Semi-global Practical Finite-time Stability Research Articles

Distributed finite-time adaptive consensus output-feedback control of multi-agent systems under switching topologies

The paper investigates the finite-time adaptive consensus control of nonlinear multi-agent systems (MASs) by output-feedback. During the process of control design, the fuzzy logic system (FLS) is employed to approximate nonlinear function, as well as constructing a fuzzy state observer to estimate unmeasured states. Combining the dynamic surface control (DSC) with adaptive backstepping method conquers the complexity explosion issue. Then, semi-global practical finite-time stability (SGPFS) for closed-loop system is obtained under arbitrary switching communication topologies. All the signals of the overall system are uniformly ultimately bounded (UUB). Finally, the availability of developed control approach will be demonstrated through a simulation.

Robust optimal triple event-triggered intermittent control for uncertain input-constrained nonlinear systems

This paper investigates the concept of finite time (FT) optimal event-triggered intermittent (ETI) control for nonlinear systems with input constraints and dynamic uncertainty. Firstly, we address a key challenge faced by existing controllers, wherein the unbounded nature of the signal function renders it impractical to handle the input-constrained FT control problem. To overcome this limitation, we derive a novel lemma of semiglobal practical finite-time stability (SGPFTS) specifically for intermittent control with the additional constant terms. By leveraging the lemma and the Hamilton–Jacobi–Bellman (HJB) equation, we obtain the optimal FT guaranteed cost intermittent control law and establish FT stability criteria for uncertain nonlinear systems. Recognizing that the general HJB theory is ill-equipped to address input-constrained optimal control problems, We introduce the model predictive control (MPC) algorithm, which has been proven to be an effective online optimization method in handling robust optimal control and constrained problems. Moreover, conventional ETI optimal control methods struggle to address intermittent control for nonlinear systems with input constraints and dynamic uncertainty. To address this limitation, we propose a triple ETI Lyapunov-based MPC strategy, which not only enhances intermittent control performance but also resolves input constraints and dynamic uncertainty issues. Finally, we present two straightforward examples of uncertain nonlinear systems to demonstrate the effectiveness of the developed strategy in practice.

Adaptive Control for Complex Systems with Dynamics and Time-Varying Powers

This work focuses on presenting a control algorithm to investigate nonlinear systems, which contain time-varying powers, inverse dynamics, and uncertainties. First, some appropriate transformations are introduced to obtain a new system. Then, a Lyapunov function, which covers quadratic and high-order components, is recursively constructed for control design. Subsequently, by introducing the neural networks, the uncertain functions encountered during the design are approximated. Based on the inequality techniques, the nonlinear terms are skillfully estimated. By defining the bounds of some unknown parameters and using the adaptive technique, some virtual controllers are selected in each step to dominate the nonlinear functions and guarantee that the derivative of the Lyapunov function satisfies the required form. Finally, a new adaptive controller is constructed and semiglobal practical finite time stability (SGPFS) is guaranteed. The proposed approach is verified with a numerical example.

Neural‐based online finite‐time optimal tracking control for wheeled mobile robotic system with inequality constraints

AbstractIn this study, a finite‐time online optimal controller was designed for a nonlinear wheeled mobile robotic system (WMRS) with inequality constraints, based on reinforcement learning (RL) neural networks. In addition, an extended cost function, obtained by introducing a penalty function to the original long‐time cost function, was proposed to deal with the optimal control problem of the system with inequality constraints. A novel Hamilton‐Jacobi‐Bellman (HJB) equation containing the constraint conditions was defined to determine the optimal control input. Furthermore, two neural networks (NNs), a critic and an actor NN, were established to approximate the extended cost function and the optimal control input, respectively. The adaptation laws of the critic and actor NN were obtained with the gradient descent method. The semi‐global practical finite‐time stability (SGPFS) was proved using Lyapunov's stability theory. The tracking error converges to a small region near zero within the constraints in a finite period. Finally, the effectiveness of the proposed optimal controller was verified by a simulation based on a practical wheeled mobile robot model.

Finite-time adaptive anti-disturbance constrained control design for dynamic positioning of marine vessels with simulation and model-scale tests

For practical and complex offshore operations, preventing violations of system constraints can ensure safety and avoid potential marine accidents in harsh environments. This paper addresses a finite-time constrained control for dynamic positioning (DP) of vessels in the presence of inherent uncertainties, ocean disturbances, full-state and input constraints. For operational safety assurance, the core logic of the proposed constrained control strategy is to constrain the state variables including position output, velocity state, input control command within the designed safe region by employing barrier function and auxiliary system, respectively. To attenuate the adverse effects of unknown disturbances on safety and stability, an adaptive neural disturbance observer (ANDO) is constructed to compensate for lumped disturbances caused by inherent uncertainties, unmodeled dynamics, and sea loads. Then, the composite finite-time anti-disturbance constrained control strategy is formally proposed, which can guarantee semi-global practical finite-time stable (SGPFS) of the closed-loop systems. In offshore engineering, control schemes are not only theoretically feasible, but also need to be accurately verified to provide practical guidance value. For this purpose, the simulation and model-scale test are carried out to realistically reproduce the time-domain motion response of the vessels under ocean disturbances. The verification results further elucidate the applicability and feasibility of the proposed control design in practical offshore engineering.

Finite-Time Fuzzy Adaptive PPC for Nonstrict-Feedback Nonlinear MIMO Systems.

This article addresses the issue of the fuzzy adaptive prescribed performance control (PPC) design for nonstrict feedback multiple input multiple output (MIMO) nonlinear systems in finite time. Unknown nonlinear functions are handled via fuzzy-logic systems (FLSs). By combining the adaptive backstepping control algorithm and the nonlinear filters, a novel dynamic surface control (DSC) method is proposed, which can not only avoid the computational complexity issue but also improve the control performance in contrast to the traditional DSC control methods. Furthermore, to make the tracking errors have the prescribed performance in finite time, a new Lyapunov function is constructed by considering the transform error constraint. Based on the designed Lyapunov functions, it is proved that all the signals of the controlled systems are semiglobal practical finite-time stability (SGPFS). Finally, a simulation example is provided to illustrate the feasibility and validity of the put forward control scheme.

Adaptive Fuzzy Finite-Time Fault-Tolerant Consensus Tracking Control for High-Order Multiagent Systems With Directed Graphs.

This article investigates the distributed adaptive fuzzy finite-time fault-tolerant consensus tracking control for a class of unknown nonlinear high-order multiagent systems (MASs) with actuator faults and high powers (ratio of positive odd rational numbers). The fault models include both loss of effectiveness and bias fault. Compared with existing similar results, the MASs considered here are more general and complex, which include the special case when the powers are equal to 1. Besides, the functions in this article are completely unknown and do not need to satisfy any growth conditions. In the backstepping framework, an adaptive fuzzy fault-tolerant consensus tracking controller is designed via adding one power integrator technique and directed graph theory so that the controlled systems are semiglobal practical finite-time stability (SGPFTS). Finally, numerical simulation results further verify the effectiveness of the developed control scheme.

Finite-time event-triggered containment control of multiple Euler–Lagrange systems with unknown control coefficients

This paper researches the finite-time event-triggered containment control problem of multiple Euler–Lagrange systems (ELSs) with unknown control coefficients. To realize an accurate convergence time, the settling-time performance function is employed to ensures the steady-state and dynamic properties of the containment errors in the resulting system. Meanwhile, to handle unknown control coefficients, adaptive neural networks (ANNs) with an additional saturated term are designed, which removes the requirement of full rank control coefficients in traditional control methods. By establishing an event-triggered mechanism, a novel finite-time event-triggered containment control law is designed, which yields the semi-global practical finite-time stable (SGPFS) of the resulting closed-loop system without Zeno phenomenon according to the finite-time stability criterion. The effectiveness of the designed methodology is verified by simulation.

Prescribed Performance Fuzzy Adaptive Output Feedback Control for Nonlinear MIMO Systems in a Finite Time

This article studies the fuzzy adaptive output feedback control design problem for nonstrict feedback multi-input–multi-output nonlinear systems with full-states prescribed performance in finite time. Fuzzy logic systems are introduced to solve the problem of unknown nonlinear dynamics. And on this basis, a fuzzy-based state observer is designed to observe the unmeasurable state. Further, by combining the adaptive back-stepping control algorithm and the nonlinear filters, a novel dynamic surface control (DSC) method is proposed, which not only solves the computational complexity explosion problem inherent in the back-stepping control algorithm, but also improves the control performance, in contrast to the traditional DSC methods with linear filters. Besides, to further improve the tracking performance under the structure of full-states prescribed performance, a new Lyapunov function is designed considering the transform error constraint. Based on the Lyapunov theory, the stability of the closed-loop system is analyzed to ensure that all signals of the closed-loop system are semiglobal practical finite-time stability. Finally, to elaborate on the feasibility and effectiveness of the proposed control method, a simulation example is provided.

Observer-based finite-time adaptive fuzzy back-stepping control for MIMO coupled nonlinear systems.

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.

Reinforcement learning-based finite-time tracking control of an unknown unmanned surface vehicle with input constraints

In this paper, subject to completely unknown system dynamics and input constraints, a reinforcement learning-based finite-time trajectory tracking control (RLFTC) scheme is innovatively created for an unmanned surface vehicle (USV) by combining actor-critic reinforcement learning (RL) mechanism with finite-time control technique. Unlike previous RL-based tracking which requires infinite-time convergence thereby rather sensitive to complex unknowns, an actor-critic finite-time control structure is created by employing adaptive neural network identifiers to recursively update actor and critic, such that learning-based robustness can be sufficiently enhanced. Moreover, deduced from the Bellman error formulation, the proposed RLFTC is directly optimized in a finite-time manner. Theoretical analysis eventually shows that the proposed RLFTC scheme can ensure semi-global practical finite-time stability (SGPFS) for a closed-loop USV system and tracking errors converge to an arbitrarily small neighborhood of the origin in a finite time, subject to optimal cost. Both mathematical simulation and virtual-reality experiments demonstrate remarkable effectiveness and superiority of the proposed RLFTC scheme.

Neural adaptive fault-tolerant finite-time control for nonstrict feedback systems: An event-triggered mechanism

The problem of event-triggered neural adaptive fault-tolerant finite-time control is investigated for a class of nonstrict feedback nonlinear systems in the presence of nonaffine nonlinear faults. The event-triggered signal is designed by using a relative-threshold to reduce communication burden. The dynamic surface control method is used to relax the assumption of the reference signal and deal with the computational complexity issue. Based on the finite-time stability, a new neural adaptive backstepping design method is developed. The event-triggered neural adaptive fault-tolerant control law is developed for the closed-loop system so that not only the semi-global practical finite-time stability is ensured, but also the tracking performance with a small residual set is guaranteed. Finally, the effectiveness of the proposed control law is verified via simulation results.

Neural network controller design for fractional-order systems with input nonlinearities and asymmetric time-varying Pseudo-state constraints

Abstract This article considers the neural adaptive control issues of a category of non-integer-order non-square plants with actuator Nonlinearities and Asymmetric Time-Varying pseudo-State Constraints. First, the original non-square non-affine system with input nonlinearities is transformed into an equivalent affine-in-control square model by defining a set of auxiliary variables and by employing the mean-value theorem. Second, Neural networks and Nussbaum functions are exploited to obviate the requirement of a complete knowledge of the system dynamics and the control directions, respectively. Third, a novel adaptive dynamic surface control method based on Caputo fractional derivative definitions and fractional order filters is developed to overcome the “explosion of complexity” problem in the traditional backstepping design process and to determine the parameter update laws and control signals, concurrently. Then, Asymmetric Barrier Lyapunov Functions with error variables are adopted to ensure the uniform stability of the closed-loop system and to prevent the violation of the full pseudo-State constraints. The novelties and contributions of this article are: (1) through the introduction of new technical Lemmas and corollaries, existing control design and stability theories linked to integer-order square systems are developed and extended to non-square non-integer-order ones. (2) all signals, including variables and errors in the closed-loop system are semi-global practical finite-time stability whereas the the tracking errors are asymptotically driven to zero without transgression of the constraints. Finally, the effectiveness and potential of the proposed control approach are substantiated by two example simulations.

Adaptive Neural Network-Based Finite-Time Online Optimal Tracking Control of the Nonlinear System With Dead Zone.

Considering the uncertain nonstrict nonlinear system with dead-zone input, an adaptive neural network (NN)-based finite-time online optimal tracking control algorithm is proposed. By using the tracking errors and the Lipschitz linearized desired tracking function as the new state vector, an extended system is present. Then, a novel Hamilton-Jacobi-Bellman (HJB) function is defined to associate with the nonquadratic performance function. Further, the upper limit of integration is selected as the finite-time convergence time, in which the dead-zone input is considered. In addition, the Bellman error function can be obtained from the Hamiltonian function. Then, the adaptations of the critic and action NN are updated by using the gradient descent method on the Bellman error function. The semiglobal practical finite-time stability (SGPFS) is guaranteed, and the tracking errors convergence to a compact set by zero in a finite time.

Finite-Time Adaptive Fuzzy Decentralized Control for Nonstrict-Feedback Nonlinear Systems With Output-Constraint

This paper addresses the finite time adaptive fuzzy decentralized control problem for interconnected large scale nonlinear systems in nonstrict feedback forms with output-constraint. The fuzzy logic systems are used to approximate the unknown nonlinear functions and a state observer is constructed to estimate the immeasurable states. In order to deal with the output constraint problem, the barrier Lyapunov function is introduced. By combining backstepping recursion design with a command filter, a finite time fuzzy adaptive decentralized control method is presented. The stability analysis can be obtained based on the finite time Lyapunov stability theory, which demonstrates that the closed-loop system are semi-global practical finite-time stability, the system outputs can track the given reference signals and keep in the given constraint bounds in a finite time. Finally, two simulation examples are provided to elaborate the effectiveness of the presented control scheme.

Adaptive Neural Networks Finite-Time Optimal Control for a Class of Nonlinear Systems

This article addresses the finite-time optimal control problem for a class of nonlinear systems whose powers are positive odd rational numbers. First of all, a finite-time controller, which is capable of ensuring the semiglobal practical finite-time stability for the closed-loop systems, is developed using the adaptive neural networks (NNs) control method, adding one power integrator technique and backstepping scheme. Second, the corresponding design parameters are optimized, and the finite-time optimal control property is obtained by means of minimizing the well-defined and designed cost function. Finally, a numerical simulation example is given to further validate the feasibility and effectiveness of the proposed optimal control strategy.

Adaptive Fuzzy Finite-time Dynamic Surface Control for High-order Nonlinear System with Output Constraints

This paper studies the problem of finite-time fuzzy adaptive dynamic surface control (DSC) design for a class of single-input and single-output (SISO) high-order nonlinear systems with output constraint. Fuzzy logic systems (FLSs) are utilized to identify the unknown smooth functions. By adopting Barrier Lyapunov function (BLF), the problem of output constrain is handled. Combining adding a power integrator and adaptive backstepping recursion design technique, a novel fuzzy adaptive finite-time DSC algorithm is proposed. Based on finite-time Lyapunov stable theory, the developed control algorithm means that all the signals of the closed-loop system are semi-global practical finite-time stable (SGPFS) and the tracking error converges to a small neighborhood of origin in finite time. In addition, the output does not violate the given constrain bound. Finally, both numerical and practical simulation examples are given to illustrate the effectiveness of the proposed control algorithm.

Adaptive finite-time fuzzy control for nonlinear systems with input quantization and unknown time delays

We investigate the finite-time adaptive control issue for a class of nonlinear systems with quantized input signals and unknown time delays in this paper. In the control design process, the nonlinear terms are approximated by the fuzzy logic systems. A hysteretic quantizer is introduced to avoid chattering in the quantized signals, and the fuzzy state observer is constructed to estimate the unmeasurable states of the system. In order to propose the finite-time control strategy, firstly, a semi-global practical finite-time stability criterion is given. On this basis, a fuzzy adaptive controller is designed by combining the dynamic surface control technology with backstepping method. The controller can not only ensure that the observer and tracking error converge to a small neighborhood of the origin in a finite time, but also keep all the signals in the closed-loop system bounded. Finally, the effectiveness and feasibility of the control method are verified by two simulation examples.

Adaptive Fuzzy Finite-Time Tracking Control for Nonstrict Full States Constrained Nonlinear System With Coupled Dead-Zone Input.

This article proposes an adaptive finite-time tracking control based on fuzzy-logic systems (FLSs) for an uncertain nonstrict nonlinear multi-input-multi-output (MIMO) full-state-constrained system with the coupled uncertain dead-zone input. By using three kinds of FLSs: the uncertain system, the uncertain dead zone, and the uncertain input transfer inverse matrix are approximated using the system function FLS, dead-zone FLS, and input transfer inverse matrix FLS, respectively. After defining the barrier Lyapunov function, the fuzzy-based adaptive tracking controllers are designed, and the fuzzy weights are updated through the proposed adaptive laws. Then, based on the extended finite-time convergence theorem, with the design parameters chosen properly, the target uncertain nonlinear system is guaranteed to be semiglobal practical finite-time stable (SGPFS); and the full-state constraints are not violated while avoiding the effects of the dead zones. Furthermore, a simulation is presented to verify the validity of the proposed algorithm.

Finite-Time Backstepping of a Nonlinear System in Strict-Feedback Form: Proved by Bernoulli Inequality

In this paper, we propose a novel state-feedback backstepping control design approach for a single-input single-output (SISO) nonlinear system in strict-feedback form. Rational-exponent Lyapunov functions (ReLFs) are employed in the backstepping design, and the Bernoulli inequality is primarily adopted in the stability proof. Semiglobal practical finite-time stability, or global asymptotically stability, is guaranteed by a continuous control law using a commonly used recursive backstepping-like approach. Unlike the inductive design of typical finite-time backstepping controllers, the proposed method has the advantage of reduced design complexity. The virtual control laws are designed by directly canceling the nonlinear terms in the derivative of the specific Lyapunov functions. The terms with exponents are transformed into linear forms as their bases. The stability proof is simplified by applying several inequalities in the final proof, instead of in each step. Furthermore, the singularity problem no longer exists. The weakness of the concept of practical finite-time stability is discussed. The method can be applied to smoothly extend numerous design methodologies with asymptotic stability with a higher convergence rate near the equilibrium. Two numerical case studies are provided to present the performance of the proposed control.