Finite-time Performance Research Articles

Finite-Time Model-Free Adaptive Control for Discrete-Time Nonlinear Systems

This paper addresses the fast trajectory tracking problem for discrete-time nonlinear systems, and whereby a finite-time model-free adaptive control (FMFAC) approach is innovatively devised. Here, the nonlinear systems’ dynamics are completely unknown and the widespread disturbances are considered. The nonparametric dynamic linearization technique and the adaptive extended disturbance observer are firstly deployed to achieve real-time linearization of the discrete-time nonlinear system, and an efficient finite-time performance index function is thereafter devised, and thereby contributing to a novel FMFAC control scheme. Theoretical analysis indicates the finite-time model-free tracking control within a stable region can be guaranteed, and the boundedness of the control input signal can be ensured rigorously, even though under the effect of various disturbances. The key points of the proposed FMFAC approach are model-free and possessing the fast regulation ability, and the corresponding effectiveness and superiority are validated via simulation studies.

Input–Output Finite-Time Stability for Switched T–S Fuzzy Delayed Systems With a Time-Dependent Lyapunov–Krasovskii Functional Approach

This research concerns the finite-time performance analysis for switched Takagi-Sugeno (T-S) fuzzy (STSF) systems subject to time-varying delay. Since the existing relevant results for finite-time synthesis of general switched systems require the finite-time stability property of the individual subsystem, a more general situation that the STSF systems comprised fully of finite-time unstable delayed subsystems are considered in the investigation. For surmounting this situation, a novel time-dependent multiple Lyapunov-Krasovskii functional (TDMLF) approach is developed by integrating a ranged dwell time switching mechanism. Then, the corresponding (input-output) finite-time stability criteria with less conservativeness are simultaneously derived for the (perturbed) STSF delayed systems to be (input-output) finite-time stable over the concerned finite-time interval. Finally, two illustrative examples are provided to demonstrate the accuracy and superiority of the developed (input-output) finite-time analysis framework.

Adaptive prescribed finite-time asymptotic tracking control for switched systems with unknown initial conditions and full-state constraints

In this paper, an adaptive prescribed finite-time asymptotic tracking control problem is considered for the unknown nonlinear switched systems with unknown initial conditions and full-state constraints. A class of nonlinear mappings (NMs) and a new prescribed finite-time performance function (PFTPF) are introduced so that the control design is independent of initial conditions of the controlled states. Based on the neural network approximation approach, NMs, PFTPF and the Barbalat's lemma, an adaptive prescribed finite-time asymptotic tracking controller with full-state constraints is obtained. To avoid overlarge initial control input, the design method with zero initial control input is adopted, the definition of input tuning function (ITF) is expanded and its effectiveness is proved theoretically. As results, the full-state constraints and the boundedness of all the signals in the closed-loop system are guaranteed, and the tracking error of the system can converge to zero asymptotically. Finally, the effectiveness and superiority of the proposed scheme are verified by the simulation results.

Finite-time convergence rates of distributed local stochastic approximation

We consider a distributed learning framework, where there are a group of agents communicating with a centralized coordinator. The goal of the agents is to find the root of an operator composed of the local operators at the agents. Such a framework models many practical problems in different areas, including those in federated learning and reinforcement learning. For solving this problem, we study the popular distributed stochastic approximation. Over a series of time epoch, each agent runs a number of local stochastic approximation steps based on its own data, whose results are then aggregated at the centralized coordinator.Existing theoretical guarantees for the finite-time performance of local stochastic approximation are studied under the common assumption that the local data at each agent is sampled i.i.d. Such an assumption may not hold in many applications, where the data are temporally dependent, for example, they are sampled from some dynamical systems. In this paper, we study the setting where the data are generated from Markov random processes, which are often used to model the systems in stochastic control and reinforcement learning. Our main contribution is to characterize the finite-time performance of the local stochastic approximation under this setting. We provide explicit formulas for the rates of this method for both constant and time-varying step sizes when the local operators are strongly monotone. Our results show that these rates are within a logarithmic factor of the comparable bounds under independent data. We also provide a number of numerical simulations to illustrate our theoretical results by applying local SA in solving problems in robust identification and reinforcement learning over multi-agent systems.

Improved finite-time prescribed performance based adaptive neural control for nonlinear systems with sensor faults

In this article, based on a novel finite-time prescribed performance function, we consider the issue of the adaptive neural fault-tolerant tracking control problem for a type of nonlinear system with sensor faults. The control performance of the system may be affected when sensor faults occur. For the controlled system with sensor faults, an improved finite-time performance function is proposed so that its initial conditions do not need to be set in advance. Compared with existing performance functions, the performance functions in this paper can ensure that the system is always controllable, even if the sensor faults occur suddenly during the steady operation. Moreover, Radial basis function (RBF) neural networks (NNs) are employed to estimate the uncertain smooth nonlinear functions. With the help of the adaptive backstepping control technique, an improved adaptive prescribed performance control technique is developed, which can realize the boundedness of every signal in the closed-loop system, and the tracking error can be limited within the neighborhood near the origin. Simulation results demonstrate the effectiveness of the proposed control scheme.

Adaptive finite-time fault-tolerant control for Robot trajectory tracking systems under a novel smooth event-triggered mechanism

The problem of adaptive finite-time fault-tolerant control with smooth event-triggered mechanism is addressed for quadrotor trajectory tracking systems. In light of recent studies on fault-tolerant control in the field of nonlinear systems, this article focuses on quadrotor trajectory tracking systems with actuator faults and disturbances. Different from the previous works, an ingenious smooth event-triggered mechanism is proposed to circumvent the discontinuous triggered signal and alleviate the communication burden simultaneously, which is of great significance to increase the operation life of the quadrotor. Subsequently, the finite-time performance function is designed to guarantee the prescribed tracking performance. Furthermore, a novel finite-time convergent adaptive fault-tolerant controller is proposed via the time-varying barrier Lyapunov function technique. The radial basis function neural networks are utilized to deal with the nonlinear approximation, and the adaptive laws are developed to accurately estimate the unknown model uncertainty, thus effectively handling the challenge of the controller design caused by the actuator faults and disturbances. Under the developed adaptive fault-tolerant controller, all the closed-loop system signals are bounded and the tracking errors are convergent within finite time. Meanwhile, the Zone behavior can be excluded by the positive sampling intervals. Finally, two examples are employed to verify the effectiveness and advantages of the suggested control scheme.

Nonlinear Two-Time-Scale Stochastic Approximation: Convergence and Finite-Time Performance

Two-time-scale stochastic approximation, a generalized version of the popular stochastic approximation, has found broad applications in many areas including stochastic control, optimization, and machine learning. Despite its popularity, theoretical guarantees of this method, especially its finite-time performance, are mostly achieved for the linear case while the results for the nonlinear counterpart are very sparse. Motivated by the classic control theory for singularly perturbed systems, we study in this paper the asymptotic convergence and finite-time analysis of the nonlinear two-time-scale stochastic approximation. Under some fairly standard assumptions, we provide a formula that explicitly characterizes the rate of convergence of the main iterates to the desired solutions. In particular, we show that the mean square error generated by the method convergences to zero at a rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(1/k^{2/3})$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> is the number of iterations. The key idea in our analysis is to properly choose the two step sizes to characterize the coupling between the fast and slow-time-scale iterates.

Finite-time ADRC formation control for uncertain nonaffine nonlinear multi-agent systems with prescribed performance and input saturation

AbstractThis paper explores finite-time formation control of multi-agent systems (MASs) with high-order nonaffine nonlinear dynamics and saturated input. Based on active disturbance rejection control theory, extended state observer is employed to identify unknown nonaffine nonlinear functions in MASs. The proposed control law consisting of backstepping control, tracking differentiator, and finite-time performance function is adopted for MASs to achieve the desired formation while reaching performance requirements. An auxiliary dynamic compensator is introduced to correct the control deviation caused by input saturation. Lyapunov stability theory is utilized to analyze the stability of the closed-loop system, which guarantees that the formation tracking error can asymptotically converge to an arbitrarily small neighborhood around zero in finite time. Finally, the simulation results show that compared to the adaptive, cooperative learning, and virtual structure methods, the proposed control algorithm has stronger tracking ability and faster setting time (1.8 s) under the influence of nonaffine nonlinear uncertainties. The integral square error for the formation control strategy in this paper is 0.16, which is much smaller than the abovementioned methods and is therefore provided to manifest the validity and feasibility of the proposed control strategy.

Reduced-Order Observer-Based Preassigned Finite-Time Control of Nonlinear Systems and Its Applications

In this article, a preassigned finite time control problem of nonlinear systems in strict-feedback form is investigated. From the perspective of arbitrary settling time, an appropriate preassigned finite-time performance function (PFPF) is constructed, and the preassigned finite-time stability (PAFS) is established, where the settling (convergence) time is not only completely unconcerned with initial conditions and design parameters but also more flexible. Furthermore, the backstepping technique and reduced-order observer are used to obtain the preassigned finite-time control scheme. The stability criteria of PAFS are developed to guarantee that the output can quickly converge to an arbitrarily small zone in preassigned time, and all signals of the closed-loop control system are PAFS. In the end, simulation examples verify the effectiveness of the presented method.

Distributed adaptive cooperative control via command filters for multi-agent systems including input unmodeled dynamics and sensor faults

This study focuses on the topic of distributed adaptive cooperative tracking control (CTC) for non-strict feedback multi-agent systems (MASs) including input unmodeled dynamics, prescribed performance, sensor faults and unknown control directions. An adaptive neural CTC tactic is raised via command filtered backstepping technique. With the help of the property of Gaussian function, the barriers produced by the non-strict feedback terms and partial sensor faults are handled. Moreover, the prescribed performance on measured synchronization error is considered by designing a finite-time performance function. By introducing normalization signals and adjusting parameters, the problems caused by input unmodeled dynamics are resolved. The compensation signals and normalization signals are integrated into the whole Lyapunov function in the stability analysis. All the variables in the controlled system are turned out to be semi-globally uniformly ultimately bounded (SGUUB). Meanwhile, the synchronization errors never exceed to predefined boundary. A simulation example is employed to confirm the viability of the constructed control method.

Finite‐time optimal tracking control for a class of nonlinear systems with prescribed performance

AbstractIn this paper, a finite‐time optimal tracking control scheme based on integral reinforcement learning is developed for partially unknown nonlinear systems. In order to realize the prescribed performance, the original system is transformed into an equivalent unconstrained system so as to a composite system is constructed. Subsequently, a modified nonlinear quadratic performance function containing the auxiliary tracking error is designed. Furthermore, the technique of experience replay is used to update the critic neural network, which eliminates the persistent of excitation condition in traditional optimal methods. By combining the prescribed performance control with the finite‐time optimization control technique, the tracking error is driven to a desired performance in finite time. Consequently, it has been shown that all signals in the partially unknown nonlinear system are semiglobally practical finite‐time stable by stability analysis. Finally, the provided comparative simulation results verify the effectiveness of the developed control scheme.

Cooperative learning formation control of multiple autonomous underwater vehicles with prescribed performance based on position estimation

This paper proposes a cooperative learning formation control method with finite-time prescribed performance based on position estimation for parametric path tracking of multiple autonomous underwater vehicles (AUVs) with uncertainties and external disturbances. The parametric path used in the control law permits the velocity to be specified independently while tracking the path accurately. The localized radial basis function neural networks learn the uncertainties cooperatively while tracking the period path, and the knowledge gained from learning is utilized to construct an empirically based formation control law using experience to cope with similar uncertainties rather than repeatedly using adaptive methods, which reduces the computing burden. The position of the leader is assumed to be available only for the leader's neighboring AUV, and a novel finite-time distributed observer is presented for the followers to estimate the leader's position. Based on this, the control law is derived from the prescribed performance control method using a finite-time performance function rather than exponential decaying function to enable the tracking error converges in finite time, which accelerates the learning process. The simulation results confirm the validity of the presented control protocol.

Robust Terminal Recurrent Neural Network for Finding Exact Solution of the TVQP Problem With Various Noises

Zeroing neural network (ZNN) with different activation functions (AFs) for finding zero-result of time-varying quadratic programming (TVQP) with no noises are revisited. To improve the convergent speed of the ZNN and resist various noises occurred in the real application, two robust terminal recurrent neural network (RTRNN) models by adding two different activation functions (AFs) are presented for the exact solution of the TVQP problem facing various noises. The appearing advantage of the pre-specified time of the RTRNN model is independent of the initial status of a generated system and the convergent time can be accelerated in advance, which is much superior than the finite time performance with regard to the initial status. In addition, the pre-specified convergent time of the RTRNN is mathematically discussed in detail under external noises. Simulated comparisons between the proposed RTRNN and the state-of-the-art neural networks substantiate the predefined time performance and strong robustness.

Finite-time prescribed performance trajectory tracking control for the autonomous underwater helicopter

To address the complex trajectory tracking problem of AUH near the seabed when performing high-precision operations such as comprehensive underwater inspections for offshore engineering structures, a prescribed performance control strategy with a finite-time performance function (FTPF) and the fast terminal sliding surface is proposed. The influence of ocean current is fully considered by the combination of ocean current velocity estimated by a current observer and ocean current disturbance in the dynamic model. An arctan-type disturbance observer and neural network are designed to compensate for environmental disturbances, model uncertainty, and thruster failure effects on the system. The system stability is proven by the Lyapunov method, and the numerical simulation shows that the proposed scheme is effective, robust, and efficient, even under disturbances and thruster failure.

Fuzzy-Based Robust Precision Consensus Tracking for Uncertain Networked Systems With Cooperative–Antagonistic Interactions

In bipartite consensus tracking (BCT) tasks for nonlinear multiagent systems, stochastic disturbances and actuator faults are regarded as essential factors that hamper effective controller formulation and tracking precision improvement. To address these difficulties, we design an improved finite-time performance function (FTPF) for a fuzzy fault-tolerant distributed cooperative control scheme to achieve finite-time robust precision BCT tasks for nonlinear multiagent systems. The parameter selection range of the improved FTPF is relaxed, which renders systems to achieve better transient performance. Benefitting from stochastic Lyapunov stability theory, it is shown that all signals of systems are semi-global uniformly ultimately bounded in probability, and bipartite consensus errors can satisfy the arbitrary precision with probability in the predefined time. Finally, to verify its effectiveness, the proposed control scheme is applied to BCT tasks of a group of vehicles, which manifests anticipated control performance under various uncertainties.

Self-triggered finite-time control for discrete-time Markov jump systems

This paper proposes a resources-aware pattern of finite-time controller design for discrete-time Markov jump systems (DTMJSs) Firstly, the performance evaluation of DTMJSs during a given interval is performed using a self-triggered mechanism that decides the subsequent execution only on the basis of historical data. Also, an adaptive self-triggered mechanism with customizable thresholds is proposed for more communication resource conservation. To examine the impact of the association between mode transitions and triggering signals on finite-time performance, two instances are explored regardless of whether it activated within the working period. Additionally, a co-design framework that calculates the adaptive self-triggered parameters and the finite-time controller gains synchronously is developed, which increases the efficiency of the resource conservation as well as facilitates its adaption.

A prescribed-performance-based adaptive finite-time tracking control scheme circumventing the dependence on the system initial condition

This paper is concerned with the prescribed finite-time tracking control problem for a class of nonlinear systems with unknown initial condition, state time-varying delays and external disturbances. A new adaptive prescribed finite-time tracking control scheme bypassing system initial condition is proposed via the prescribed performance method. Several nonlinear mapping functions (NMFs) and a new prescribed finite-time performance function (PFTPF) combining finite-time control with prescribed performance control are constructed to obtain the scheme. In this paper, the assumptions on the time-delay terms are removed by means of the designed Lyapunov–Krasovskii functions. In addition, to avoid step impact effect arisen by an overlarge initial control input, a control input with zero initial value is obtained. Aiming at the design of zero initial control input, a new Lyapunov stability criterion form is put forward. Two practical examples are presented to confirm the effectiveness and superiority of the proposed scheme.

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.

Fixed-Time Fault-Tolerant Formation Control for a Cooperative Heterogeneous Multiagent System With Prescribed Performance

This article investigates the fixed-time fault-tolerant formation control problem of a leader–follower heterogeneous multiagent system (HMAS), including multiple unmanned aerial vehicles (UAVs) and multiple unmanned ground vehicles (UGVs) under loss of effectiveness actuator faults and disturbances. Different from the existing fixed-time formation results, to realize the special application, a finite-time performance function (FTPF) is considered, which can guarantee that formation error converges to a prescribed arbitrarily small region within a known time. Then, based on sliding mode control and bi-limit homogeneity, distributed and decentralized fixed-time formation control algorithms are constructed for the HMAS in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$y$ </tex-math></inline-formula> axis and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$ </tex-math></inline-formula> axis, respectively, which can steer the whole system achieving target formation configuration within a scheduled time. In addition, based on local state information, adaptive online updating strategies for unknown actuator efficiency factors and lumped uncertainties are proposed. Then, under the online updating parameters, two novel distributed and decentralized adaptive fault-tolerant formation control laws are presented using practical fixed-time stability theory, which not only achieves stable formation tracking with finite-time prescribed behavioral metrics but also ensures that the formation errors are uniformly bounded within a settling time. Finally, the effectiveness of the developed control schemes is verified by simulation examples.

Performance optimization on finite-time quantum Carnot engines and refrigerators based on spin-1/2 systems driven by a squeezed reservoir

We investigate the finite-time performance of a quantum endoreversible Carnot engine cycle and its inverse operation — Carnot refrigeration cycle, employing a spin-1/2 system as the working substance. The thermal machine is alternatively driven by a hot boson bath of inverse temperature β h and a cold boson bath at inverse temperature β c (>β h). While for the engine model the hot bath is constructed to be squeezed, in the refrigeration cycle the cold bath is established to be squeezed, with squeezing parameter r. We obtain the analytical expressions for both efficiency and power in heat engines and for coefficient of performance and cooling rate in refrigerators. We find that, in the high-temperature limit, the efficiency at maximum power is bounded by the analytical value , and the coefficient of performance at the maximum figure of merit is limited by , where η C = 1 – β h/β c and ε C = β h/(β c – β h) are the respective Carnot values of the engines and refrigerators. These analytical results are identical to those obtained from the Carnot engines based on harmonic systems, indicating that the efficiency at maximum power and coefficient at maximum figure of merit are independent of the working substance.