Finite-time Function Research Articles

Auto-berthing Control for MSVs with a Time-based Generator under Actuator Faults: A Concise Neural Single-Parameter Approach

Abstract In this paper, we study the control problem of auto-berthing marine surface vessels (MSVs) within a predefined, finite time in the restricted waters of a port, in the face of internal and external uncertain dynamics and actuator faults. We first use radial basis function neural networks to reconstruct the internal uncertainties of the system; then, using the minimum learning parameter method, we transform the weights of the neural networks, the external disturbances of the system, and the bias fault factors into an indirect single-parameter neural learning mode. We also apply a robust depth information adaptation technique to estimate the upper bound on the composite disturbances online. Dynamic surface control technology alleviates the burden of virtual control derivative calculations. Finite-time convergence of the system is guaranteed by a predetermined finite-time function based on a time-based generator (TBG). Based on these methods, we design a finite-time fault-tolerant auto-berthing control scheme based on TBG. The stability of the system is analysed based on Lyapunov stability theory. Finally, we verify the effectiveness of the proposed control scheme through simulation.

Cooperative Control for Stochastic Multiagent Systems With Deferred Dynamic Constraints via a Novel Universal Barrier Function Approach.

This article investigates the cooperative control problem for stochastic multiagent systems (MASs) with dynamic constraints. A new universal barrier function is proposed, which is applicable to many systems with different types of constraint functions, even unconstrained systems. Several mapping functions are constructed to constrain the state variables directly without feasibility conditions, and the tracking control is achieved for stochastic MASs with deferred full-state constraints under the backstepping framework. In order to regulate the tracking error more precisely, the funnel error transformation is improved and the deferred funnel controller is developed by introducing a preassigned finite-time function. Based on the deferred funnel controller, the tracking error can be maintained within the predetermined funnel in the preassigned time. The convergence time can be defined according to the actual requirements, and it is independent of the design controller parameters and initial conditions. Finally, some simulation results are given to demonstrate the effectiveness of the proposed control algorithm.

Adaptive practical prescribed-time formation tracking of networked nonlinear multiagent systems with quantized inter-agent communication

This paper presents an adaptive practical prescribed-time (PPT) control design for distributed time-varying formation tracking of networked uncertain strict-feedback nonlinear systems with quantized inter-agent communication under a directed network. The primary contribution of this study is to develop a time-varying formation tracking strategy to resolve the quantized inter-agent communication problem in the prescribed-time control field. A practical finite-time function is introduced to design an adaptive PPT formation tracker using quantized output information of neighbors, which can be used continuously after a prescribed time. A neural-network-based design methodology that utilizes the quantization-based distributed errors is presented to deal with the unknown virtual and actual control coefficient functions in the command-filtered backstepping design. Distributed adaptive compensating signals are constructed using the practical finite-time function to compensate for command-filter errors, unknown nonlinearities, and quantization errors in the PPT tracking framework. We prove that despite the presence of quantized inter-agent communication, the time-varying formation tracking errors converge to a compact set including the origin within the pre-assigned convergence time, where the compact set can be adjusted by choosing a design parameter of the practical finite-time function, and the prescribed settling time is independent of the initial system conditions and design parameters. The effectiveness of the proposed theoretical approach is confirmed through two simulation examples.

Synchronous oscillation characteristic and finite-time function projection synchronization control method for microgrids

Due to the nonsynchronization of each microsource node in a microgrid, the physical parameters of each node are not uniform. Therefore, unstable oscillation will occur for the whole microgrid system. To solve the oscillation problem caused by the nonsynchronization of each microsource node in the microgrid, a hierarchical control structure microgrid model is researched in this paper. Based on the theory of chaotic synchronization and finite time, a new microgrid synchronous oscillation characteristic and finite-time function projection synchronization control method is proposed. First, combining complex networks and microgrids, a nonlinear dynamic model of microgrid hierarchical control is established, and the abilities of the small-world network model and the formal network model to adjust for asynchronous oscillations are verified by comparing the two models. Then, aiming at the unsynchronized oscillations caused by external system noise, a new finite-time function projection synchronization control method is proposed. According to the verification results, the method can control external disturbances, avoiding system oscillation.

Adaptive pre-assigned finite-time control of uncertain nonlinear systems with unknown control gains

This paper mainly studies an adaptive finite-time control problem for a kind of uncertain strict feedback systems with unknown control gains. First, the original strict-feedback system is transformed into a pure-feedback system. And then, we propose a modified adaptive finite-time design idea on the basis of the property of pre-assigned finite-time function (PFTF) and Nussbaum gain. The designed controller can make sure that all states converge to an arbitrarily region in finite-time and signals in the closed-loop system are finite-time bounded. Moreover, the presented controller is smooth and the settling time does not rely on the initial values and design parameters. Finally, the simulation study is made to illustrate the innovativeness for the proposed scheme.

Preassigned finite-time attitude control for spacecraft based on time-varying barrier Lyapunov functions

The problem of preassigned finite-time control is addressed in this paper for attitude tracking of the rigid spacecraft with parameter uncertainty and external disturbance. First, the attitude tracking error system of the rigid spacecraft is constructed. Then, a kind of preassigned finite-time functions is used to impose a priori desired performance index on the state of the constructed error system. By applying the backstepping technique, a preassigned finite-time controller is proposed to stabilize the attitude tracking error system via employing a time-varying barrier Lyapunov function. In addition, an extended state observer is introduced to estimate the lumped disturbance in the rigid spacecraft system. It is proven that the practically preassigned finite-time stability of the resultant closed-loop system can be guaranteed by the proposed controller despite the presence of parameter uncertainty and external disturbance. Finally, simulation results are presented to demonstrate the effectiveness of the developed controller design method.

Neural Network-Based Distributed Adaptive Pre-Assigned Finite-Time Consensus of Multiple TCP/AQM Networks

In this study, a class of finite-time consensus of multiple transmission control protocol/active queue management (TCP/AQM) networks is investigated on the basis of a design idea of multi-agent systems, and for the first time, to our knowledge, a novel congestion control concept with neural networks is proposed. First, the problem statement and design goal of the consensus of multiple TCP/AQM networks is given. Then, a pre-assigned finite-time function is introduced to ensure that the tracking error approaches a pre-defined area within finite time. Furthermore, by combining a barrier Lyapunov function and backstepping technique, a neural network-based distributed adaptive finite-time control protocol for the output consensus of multiple TCP/AQM networks is presented, which can effectively generate the desired controls and ensure that the convergent time of all errors has nothing to do with the initial condition and design parameters. In addition, all signals in the closed-loop system are bounded. Finally, an example is given to further illustrate the effectiveness of the theoretical finding presented.

Performance Guaranteed Consensus Tracking Control of Nonlinear Multiagent Systems: A Finite-Time Function-Based Approach.

In this article, we study the performance guaranteed consensus tracking problem for a class of high-order nonlinear multiagent systems subject to mismatched uncertainties and external disturbances. We first construct a finite-time function, with which a performance function is introduced that links the convergence time of the relative consensus errors with the neighbor agents. We then introduce two new lemmas that play a virtual role in addressing the consensus stability of closed-loop multiagent system, where a fully distributed adaptive control without using global information of the topology is developed. Different from most existing works for multiagent systems with prescribed performance that can only achieve uniformly ultimately bounded consensus, the proposed control scheme is able to ensure that the consensus errors converge to the pregiven compact sets within preassigned finite time rather than infinite time and the outputs of all the agents track the leader's trajectory asymptotically. Simulation verification also confirms the effectiveness of the proposed approach.

Finite-time function projective synchronization control method for chaotic wind power systems

Wind power is a rapidly growing renewable energy source that plays an increasingly important role in power systems. However, its dynamic behaviors are complex because of the instability of wind speed, strong coupling, highly nonlinear subsystems, and mass grid connections. Chaotic oscillation is one of the most typical complex dynamic behaviors of wind power systems. This behavior can seriously influence the stable operation of wind power systems and cause great harm. This study proposed a control method for finite-time function projective synchronization on the basis of the chaos synchronization principle and finite-time theory for wind power systems. Wind power systems with or without uncertain parameters were considered. First, we built a high-dimensional wind power system and analyzed its chaotic behaviors. Lyapunov exponents were derived to prove the existence of chaos and bifurcation. Second, we aimed to increase the robustness of the controller by adding parameter observers to the controller. The result helped solve the problem of unknown parameters. If a wind power system comprises unknown parameters, the unknown parameters can be defined as the system's states. An unknown parameter observer was designed to realize the identification of unknown parameters. Third, we proposed a control method for finite-time function projective synchronization. Finite-time stability theory and function projective synchronization theory were used to construct the controller. These theories can ensure the quick synchronization of a chaotic wind power system with a stable wind power system in finite time. Finally, the mathematical proof of the stability theorem was derived, and a corresponding numerical simulation was performed to validate the chaos control method for wind power systems.

Finite-time Function Projective Synchronization in Complex Multi-links Networks and Application to Chua’s Circuit

The article focuses on the problem of finite-time function projective synchronization which is happened in complex multi-links networks with constant time delay or time-varying delay problems and it is applied to Chua’s circuit. The main contribution is that a special class of nonlinear feedback controllers are proposed to make finite-time function projective synchronization. The proposed two nonlinear feedback controllers contain the constant time delay or time-varying delay and they all can make finite-time function projective synchronization in complex multi-links networks with constant time delay or time-varying delay problems. In addition, their finite-time criteria are derived based on finite-time stability theory and the convergence time are estimated. At last, the presented controllers are applied to Lorenz system and Chua’s circuit the numerical simulations demonstrate the power of our method.

Semi-Globally Practical Finite-Time ${H}_{\infty}$ Control of TCSC Model of Power Systems Based on Dynamic Surface Control

A less-complex semi-globally practical finite-time stability (SGPFS) result is presented for thyristor-controlled series compensation (TCSC) model of the power system by using dynamic surface control (DSC), H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control and prescribed performance control (PPC) in this paper. Meanwhile, a set of preassigned finite-time functions (PFTF) are chosen. The designed controller makes the rotor angle converge to a predefined arbitrary small area within a finite-time interval and other states of the closed-loop system are bounded. In addition, the proposed design method is simpler and the presented result is also easier to be achieved. Finally, simulation results are given to verify the effectiveness and superiority of the theoretical finding.

具有时延和随机扰动的未知C-G神经网络的有限时间函数投影同步及其在保密通信中的应用

The finite-time function projective synchronization of unknown Cohen-Grossberg neural networks with time delays and stochastic disturbances was investigated. A hybrid control scheme combining open-loop control and feedback control was designed to guarantee that the drive and response networks can be synchronized up to a scaling function in a finite time with parameter identification by means of the finite-time stability theory. Besides, the upper bounds of the settling time of synchronization were estimated. Finally, the corresponding numerical simulation and its application in secure communication were provided to demonstrate the validity of the presented synchronization method.

Varying-Parameter RNN Activated by Finite-Time Functions for Solving Joint-Drift Problems of Redundant Robot Manipulators

Joint-drift problem may lead to task execution failure or robot damage. To solve this problem, a finite-time varying-parameter recurrent neural network (FT-VP-RNN) is proposed and investigated in this paper. First, a quadratic programming (QP) based joint-drift-free (JDF) scheme is developed, which consists of an optimization criterion and a kinematic equation at velocity layer. A feedback control is then added into the kinematic equation as the equality constraint, and a feedback-considered joint-drift-free (FC-JDF) scheme is obtained. Second, a novel FT-VP-RNN is designed to solve the FC-JDF scheme and a corresponding finite-time convergence theorem is proposed. The outstanding advantages of the proposed FT-VP-RNN are the real-time computation, exponential convergence, and the ability to eliminate the initial errors. Finally, three path-tracking simulations and comparisons are conducted to verify the effectiveness, accuracy, practicability, and safety of the proposed FT-VP-RNN for solving the joint-drift problems of redundant robot manipulators.

Elimination of Nonstationary Oscillations of an Elastic System at the Stopping Time after Finite Rotation by the Given Law via the Tuning of Eigenfrequencies

The article deals with an arbitrary elastic 3D-system (body) that performs a controlled finite rotation with respect to some fixed axis and small nonstationary oscillations. The system oscillations occur due to external load (power control) or inertial load of the rotational transportation of the carrying body (kinematic control). The linear equations of oscillations are used in normal coordinates, in which motion is represented by eigenmodes of vibrations for system that is free in the rotation angle (including system rotation as a solid body in the case of power control) and for system fixed in rotation angle in the case of kinematic control. It is assumed that the (power or inertial)load acting on the system is proportional to some controlling finite time function from a certain class. The purpose of this article is to solve the problem of system rotation for a certain time from one rest position to another at a given finite angle using the given control function and to eliminate the elastic oscillations on the several lowest eigenmodes at the stopping time. The relations between the time of the system rotation under the action of a given control function and the eigenmodes frequencies for oscillations being eliminated are obtained on the basis of the exact solutions of the equations in normal coordinates. These relations satisfy the zero initial and final conditions. They are “tuned” by minimizing the positive definite quadratic form written for them by varying the system parameters to fulfill these relations simultaneously for several eigenfrequencies. As an example, the calculations for a model of a symmetrical spacecraft with two identical elastic solar cell panels consisting of four planar non-deformable sections connected by elastic hinges are carried out for comparison and analysis of the results accuracy. The finite rolling motion of the system with the damping at the stopping time of rotation for several (from one to three) lowest eigenmodes of antisymmetric vibrations is considered. The comparisons of the initial equations of motion for the system in generalized coordinates using several simple control functions and the found parameters of the “tuned” system with numerical solutions are accomplished.

Generalized finite-time function projective synchronization of two fractional-order chaotic systems via a modified fractional nonsingular sliding mode surface

This paper addresses the problem of generalized finite-time function projective synchronization (GFFPS) of fractional-order chaotic systems. A modified fractional nonsingular terminal sliding mode surface and an appropriate robust fractional sliding mode control law are proposed, taking into account the effects of model uncertainties and of the external disturbances. An appropriate Lyapunov functional candidate is used to prove the finite-time existence of the sliding motion. Compared with the existing nonsingular sliding mode surface, our sliding mode surface permits to reduce the settling time of synchronization. Finally, some numerical simulations taking into consideration the Gaussian white noise produced by the electrical line are presented to demonstrate the effectiveness and applicability of the proposed technique.

Finite-Time Function Projective Synchronization in Complex Multi-links Networks with Time-Varying Delay

This paper investigates the problem of finite-time function projective synchronization in complex multi-links networks with time-varying delay. A nonlinear feedback controller is designed to achieve finite-time function projective synchronization. Some novel and useful finite-time function projective synchronization criteria are derived based on finite-time stability theory. And another controller is designed to ensure function projective synchronization of complex multi-links networks with time-varying delay. Finally, illustrative examples are given to show the feasibility of the proposed method.

Nonlinear multi-objective receding horizon design utilizing state-dependent formulation

The art of multi-objective design is to extract the best compromise among conflicting requirements. The analytical multi-objective parameter synthesis adopts closed-form specifications that make the multi-objective design in linear systems computationally efficient. In this paper, the analytical multi-objective parameter synthesis method is extended to nonlinear systems via the state-dependent coefficients parametrization method in combination with the receding horizon control technique. The novel contributions presented in this paper are demonstrated on two fronts. First, the objective functions in infinite-time domain are replaced by equivalent finite-time functions with certain terminal terms, where the analytical formulations for the finite-time functions are made available and offer a computationally cost-effective approach. Second, the stability is addressed by adopting the receding horizon control technique. In addition, the proposed design approach shows benefits over the conventional nonlinear optimal control method. Two numerical examples further demonstrate the promising features of the proposed design framework.