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In this paper, a novel controller designed for robust tracking control of a flexible‐link manipulator operating in the presence of parameter uncertainties and external disturbances within the joint space is introduced. The proposed controller employs an adaptive sliding mode control approach, incorporating an improved barrier function, to ensure that trajectory errors remain within predefined performance bounds. This design enhances the tracking performance without overestimating control‐switching gains. Additionally, a fixed‐time adaptive sliding mode control, featuring a rapid nonsingular terminal sliding mode variable, is introduced to expedite the convergence rate of the system state during the initial stages. The efficacy of the proposed control scheme is established through the Lyapunov method, demonstrating finite‐time convergence of the trajectory error to a specified neighborhood of zero. Experimental validation on a flexible‐link system supports the effectiveness and advantages of the proposed control strategy, as evidenced via comparisons with two existing adaptive control schemes. [ABSTRACT FROM AUTHOR]

A time-synchronized (TS) convergence control method for robotic manipulators is proposed. Adversely to finite-time control, a notion of time-synchronization convergence is introduced based on the ratio persistence property, which can ensure that all system components converge simultaneously in a finite time. Firstly, a robust disturbance observer is constructed to be compatible with the time-synchronized control framework and precisely estimate system uncertainties. Furthermore, we design a (finite) time-synchronized controller to ensure that all states of the robotic manipulator simultaneously converge to an equilibrium point, irrespective of initial conditions. Stability analysis shows the feasibility of the proposed TS control method. At last, simulations are performed with a two-link rehabilitation robotic system, and the comparison results indicate its superiority. [ABSTRACT FROM AUTHOR]

For nonlinear systems with uncertain state time delays, an adaptive neural optimal tracking control method based on finite time is designed. With the help of the appropriate LKFs, the time-delay problem is handled. A novel nonquadratic Hamilton–Jacobi–Bellman (HJB) function is defined, where finite time is selected as the upper limit of integration. This function contains information on the state time delay, while also maintaining the basic information. To meet specific requirements, the integral reinforcement learning method is employed to solve the ideal HJB function. Then, a tracking controller is designed to ensure finite-time convergence and optimization of the controlled system. This involves the evaluation and execution of gradient descent updates of neural network weights based on a reinforcement learning architecture. The semi-global practical finite-time stability of the controlled system and the finite-time convergence of the tracking error are guaranteed. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time disturbance estimation and tracking control for robotic manipulators subjected to model perturbation and external disturbance. First, an adaptive sliding mode disturbance observer (ASMDO) is raised to estimate the lumped uncertainties, which does not need to consider the upper boundary prior knowledge of lumped uncertainties' derivative, and excessive gain coefficients are avoided, meanwhile, which decrease the chattering phenomenon. Next, a finite-time prescribed performance control (FPPC) is established to guarantee the system converges within a finite time and promote transient performance. Then, together with the FPPC, a finite-time nonsingular fast terminal sliding mode variable is established, which handles singularity problem in terminal sliding mode. In the meantime, a finite-time adaptive nonsingular fast terminal sliding mode controller (FANFTSMC) is constructed based on ASMDO and FPPC. The Lyapunov theorem is given to clarify that the system can reach the stable state within a finite time. Theoretical analysis and experiments reveal that FANFTSMC has better tracking performance and stronger robustness. [ABSTRACT FROM AUTHOR]

Intelligent truck platoons can benefit road transportation due to the short gap and better fuel economy, but they are also subject to dynamic uncertainties and external disturbances. Therefore, this paper develops a novel robust control algorithm for connected truck platoons. By introducing a linearized expression method of platoon error dynamics based on state measurement, the state feedback mechanism combined with a nonsmooth controller for a truck platoon is proposed in the development of the distributed control method. The state-feedback controller can drive the nominal platoon system to the state of second-order consensus, and the nonsmooth controller counterparts the uncertainties and disturbances. The convergence and string stability of the proposed control algorithm are demonstrated both theoretically and experimentally, and the effectiveness and robustness are also verified by simulation tests. [ABSTRACT FROM AUTHOR]

This paper investigates the robust control problem of the speed tension and screw down system of Reversible Cold Strip Rolling Mill (RCSRM). A finite-time observer is proposed to observe the uncertainties of the system. Based on the finite time observer, a fractional-order backstepping sliding mode controller is designed for each sub-system of the speed tension and screw down system of RCSRM. The Particle Swarm Optimization (PSO) algorithm is used to optimize the main parameters of the designed controller. By Lyapunov stability, the tracking error of the system can converge to the neighbourhood of the equilibrium point in a finite time. Finally, simulation research is carried out on the actual data of a 1422 mm RCSRM, and the effectiveness of the designed controller is verified.

With the increasing scale of microgrids, the rapid and stable achievement of secondary control objectives is an urgent problem that needs to be addressed. Therefore, a distributed adaptive finite-time control was proposed to tackle the issue of convergence speed of existing distributed secondary controllers in microgrids. The proposed controller, in different scenarios, can obtain the convergence coefficient of the most suitable finite-time controller through a distributed approach, thus accelerating the speed of secondary control. Furthermore, to address the problem of disturbances that can hinder the distributed controller from achieving control objectives, a distributed finite-time controller based on sliding mode control was designed to eliminate the impact of disturbances. The stability and feasibility of the proposed strategy were analyzed using the Lyapunov function proof method. Finally, the effectiveness and feasibility of the proposed control strategy were validated through the construction of simulation models in MATLAB/ Simulink, considering four different scenarios. [ABSTRACT FROM AUTHOR]

The paper investigates a modified adaptive super-twisting sliding mode control (ASTSMC) for robotic manipulators with input saturation. To avoid singular perturbation while increasing the convergence rate, a modified sliding mode surface (SMS) is developed in this method. Using the proposed SMS, an ASTSMC is developed for robot manipulators, which not only achieves strong robustness but also ensures finite-time convergence. The boundary of lumped uncertainties cannot be easily obtained. A modified adaptive law is developed such that the boundaries of time-varying disturbance and its derivative are not required. Considering input saturation in practical cases, an ASTSMC with saturation compensation is proposed to reduce the effect of input saturation on tracking performances of robot manipulators. The finite-time convergence of the proposed scheme is analyzed. Through comparative simulations against two other sliding mode control schemes, the proposed method has been validated to possess strong adaptability, effectively adjusting control gains; simultaneously, it demonstrates robustness against disturbances and uncertainties. [ABSTRACT FROM AUTHOR]

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The JETC Conference held in Salerno (June 12–17, 2023) was the opportunity to honor the two centuries anniversary of the booklet publication of Sadi Carnot. The paper reports on a selective review summarizing the evolution of the ideas and concepts proposed by Carnot. We consider mainly: a. The Carnot cycle relative to thermomechanical engine, b. The concept of efficiency (Carnot efficiency), c. The forms of energy (thermal energy or heat, Q, and mechanical energy or work, W), d. The concept of entropy, rediscovered and completed by Clausius. We show the importance of the energy conversion irreversibilities that started to be considered more recently by two methods, namely, the ratio method and the entropy production method. The second approach provides more significant results from a global point of view, also with more local modeling (cycle process modeling). Some examples are given that illustrate the proposal: Carnot cycle in endo-irreversible or exo-reversible configuration, Chambadal modeling, Curzon–Ahlborn modeling. More generally, the modeling is done in the frame of FTT (Finite Time Thermodynamics), FST (Finite Speed Thermodynamics), or FDOT (Finite physical Dimensions Optimal Thermodynamics). Preliminary conclusions and perspectives are proposed. [ABSTRACT FROM AUTHOR]

This paper designs a ratio consistency algorithm based on event triggering mechanism aiming at the frequency recovery deviation caused by traditional droop control in microgrid. It achieves secondary frequency modulation in microgrid by adjusting the active power setting value. The max-min consistency algorithm is proposed to realize asymptotic consistency of distributed power supply in a finite time. Communication delay is added to ensure the accuracy of frequency update and verifies the robustness of the algorithm against itself. Meanwhile, the validity of event triggering conditions is verified. Finally, the simulation examples are carried out to prove the correctness and superiority of the proposed finite-time control strategy. [ABSTRACT FROM AUTHOR]

Adaptive control of robot manipulators has been widely used in the last decades. The main control goal is usually trajectory tracking, but exact parameter estimation is always desirable. In the recent years, the so called dynamic regressor extension and mixing (DREM) procedure was developed to provide an alternative in the design of adaptive laws with more relaxed parameter convergence conditions than the Persistency of Excitation (PE). This article proposes an innovative DREM based adaptive scheme with the ability of increasing a minimal amount of excitation to the level necessary to obtain exact parameter estimation in finite time. Furthermore, a new robust control law is proposed to guarantee trajectory tracking even if exact parameter estimation does not take place. Simulation results are in good accordance with the developed theory. [ABSTRACT FROM AUTHOR]

In view of the finite time consistency tracking problem for second-order multi-agent systems with channel fading, a distributed control algorithm based on sliding mode strategy is proposed in this study. According to the topology structure of the agent, a mathematical model is built to construct the consistency error function under the influence of random channel fading. The consistency protocol based on errur function is designed to transform the consistency problem into the stability problem of tracking error system. In this study, an exponential non singular terminal sliding mode surface is designed, and the finite-time stability and sliding mode accessibility of the error system are analyzed by combining Lyapunov stability theory and sliding mode control theory. A multi-agent model with one leader and four followers is used to conduct simulation experiments. The results show that four followers can accurately track the leader and achieve the tracking consistency of the system, and the error function curve tends to 0 at 10s, which proves the effectiveness of the control strategy. [ABSTRACT FROM AUTHOR]

This paper, the adaptive fuzzy control problem for finite-time command filtering is studied at the twin roll inclined casting system. An explosion of complexity caused by a differential surge can be avoided by constructing adaptive fuzzy controller combined with command filtering and backstepping schemes. The designed adaptive fuzzy controller ensures simultaneously the stability and tracking performance of the closed-loop system in a limited time, and the tracking error converges in a small neighborhood of the origin. Eventually, a simulation example is given to verify the effectiveness of the proposed scheme.

A time-synchronized (TS) convergence control method for robotic manipulators is proposed. Adversely to finite-time control, a notion of time-synchronization convergence is introduced based on the ratio persistence property, which can ensure that all system components converge simultaneously in a finite time. Firstly, a robust disturbance observer is constructed to be compatible with the time-synchronized control framework and precisely estimate system uncertainties. Furthermore, we design a (finite) time-synchronized controller to ensure that all states of the robotic manipulator simultaneously converge to an equilibrium point, irrespective of initial conditions. Stability analysis shows the feasibility of the proposed TS control method. At last, simulations are performed with a two-link rehabilitation robotic system, and the comparison results indicate its superiority.

The stability of the teleoperated cyber–physical system with model uncertainty, external disturbance, and actuator fault is addressed in this study by using a suitable fractional-order sliding mode control (SMC) strategy. First, the sliding surface is designed to ensure the better tracking performance of the system. Second, the suggested control method combines SMC with an adaptive strategy to ensure that the system is stable in finite time. Third, neural network (NN) and fuzzy logic system (FLS) are used to estimate the model uncertainty, time-varying delay, external disturbance and unknown coefficient matrices of sliding mode surface, respectively. Finally, the advantages of the proposed control scheme are confirmed by the simulation example. • A fractional-order sliding mode control method is proposed for the finite-time tracking of the teleoperated cyber–physical system with actuator fault. • Neural network and fuzzy logic system are used to estimate the unknown term. • The boundedness of tracking error is proved by taking fractional-order derivative of Lyapunov function. • The simulation results verify the superiority of the results compared with other literatures. [ABSTRACT FROM AUTHOR]

This paper proposes a new adaptive super-twisting global integral terminal sliding mode control algorithm for the trajectory tracking of autonomous robotic manipulators with uncertain parameters, unknown disturbances, and actuator faults. Firstly, a novel global integral terminal sliding mode surface is designed to ensure that the tracking errors of autonomous robotic manipulators converge to zero in finite time and the global robustness of the system is also enhanced. Then a new adaptive method is devised to deal with the adverse effect of nonlinear uncertainty. To suppress the chattering phenomenon, the adaptive super-twisting algorithm is used in this paper, which can ensure that the control torque is a continuous input signal. Based on the adaptive mechanism, the adaptive super-twisting global integral terminal sliding mode controller is developed to provide superior control performance. The stability analysis of the system is demonstrated by using the Lyapunov method. Ultimately, the effectiveness of the control scheme is confirmed by a simulation study. • A novel adaptive finite-time global integral terminal sliding mode control scheme is designed. • A novel global integral terminal sliding mode surface is proposed to ensure faster convergence and better global robustness. • A novel adaptive law is designed to adjust the estimation parameters according to the change of system state to avoid overestimation. • The actuator fault is considered to make the proposed control logic more suitable for practical applications. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the finite-time output feedback control for discrete asynchronous switched systems with input saturation and output saturation based on MDADT. Firstly, we solve the input saturation and output saturation problem by employing a low-gain output feedback controller and the sector nonlinear condition. Secondly, we consider the asynchronism under event-triggered strategy and use the MDADT approach for finite-time stabilization and boundedness of the discrete-time switched systems under asynchronous switching. Some sufficient conditions in terms of LMIs and the appropriate MDADT are provided. Finally, two examples are given to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Position control of servo motor systems is a challenging task because of inevitable factors such as uncertainties, nonlinearities, parametric variations, and external perturbations. In this article, to alleviate the above issues, a practical adaptive fast terminal sliding mode control (PAFTSMC) is proposed for better tracking performance of the servo motor system by using a state observer and bidirectional adaptive law. First, a smooth-tangent-hyperbolic-function-based practical fast terminal sliding mode control (PFTSM) surface is designed to ensure not only fast finite time tracking error convergence but also chattering reduction. Second, the PAFTSMC is proposed for the servo motor, in which a two-way adaptive law is designed to further suppress the chattering and overestimation problems. More importantly, the proposed adaptive technique can update the switching gain according to the system uncertainties, which can provide high gain in the reaching phase and then decrease to the smallest value in the sliding phase to avoid the monotonically increasing gain that exists in most adaptation methods. Third, the finite-time stability of the closed-loop system is proved based on the Lyapunov theorem. Finally, the simulation studies and experimental tests verify the effectiveness of the proposed control in terms of better tracking, strong robustness, and reduced chattering, compared to existing algorithms. [ABSTRACT FROM AUTHOR]

Aim to solve the problem of over-dependence on dynamics model and low tracking accuracy of robotic manipulators under uncertainties and backlash hysteresis, an adaptive continuous nonsingular fast terminal sliding mode controller combining time delay estimation (TDE) and prescribed performance control (PPC) is formulated. Firstly, TDE is applied to estimate the model information and external disturbances, so that the dynamics model of robotic manipulators is simplified into a local model. Then, an adaptive terminal sliding mode controller is established based on the local model and PPC, which solves the singularity problem of traditional terminal sliding mode and improves the transient and steady-state performance of robotic manipulators. Next, by combining the reaching law with the adaptive term, robotic manipulators achieve favorable tracking performance, fast convergence time, and chattering suppression under complex disturbances. And the Lyapunov theory is applied to prove that the robotic manipulators can reach the steady state in finite time. Meanwhile, a saturation compensator is formulated to settle actuator saturation and the compensator can converge within a finite time. Finally, the simulation is applied to verify the formulated control strategy can effectively improve the tracking performance and enhance the robustness against disturbances. [ABSTRACT FROM AUTHOR]

For nonlinear systems with uncertain state time delays, an adaptive neural optimal tracking control method based on finite time is designed. With the help of the appropriate LKFs, the time-delay problem is handled. A novel nonquadratic Hamilton–Jacobi–Bellman (HJB) function is defined, where finite time is selected as the upper limit of integration. This function contains information on the state time delay, while also maintaining the basic information. To meet specific requirements, the integral reinforcement learning method is employed to solve the ideal HJB function. Then, a tracking controller is designed to ensure finite-time convergence and optimization of the controlled system. This involves the evaluation and execution of gradient descent updates of neural network weights based on a reinforcement learning architecture. The semi-global practical finite-time stability of the controlled system and the finite-time convergence of the tracking error are guaranteed.

Intelligent truck platoons can benefit road transportation due to the short gap and better fuel economy, but they are also subject to dynamic uncertainties and external disturbances. Therefore, this paper develops a novel robust control algorithm for connected truck platoons. By introducing a linearized expression method of platoon error dynamics based on state measurement, the state feedback mechanism combined with a nonsmooth controller for a truck platoon is proposed in the development of the distributed control method. The state-feedback controller can drive the nominal platoon system to the state of second-order consensus, and the nonsmooth controller counterparts the uncertainties and disturbances. The convergence and string stability of the proposed control algorithm are demonstrated both theoretically and experimentally, and the effectiveness and robustness are also verified by simulation tests.

This paper investigates distributed Nash equilibrium (NE) seeking problems. A bilateral bounded gradient approach, a novel optimization algorithm, is utilized to solve strongly convex problems. Furthermore, for a strongly monotone game, the NE can be obtained in finite time by the bilateral bounded gradient algorithm. In the distributed manner, two types of algorithms are proposed for seeking the NE: consensus‐based strategy and passivity‐based strategy. For each player, nonlinear protocols are proposed to estimate the actions of their rivals, enabling these estimations to converge to the actual actions in fixed time. To solve the optimization problem, the bilateral bounded gradient algorithm is employed, ensuring that all players' actions converge to the NE in finite time. Moreover, to reduce the communication consumption, event‐triggered schemes are introduced in the information exchange of players. Finally, swarm roundup behavior is analyzed by a non‐cooperative game in which the proposed algorithms drive all tanks to hunt the target in finite time. The roundup effectiveness is verified by the simulations. [ABSTRACT FROM AUTHOR]

This study investigates the problem of robust fault diagnosis for nonlinear systems subjected to actuator faults and unknown input disturbances. A novel adaptive fast smooth super-twisting observer based on the super-twisting and adaptive dual-layer algorithms is presented, and a robust fault-diagnosis scheme based on an adaptive threshold is proposed to take the estimation error generated by the observer as the residual. In the adaptive fast smooth super-twisting observer, additional fractional powers less than 1 and linear terms are added to improve the smoothness and rapidity of the observer. The finite-time stability of the adaptive fast smooth super-twisting observer is then analyzed based on the Moreno–Lyapunov function algorithm, and rigorous proof confirms that the estimation-error dynamic is robust to unknown input disturbances and can converge to a region of zero in finite time. Finally, simulations of the rigid spacecraft attitude kinematics and dynamics are used to validate the effectiveness of the developed adaptive fast smooth super-twisting observer and the designed robust fault-diagnosis scheme. [ABSTRACT FROM AUTHOR]

A finite-time fully distributed consensus (FTFDC) control problem is studied for a second-order multi-agent system (MAS) with input saturation, limited communication resources and external bounded disturbances. Firstly, to deal with the input saturation characteristics, a second-order auxiliary system is designed to obtain the compensation signal. Secondly, because the leader information can only be obtained by a group of agents connected with the leader, a distributed estimator for each agent is designed to estimate the leader information. Then, to save communication resources, an event trigger condition is designed without continuous communication between agents. Based on the estimator and event trigger condition, a FTFDC controller is designed to realize the finite time fully distributed consensus control of MAS under limited communication resources and external bounded disturbances. Finally, the designed controller is verified by simulation on a multi-spacecraft attitude system model. [ABSTRACT FROM AUTHOR]

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Event-triggered finite-time formation control is considered for second-order leader-following multi-agent systems with nonlinear term time delay in this study. Collision avoidance radius is designed for a class of second-order nonlinear multiagent systems to avoid collisions between agents. Collision avoidance control is realised by detecting the flight radius. Control cost is economised, and communication volume is reduced by controlling key nodes and designing an event-triggered control strategy. The system can realise formation control in finite time by designing an FTC function. Some sufficient conditions for the formation of the second-order multi-agent system in finite time are obtained by using Lyapunov stability theory and analysis. The integral sliding mode control algorithm and finite-time stability theory are used to enhance the robustness of the system, and the upper bound of finite time is given. At the same time, the ability of the designed event-triggered function to avoid Zeno behaviour is proven. Finally, the feasibility of the results is verified through a numerical simulation. [ABSTRACT FROM AUTHOR]

Aiming at the attitude tracking control problem of rigid spacecraft under the condition of unmeasurable angular velocity information, a velocity‐free adaptive nonsingular fast terminal sliding mode finite‐time tracking control method is proposed. The finite‐time extended‐state observer is used to estimate the attitude tracking speed errors and the integrated disturbances. Combined with the above control method, a fast nonsingular terminal sliding mode controller with attitude measurement is designed and the adaptive technology is introduced to compensate for the influence of observation errors on the controller. The finite‐time convergence of the observer and the control method was demonstrated based on Lyapunov theory, and the effectiveness of the proposed method is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

The paper investigates a modified adaptive super-twisting sliding mode control (ASTSMC) for robotic manipulators with input saturation. To avoid singular perturbation while increasing the convergence rate, a modified sliding mode surface (SMS) is developed in this method. Using the proposed SMS, an ASTSMC is developed for robot manipulators, which not only achieves strong robustness but also ensures finite-time convergence. The boundary of lumped uncertainties cannot be easily obtained. A modified adaptive law is developed such that the boundaries of time-varying disturbance and its derivative are not required. Considering input saturation in practical cases, an ASTSMC with saturation compensation is proposed to reduce the effect of input saturation on tracking performances of robot manipulators. The finite-time convergence of the proposed scheme is analyzed. Through comparative simulations against two other sliding mode control schemes, the proposed method has been validated to possess strong adaptability, effectively adjusting control gains; simultaneously, it demonstrates robustness against disturbances and uncertainties.

The study of the blow-up phenomenon for fractional reaction–diffusion problems is generally deemed of great importance in dealing with several situations that impact our daily lives, and it is applied in many areas such as finance and economics. In this article, we expand on some previous blow-up results for the explicit values and numerical simulation of finite-time blow-up solutions for a semilinear fractional partial differential problem involving a positive power of the solution. We show the behavior solution of the fractional problem, and the numerical solution of the finite-time blow-up solution is also considered. Finally, some illustrative examples and comparisons with the classical problem with integer order are presented, and the validity of the results is demonstrated. [ABSTRACT FROM AUTHOR]

A finite‐time suboptimal control strategy named θ−D$$ \theta -D $$ technique is proposed for the control of a class of control‐affine nonlinear dynamic systems in this study. The nonlinear dynamic is expressed as a pseudo‐linear form without linearization. By adding vanishing perturbation terms into the quadratic cost functional and using a power series to represent the co‐state, an approximate solution to the Hamilton–Jacobi–Bellman (HJB) equation can be obtained through solving a differential Riccati equation offline and a series of linear Lyapunov equations with analytical solutions. The obtained suboptimal controller is in a state feedback closed‐form. By tuning the parameters in the perturbation terms, semi‐global stability can be guaranteed. In contrast to the finite‐time state‐dependent Riccati equation technique, the proposed method does not need intensive and iterative numerical computations, which facilitates real‐time implementation. Two examples are utilized to demonstrate the effectiveness and efficiency of this proposed technique. [ABSTRACT FROM AUTHOR]

In this paper, we propose a distributed finite-time optimization protocol for single-integrator continuous-time multi-agent systems, which utilizes a modified Newton–Raphson method. The inverse of Hessian matrix, sign function and the gradient are adopted for the design of the algorithms. The proposed algorithms make agents converge to the network optimizer under any initial state and finite time, respectively. Lyapunov method and the properties of sign function are employed to verify the convergence of the proposed algorithms. Besides, the adaptive method is also considered to avoid complex parameter conditions and centralized parameters. Finally, numerical simulations are provided to testify the presented results. [ABSTRACT FROM AUTHOR]

A nonlinear Cauchy problem of a wave equation with variable exponents is considered. The damping term is subjected to a coefficient of both variables space and time. We prove the local existence of solutions using the Galerkin approach while the blow-up result is obtained via the perturbed energy method. We finally end our paper with some numerical illustrations. Problems that are frequently used in the literature are special cases. [ABSTRACT FROM AUTHOR]

This article focuses on the stable imaging problem of photoelectric imaging system that depends on the synchronous rotation of mirror and detector. When there is a relative movement between the mirror and the detector, it will cause image rotation, resulting in information loss and reduced tracking accuracy. It is difficult to achieve the high-precision synchronous movement between the mirror and the detector using the traditional unilateral control method. Different from the existing results of the traditional unilateral tracking method, this paper introduces the bilateral control structure in the field of robot teleoperation and proposes a novel compound control strategy based on the bilateral control structure. First, a robust disturbance observer is proposed to reduce the disturbance of the system, in which a new robust H ∞ mixed sensitivity control algorithm is designed to optimize the filter. Then, a novel generalized sliding mode predictive (NSMP) control strategy based on hybrid reaching law is proposed to eliminate the image rotation problem caused by time delay. Besides, a new power function is designed to replace the switching function in the reaching law to reduce chattering. Finally, the finite time theory and the Lyapunov theory are used to prove that the proposed control scheme can ensure that the system is stable and reach its steady state in a finite time. The simulation results show the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the finite-time flocking problem for a modified Cucker-Smale model with unknown Hölder continuous intrinsic dynamics. Firstly, we use the energy method to show conditional finite-time flocking would occur under some conditions depending on initial data, exponent $ \beta $ and Hölder constant $ L $. Then we give an example consisting of two agents to show that for any $ \beta>0 $ or large enough $ L $, there is no unconditional finite-time flocking occurrence. Finally, we present some numerical simulations to show our theoretical results are valid. [ABSTRACT FROM AUTHOR]

In this paper, a modified distributed Nash equilibrium seeking problem with input saturation has been investigated. The payoff function of each player is related to the communication topology, which is closer to the actual scenes. The sigmoid function is utilized to limit the range of the input. Through the network communication between players and the gradient of the players' payoff functions, the finite-time and fixed-time distributed Nash equilibrium seeking protocols with input saturation are given. Using the Lyapunov stability analysis, it is determined that the action of each player converges to the Nash equilibrium if all the players update their action according to the proposed algorithms. The numerical simulations are also provided to testify the algorithms. [ABSTRACT FROM AUTHOR]

This paper focuses on the finite-time formation-control problem of a multi-AUV formation under unknown perturbations with prescribed performance. First, the nonlinear AUV model is transformed into a second-order integral model using feedback linearization. Suitable prescribed performance functions are selected to constrain the control errors of AUVs within a preset range and convert AUV tracking errors into unconstrained tracking errors using an error-conversion function to facilitate controller design. Finite-time sliding-mode disturbance observers are designed for unknown disturbances in the ocean so that they can accurately estimate the unknown disturbances in finite time. Based on the unconstrained tracking error and the unknown disturbance observer, the fast terminal sliding-mode formation controller is designed so that the multi-AUV formation can converge in finite time. Finally, the simulation experimental results show that the finite-time formation-control method with prescribed performance proposed in this paper can better cancel the unknown disturbance in the ocean in finite time and improve the robustness of the multi-AUV formation control. [ABSTRACT FROM AUTHOR]

This paper examines a finite-time command-filtered backstepping control proposed for a class of strict-feedback nonlinear systems with input delay and time-varying asymmetric full-state constraints. The existing control method either ignores the effect of input delay or converges asymptotically in infinite time. A command-filtered backstepping design is used to decrease computational burden. A first-order Levant differentiator is employed to replace the command filter for estimating the virtual control signals in finite time. The time-varying asymmetric barrier Lyapunov function (TVABLF) and command-filtered backstepping design are applied to alleviate the significant challenges caused by the backstepping approach and full-state constraints. A novel finite-time delay compensation mechanism is proposed to remove the impact of input delay. The closed-loop signals are proved to be practical bounded. Simulation results are provided to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this article, the line-of-sight (LOS)-based on the control principle of path following is presented to apply to a marine surface vessel (MSV) with an unknown time-varying sideslip angle. The input saturation and the uncertain model are taken into account. The presented finite-time predictor-based adaptive integral line-of-sight (FPAILOS) guidance principle can estimate the unknown time-varying sideslip angle while compensating for the drift force. The FPAILOS guidance law offers the desired yaw angle. The drift force can be caused by the ocean currents, which are taken into account in the kinematic model for the MSV. For the input saturation problem, we select the finite-time auxiliary system to limit inputs. Designing path following control signals adopts the finite-time dynamic surface control (FDSC) method. The finite-time low-frequency learning-based fuzzy system is designed to solve the uncertain model problem for the MSV. Finally, the stability of the system is demonstrated and numerical simulations are performed, where the objective is to evaluate the proposed theoretical results. With the presented control strategy, the track errors can converge into arbitrary small neighborhoods around zero in finite time. • FPAILOS is firstly presented to offer the desired yaw, estimating the sideslip angle. • FLLFS is designed to estimate the uncertainties and unknown external disturbances. • FDSC is introduced to design the controller to realize path following. [ABSTRACT FROM AUTHOR]

The main task of this paper is to control a class of nonlinear systems with input delay in finite time. The Pade approximation approach is used to reduce the impact of input delay. In addition, unknown functions are approximated by fuzzy logic systems (FLSs). Then the adaptive controller is intended by backstepping technique, which make sure the the stability of the system in finite time and also the close-loop signals are bounded in finite time. Finally, a simulation shows that the proposed method is effective. [ABSTRACT FROM AUTHOR]

In this work, we establish a complete procedure for the output regulation problem with prescribed performance for a class of switched strict-feedback systems by employing barrier Lyapunov function and speed function method. Under the framework of output regulation control for general switched nonlinear systems, a switched regulator equation is constructed. Compared to the existing works which require the solvability of output regulation for each subsystem, the designed switched regulator equation based method need not each subsystem has a solution to the problem, which releases the conservatism. Moreover, the state feedback control scheme based on speed function technique and a new state dependent switching rule are constructed to achieve that the error output keeps in a prescribed performance bound in a given finite time and tracks a desired trajectory asymptotically. The effectiveness of the results is demonstrated by a simulation example. [ABSTRACT FROM AUTHOR]

ObjectiveAiming at the problems of dynamic uncertainty and unknown disturbance in the trajectory tracking control of underactuated surface ships, an adaptive neural network finite time trajectory tracking control scheme is designed. MethodThe underactuated variation is carried out using the method of kinematic virtual control law transformation and bounded constraints. Under the framework of Backstepping, neural networks are used to reconstruct unknown dynamics, and an adaptive law is designed to approach the upper bound of unknown disturbances. The Lyapunov direct method provides a rigorous theoretical analysis which proves that all the signals of the closed-loop system are bounded, and the tracking error converges to a bounded interval. ResultsThe simulation results show that this control scheme can make an underactuated ship track the desired trajectory in a limited time, the convergence speed of the system error is faster than that of the traditional control scheme, and the upper and lower bounds of the error are also smaller. It also shows good robustness in the face of unknown time-varying interference from the outside world. ConclusionThe results of this study can provide valuable references for the tracking and control of ship trajectories, giving it great practical engineering significance.

An attempt is made in this paper to devise a finite-time adaptive fuzzy back-stepping control scheme for a class of multi-input and multi-output (MIMO) coupled nonlinear systems with immeasurable states. In view of the uncertainty of the system, adaptive fuzzy logic systems (AFLSs) are used to approach the uncertainty of the system, and the unmeasured states of the system are estimated by the finite-time extend state observers (FT-ESOs), where the state of the observer is a sphere around the state of the system. The accuracy and efficiency of the control effect are ensured by combining the back-stepping and finite-time theory. It is proved that all the states of the closed-loop adaptive control system are semi-global practical finite-time stability (SGPFS) by the finite-time Lyapunov stability theorem, and the tracking errors of the system states converge to a tiny neighborhood of the origin in a finite time. The validity of this scheme is demonstrated by a simulation.

In this paper, a novel finite-time fault-tolerant trajectory tracking controller is created to render a marine vehicle to enhance tracking performance in the presence of complex unknown variables, including model uncertainties, environmental disturbances, and actuator faults. An adaptive fault-tolerant finite-time sliding mode controller is designed by introducing adaptive control techniques, the non-singular fast terminal sliding mode (NSFTSM) function, and a radial base function (RBF) neural network. The radial base function neural network (RBFNN) is developed to eliminate the influences of model uncertainties and environmental disturbances. A fault compensation by integrating the adaption technique is designed to reduce the effects of actuator faults and approximation errors. Suffering from uncertainties and actuator faults, the proposed finite-time tracking controller can track the desired trajectory with high precision. Simulation results and compared simulations indicate the efficiency and superiority of the proposed controller. [ABSTRACT FROM AUTHOR]