentially noise-to-state stability in the mean square is analyzed rigorously by the Lyapunov method, which guarantees the consensus of the considered multi-agent systems and all the agents’ outputs are bounded in probability. Two simulation examples are provided to verify the effectiveness of the suggested control strategy.

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

The paper presents a new Lyapunov-type predefined-time stabilization control algorithm for stochastic high-order nonlinear systems with asymmetric output constraints. In contrast to stochastic finite-time and fixed-time stabilization, the average value of the settling-time function for stochastic predefined-time stabilization control is independent of both the initial value and the control factors. To mitigate the significant uncertainties arising from the asymmetric output constraint, a tan-type barrier Lyapunov function is formulated. Furthermore, by harnessing the previously mentioned barrier Lyapunov function and integrating the power integrator technique, a controller design strategy is formulated based on the backstepping method. The rigorous analysis in this study proves that the designed controller ensures both the attainment of predefined-time convergence of the system states to the origin in probability and the satisfaction of the output constraint. Finally, an example of a roll angle subsystem for quadrotor UAVs and a numerical illustration are presented to corroborate the theoretical analysis.

Robust adaptive tracking control for dynamic positioning ships subject to dynamic safety constraints and actuator saturation

This paper proposed a novel robust adaptive trajectory tracking control scheme for dynamic positioning (DP) ships subjected to unknown time-varying disturbances, unknown model parameters, dynamic safety constraints, and actuator saturation. The dynamic safety constraints were guaranteed based on the tan-type barrier Lyapunov function (BLF) technique, which ensured the position and velocity of the DP vessel within the given constraints. Moreover, the radial basis function neural network (RBFNN) was adopted to approximate the unknown parameters of the dynamics model, and an adaptive neural disturbance observer (ANDO) was designed to compensate for lumped disturbances. An anti-windup system was developed to handle the actuator saturation effect. By combining the above techniques and back-stepping method, the final control law was presented, and the semi-global asymptotic convergence was achieved via rigorous theoretical analysis and Lyapunov proof. The results of simulations demonstrated the superiority and robustness of this approach in resolving the trajectory tracking challenges of DP ships. Moreover, the proposed control scheme is highly effective in optimizing the trajectory tracking of DP ships, as it takes into account the multiple constraints that may arise during the process, which is a valuable contribution to the field of DP ship trajectory tracking, providing a more comprehensive and effective solution to this complex problem.

Event‐triggered adaptive neural network control design for stochastic nonlinear systems with output constraint

SummaryThis paper is concerned with the adaptive neural network event‐triggered control (ETC) problem for stochastic nonlinear systems with output constraint. The influence of stochastic disturbance inevitably exists in many practical systems, which leads to system instability. Meanwhile, a novel tan type barrier Lyapunov function (Tan‐BLF) structure is proposed to deal with the constraint requirements of stochastic systems. In the sense of probability, the output constraints will not be violated during the operation of the system. In addition, the ETC strategy is adopted to reduce the burden of communication. The asymptotic stability of the closed‐loop system is guaranteed without violating output constraints. Meanwhile, the tracking error converges to a small region of the origin. Two simulations results demonstrate the effectiveness of theoretical analysis.

Approach to Gait Coordination: Adaptive Fuzzy Finite-Time Control of a Stochastic Prosthesis-Human Symbiosis With Intentional Delay

The generation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">intentional delay</i> in response to the stride frequency is seldom considered in prosthesis-human symbiosis. Unfortunately, such intentionally delayed human-robot interaction poses a new challenge to their gait coordination in stochastic environments. Utilizing fuzzy logic systems (FLSs), we investigate an adaptive fuzzy finite-time control of a stochastic prosthesis-human symbiosis with intentional delay to address this issue. Noting that the intentional delay is related to walking velocity, this work conducts experiments on ten healthy subjects to identify the intentional delays at different velocities using the FLS. Introducing the FLS-identified delay and contralateral healthy limb gaits, we propose a prosthetic gait planner to simultaneously determine the reference stride frequency and stride length, thus properly regulating the desired velocity. Considering the adverse effects of the required intentional delay and state constraints in the stochastic framework, we propose a new statistical Lyapunov-Krasovskii functional, together with a Tan-type barrier Lyapunov function. Correspondingly, an adaptive fuzzy controller is developed via a backstepping design, thus solving the semi-global finite-time stable in probability with intentional delay, unknown nonlinearities, and state constraints. Application studies validate the efficacy of the proposed approach. The results show that our approach can predict walking behavior while performing gait coordination.

Adaptive Fuzzy Event-Triggered Cooperative Control for Multi-Robot Systems: A Predefined-Time Strategy.

A predefined-time adaptive fuzzy cooperative controller with event triggering is proposed for multi-robot systems that takes into account external disturbances, input saturation, and model uncertainties in this paper. First, based on the asymmetric tan-type barrier Lyapunov function, a predefined-time controller is proposed to acquire a quick response and more precise convergence time under the directed communication topology. Second, predefined-time fuzzy logic systems are developed to approximate external disturbances and model uncertainties. Third, a dynamic relative threshold event-triggered mechanism is improved to save the communication resources of the robots. Subsequently, the proof procedure for the predefined-time stability is given using the Lyapunov stability theorem. Finally, some simulation examples, including a comparative experi-ment on multi-robot systems, are provided to test the effectiveness of the above algorithm.

Adaptive neural network control for nonholonomic systems with partial/full or without state constraints

In this paper, we present a unifying neural networks-based adaptive control framework for nonholonomic systems with partial/full state constraints or without constraint requirements. By considering the tan-type barrier Lyapunov function, constraint requirements are handled for the x0-subsystem. A novel nonlinear state-dependent function is constructed to meet asymmetric time-varying state constraints for the x-subsystem. Combined with backstepping method, a coordinate transformation is designed to transform the original constrained system into unconstrained system. Then, we put forward the dynamic surface control to eliminate feasibility conditions of virtual controllers. In addition, neural networks can be introduced to compensate for the uncertainties of nonholonomic systems. It is demonstrated that without modifying control structure the adaptive neural networks controller guarantees the stability of nonholonomic systems, while asymmetric time-varying state constraints can be satisfied. Simulation examples of mobile robot systems further validate the efficacy of the devised algorithm.

Event-Based Fuzzy Adaptive Consensus Tracking for Stochastic High-Order Nonlinear Multiagent Networks With Specified-Time Convergence

In this paper, a specified-time event-triggered fuzzy adaptive control algorithm is developed to solve the consensus tracking control problem for stochastic high-order nonlinear multi-agent networks, which is intrinsically challenging due to the existence of stochasticity and high-order (positive odd integers greater than one) terms. More precisely, a novel specified-time performance function (STPF) is incorporated into time-varying high-order tan-type barrier Lyapunov function to guarantee that the tracking errors remain under time-varying constraints within specified time. Combining fuzzy logic systems with the adding on power integrator technique, an adaptive approximation policy is introduced to handle the system uncertainties. Moreover, a new switching threshold event-triggered mechanism is devised to determine the control signals updating instants, which reduces the transmission and computation burden, while resizing the triggering threshold in real-time. The Zeno phenomenon is excluded by guaranteeing that the triggering intervals is lower bounded by a positive constant. Two simulation examples are provided to demonstrate the effectiveness of the designed algorithm.

Fixed-time velocity-free safe formation control of AUVs with actuator saturation and unknown disturbances

This paper designs a fixed-time formation control law for multiple autonomous underwater vehicle (AUV) system (MAS) subjected to unmeasurable velocities, actuator saturation and time-varying disturbances. To address these challenges, the actuator saturation and time-varying disturbances are initially integrated into lumped disturbances, the initial step is to integrate actuator saturation and time-varying disturbances into lumped disturbances, followed by designing a fixed-time extended state observer (FTESO) to estimate the unavailable velocities and the lumped disturbances in fixed time. Moreover, a nonlinear filter is also utilized to eliminate the problem of computational explosion that arises due to derivatives in the controller design process. Additionally, a tan-type barrier Lyapunov function (TT-BLF) is presented to constrain the tracking errors within a predetermined time-varying constraint function. Then, a novel fixed-time formation control algorithm based on FTESO and TT-BLF is further designed to ensure that the formation tracking errors converge to a small neighborhood near origin in fixed time, and the fast formation task can be completed within a fixed time. Finally, the simulation experiments verify the effectiveness of the proposed controller.

Adaptive Performance-Constrained Synchronization Control for Hypersonic Flight Vehicle Swarms: A Novel Finite-Time Convergence Protocol Methodology

This paper proposes a novel neural adaptive performance-constrained synchronization tracking control algorithm for multiple hypersonic flight vehicles (HFVs), which are subject to actuator faults and full-state constraints. The proposed method is based on advanced Lyapunov finite-time stability theory and a sophisticated backstepping design scheme. The longitudinal model of HFV is converted into velocity and altitude subsystems through functional decomposition. Our method presents three significant contributions over the existing state-of-the-art approaches: (a) ensuring finite-time convergence of HFVs systems by guaranteeing that the setting time is lower bounded by a positive constant that is related to the initial states; (b) utilizing a tan-type Barrier Lyapunov function (BLF) to ensure that the synchronization tracking errors of velocity, altitude, flight path angle, angle of attack, and pitch angle rate are maintained within certain performance bounds; and (c) designing a neural adaptive control algorithm and adaptive parameter laws by combining the backstepping design technique and radial basis function neural networks (RBFNNs) to handle unknown actuator faults and modeling uncertainties. Finally, comparative simulations are conducted to validate the efficacy of the proposed scheme.

An adaptive finite-time control method for antilock braking system with experimental analysis

The antilock braking system (ABS) is a representative technology to improve the safety of hard braking in automobiles. The slip rate control has been a challenging issue due to the complicated characteristics of tires and the strong nonlinearity of the system. In this paper, a novel adaptive finite-time controller for ABS is developed to improve braking performance. Different from the current control strategies for ABS, the extended finite-time stability theory and state constraint are comprehensively considered in the proposed control strategy. The extended finite-time stability theory is applied to deal with the system uncertainties, by which the convergence of slip rate tracking error is achieved. And the asymmetric tan-type barrier Lyapunov function (BLF) is used to ensure that the wheel slip ratio is within a smaller and more stable area. Finally, according to the simulation and experiment, compared with the existing BLF controller, a faster convergence rate, better robustness and anti-disturbance performance of ABS can be achieved with the proposed strategy.

Adaptive tracking control for a class of stochastic nonlinear systems with full-state constraints and dead-zone

This paper seeks to address the problem of state-feedback tracking control for a class of stochastic systems whose states are constrained and input is perturbed by dead-zone. A tan-type barrier Lyapunov function (BLF) and a finite-time adaptive law are proposed such that all states of the system are constrained in the defined bounded compact sets. Based on stochastic Lyapunov theorem, an adaptive state-feedback tracking controller is designed to ensure that the considered stochastic system is semiglobally finite-time stable in probability (SGFSP) and the tracking error signal is bounded. Different from the existing control strategies for stochastic systems, the form of BLF can be used for asymmetric constraints without changing the controller, so the analysis of symmetric or asymmetric full-state constraints is unified. Finally, illustrative simulations are provided to verify the effectiveness of the proposed control strategy.

Fixed-time coordinated guidance for containment maneuvering of unmanned surface vehicles under delayed communications: Theory and experiment

The purpose of this paper is to develop a new cooperative controller to solve the containment maneuvering problem for multiple unmanned surface vehicles (USVs) that track one parameterized path in a fixed time. The required velocities and heading angles of the USVs are designed based on Line-of-Sight (LOS) guidance laws. To steer along-track errors and cross-track errors to certain sets in fixed time, the coordinated guidance laws are derived by tan-type barrier Lyapunov functions (BLFs). For the coordination level, time-delayed coordination update laws are proposed for containment maneuvering. Comparing with the current containment maneuvering, the main features are: (i) LOS-based guidance laws are improved with the performance of fixed-time convergence, the convergence time can be determined by user-defined time; (ii) A novel containment maneuvering path variable controller is derived with time delays and without the assumption of setting individual paths following errors to be 0. (iii) the advantages of the proposed containment maneuvering control strategy are illustrated both through theoretical analysis and experimental result.

Unified neuroadaptive fault-tolerant control of fractional-order systems with or without state constraints

The problem of controlling fractional-order nonlinear systems remains interesting and challenging due to the powerful and hereditary memory features of such systems. In this paper, we investigate the adaptive tracking control problem for a class of fractional-order nonlinear systems with or without state constraints. The tan-type barrier Lyapunov function (BLF) is adopted for the first time in fractional Lyapunov direct method. Such technique allows for the accommodation of the situations with and without state constraints in a unified framework. Moreover, neural network (NN) is utilized to reconstruct the sophisticated nonlinear functions arising from the fractional-order differentiation of the virtual controller, resulting in a neuroadaptive fault-tolerant control scheme. It is shown that, with the proposed unified control, all the closed-loop signals are semiglobally ultimately uniformly bounded whether state constraints are imposed or not. Both theoretical analysis and numerical simulation confirm the effectiveness of the developed approach.

Tan-Type BLF-Based Attitude Tracking Control Design for Rigid Spacecraft with Arbitrary Disturbances

This study deals with the problem of disturbances in observer-based attitude tracking control for spacecraft in the presence of inertia-matrix uncertainty and arbitrary disturbance. Following the backstepping control, a tan-type barrier Lyapunov function (BLF)-based attitude tracking control method with prescribed settling time and performance is systematically developed. The proposed control framework possesses three advantages over the existing attitude controllers. Firstly, the singularity problem associated with the use of fractional power in fixed-time control is effectively resolved without employing any command filter or piece-wise continuous function. Secondly, inspired by the concept of the tan-type BLF approach, any desired performance for the attitude tracking error is satisfied. Lastly, the total disturbance, including the system’s uncertainty, external disturbances, and time-derivative of the virtual control, is precisely reconstructed during a predefined time, even if the initial estimation error tends to infinity. Moreover, this time is determined as a tunable gain in the observer. The numerical simulations confirm the superior performance of the proposed control strategy in comparison with the existing pertinent works.

Unified neural output-constrained control for space manipulator using tan-type barrier Lyapunov function

In this paper, a unified neural control scheme is presented for the output-constrained trajectory tracking of space manipulator under unknown parameters and external perturbations. By utilizing the backstepping control technique as the main framework, the proposed controller is developed with the help of neural network (NN) and tan-type barrier Lyapunov function (BLF). The NN is introduced to identify the unknown part in the dynamic model of the space manipulator. Benefiting from the neural identification, the proposed controller is model-free and insensitive to external perturbations. Moreover, the BLF is adopted to guarantee the position tracking errors never exceed the predefined output constraints. Different from log-type BLF, the tan-type BLF is employed for the control design, which makes the proposed controller universal for the cases with and without considering the output constraints. The semiglobal uniform ultimate boundedness of the resulting closed-loop system is strictly obtained through stability argument. All error variables in the closed-loop system can eventually stabilize to the small residual sets about zero under the proposed controller. Lastly, simulations and comparisons are given to demonstrate the effectiveness and excellent tracking performance of the proposed control scheme.

Output feedback control with time-varying asymmetric constraints for nonlinear cascade systems

In this paper, the output feedback problem is studied for a class of nonlinear cascade systems with integral input to state stability (iISS) inverse dynamics and an unknown control direction. The tan-type barrier Lyapunov function (UBLF) is introduced for an asymmetric time-varying output constraint, which can be equal to the standard Lyapunov function of an unconstrained system, thereby solving the requirement for the asymmetric time-varying output constraint. A design strategy based on backstepping is proposed to construct a dynamic output feedback control law, and an output feedback controller is designed using the barrier function. The proposed strategy satisfies the constraint condition while keeping all other closed-loop signals bounded. Finally, the effectiveness of the proposed strategy is proven by the simulation results.

Fuzzy variable impedance-based adaptive neural network control in physical human–robot interaction

This article focus on the problems of trajectory tracking and motion constraint for physical human–robot interaction, and a compliant adaptive control method is proposed for stable and safe physical human–robot interaction during the interaction. First, a fuzzy variable impedance control strategy is given to make the robot to use suitable impedance parameters in different motion states, which can improve positioning accuracy and reduce the interaction force. Second, by transforming the safety interaction constraint into output constraint, a tan-type barrier Lyapunov function is presented to guarantee the safety of human partner in physical human–robot interaction. Third, an adaptive neural network is employed to design the adaptive controller to handle with the dynamic uncertainties and improve the robustness of the system. Finally, simulation results of a 2-degree-of-freedom manipulator are presented to show the effectiveness of the proposed method.