Finite-time Performance Research Articles

Adaptive learning-based finite-time performance of nonlinear switched systems with quantization behaviors and unmodeled dynamics

This paper proposes a novel finite-time adaptive learning strategy for a class of nonlinear switched systems with quantization behaviors and unmodeled dynamics under unpredictable switchings. The neural network learning framework is introduced to manifest the characteristics of nonlinear systems to obtain better performances. The system nonlinearities include more complicated non-strict feedback structure and full-state dependent unmodeled dynamics. In virtue of the nonlinear decomposition technique and the finite-time criterion, an adaptive learning strategy is developed step by step. Under the proposed strategy, a common Lyapunov function for all the subsystems is constructed to guarantee that in finite time all the signals of the switched system converge to a small domain near the origin under arbitrary switchings. An illustrative example is finally given to verify the effectiveness of the proposed main results.

Direct Adaptive Preassigned Finite-Time Control With Time-Delay and Quantized Input Using Neural Network.

This paper investigates an adaptive finite-time control (FTC) problem for a class of strict-feedback nonlinear systems with both time-delays and quantized input from a new point of view. First, a new concept, called preassigned finite-time performance function (PFTF), is defined. Then, another novel notion, called practically preassigned finite-time stability (PPFTS), is introduced. With PFTF and PPFTS in hand, a novel sufficient condition of the FTC is given by using the neural network (NN) control and direct adaptive backstepping technique, which is different from the existing results. In addition, a modified barrier function is first introduced in this work. Moreover, this work is first to focus on the FTC for the situation that the time-delay and quantized input simultaneously exist in the nonlinear systems. Finally, simulation results are carried out to illustrate the effectiveness of the proposed scheme.

Finite-time reliable attitude tracking control design for nonlinear quadrotor model with actuator faults

This paper is focused on a finite-time reliable control design for nonlinear quadrotor attitude dynamic model against the actuator faults and external disturbances. By the utilization of an appropriate Lyapunov–Krasovskii functional, a finite-time performance analysis criterion is derived to obtain the robust reliable tracking control design for quadrotor dynamic model. Then, a fault-tolerant tracking control is designed such that the attitude of the quadrotor is reliable in the sense that it is finite-time bounded and satisfies the suggested mixed $$H_\infty $$ and passivity performance index under given constraints. Also, the finite-time fault-tolerant controller gain is derived by solving the obtained linear matrix inequalities based on the convex optimization technique. Finally, simulation results are provided to verify the effectiveness and robustness of the proposed control design law.

Adaptive neural practically finite-time congestion control for TCP/AQM network

Inspired by the prescribed performance control (PPC), a new performance function, called finite-time performance function (FTPF), is first defined in this paper, by which a novel finite-time control design process is introduced. This work is also the first to solve the finite-time control issue for a class of transmission control protocol/active queue management (TCP/AQM) networks. Meanwhile, with the aid of FTPF, PPC and neural networks, a new adaptive practically pre-assigned finite-time controller is designed, which guarantees that the queue length q(t) tracks the desired queue qref in finite-time and all the signals of the closed-loop system are semi-globally practical finite-time stable (SGPFS). Finally, simulation results are shown to illustrate the effectiveness of the proposed method.

A Novel Finite-Time Adaptive Fuzzy Tracking Control Scheme for Nonstrict Feedback Systems

This work investigates a finite-time adaptive fuzzy tracking control problem for a class of nonstrict feedback nonlinear systems from a new point of view. A new concept, named finite-time performance function (FTPF), is defined in this paper for the first time. Moreover, a finite-time adaptive state feedback fuzzy tracking controller is derived based on fuzzy approximation, backstepping technique and prescribed performance control (PPC), which guarantees that all the signals of the closed-loop system are bounded, the output tracking error converges to a prescribed arbitrarily small region within a finite-time interval, and maximum overshoot is not more than a predefined level. In addition, a controller design process is given which is less complex than the existing finite-time control design methods. Three simulation studies are provided to verify the feasibility and effectiveness of the theoretical finding in this study.

Review on Performance Optimization of Absorption Heat Pump Systems Based on Finite-Time Thermodynamics

Most of industrial processes use a lot of thermal energy by burning fossil fuel to produce steam or heat for the purpose. After the processes, heat is rejected to the surrounding as waste. The absorption heat pump is becoming more important because it can be powered by these industrial energy wastes and hence, it poses no danger to the environment. In this paper, a literature review of the theoretical finite-time thermodynamic-based performance optimization of absorption heat pump systems independent of the used mixtures is presented. The review describes and discusses the performance objective functions for the various absorption heat pump cycle models. It covers the endoreversible and irreversible three-heat-source cycle models, four-heat-source cycle models and absorption heat transformer cycles with respect to the following aspects: the heat transfer law models, the effect of heat resistance and other irreversible loss models on the performance. Findings from published works considering the heating load, the coefficient of performance, the total heat transfer area, the thermo-economic function, the ecological function, the exergy-based ecological function and the ecological coefficient of performance as objective functions have been summarized in a table. It appears that design parameters based on the maximum of the ecological coefficient of performance conditions represent a best compromise between the heating load and the loss rate of availability.

Adaptive fuzzy finite-time stability of uncertain nonlinear systems based on prescribed performance

The semi-globally practical finite-time stability (SGPFS) problem for a class of uncertain strict-feedback nonlinear systems is discussed in this paper. A novel performance function called finite-time performance function (FTPF) is first defined. Moreover, this paper is the first to solve an adaptive semi-globally practical finite-time control issue by combining with backstepping, prescribed performance control (PPC) and fuzzy logic systems. Furthermore, it is proven that the designed control law not only guarantees that all the states converge to a predefined zone in finite-time, but also all the signals of the closed-loop systems are SGPF-stable. Simulation examples are worked out to illustrate the superiority and feasibility of the proposed design method.

Prescribed Performance Finite-Time Tracking Control for Uncertain Nonlinear Systems

This work investigates the finite-time tracking control problem for a class of uncertain strict-feedback nonlinear systems from a new perspective. First, a novel concept called finite-time performance function (FTPF) is defined. Further, a new sufficient condition of finite-time stability is derived and the tracking error can converge to a predefined region within a finite-time interval. The design process of the proposed technique is simpler. Finally, four simulation examples are carried out to illustrate the effectiveness of presented method.

A Nonsmooth Composite Control Design Framework for Nonlinear Systems With Mismatched Disturbances: Algorithms and Experimental Tests

In this paper, a nonsmooth composite control design methodology is investigated to tackle the exact tracking control problem for a general class of nonlinear systems with mismatched disturbances. By first introducing a saturated homogeneous disturbance observer to realize a finite-time performance recovery, a simple composite controller is then made feasible by virtue of the nonrecursive synthesis approach. A new feature is that under a less ambitious control objective, namely, semiglobal stability, various nonlinearity growth constraints for nonsmooth design approaches are essentially relaxed. Rigourous proof is provided to demonstrate the theoretical justifications. In order to illustrate the practical nature of the proposed design framework, a practical control application to series elastic actuator is presented. Experimental comparison results with the PID and finite-time controllers show significant performance improvements.

Practical finite-time almost disturbance decoupling strategy for uncertain nonlinear systems

A new practical finite-time almost disturbance decoupling result is presented for a class of strict-feedback nonlinear systems with multiple disturbances. Meanwhile, a novel performance function called finite-time performance function is first defined. Further, a practical finite-time tracking controller is designed by means of prescribed performance control, almost disturbance decoupling and backstepping technique. The designed controller makes the output error converge to a predefined arbitrary small area within a finite-time interval. The proposed design method is simpler and is easier to be achieved. Finally, it can be found from simulation examples that the effectiveness and superiority of this work is illustrated well.

Adaptive neural networks finite-time tracking control for non-strict feedback systems via prescribed performance

This paper focuses on the semi-globally practical finite-time tracking control problem for a class of nonlinear systems with non-strict feedback structure. Inspired by prescribed performance control (PPC), a new performance function called finite-time performance function (FTPF) is defined for the first time. With the aid of neural networks and backstepping, an adaptive finite-time tracking controller is properly designed. Different from the existing finite-time results, the proposed method can guarantee that the tracking error converges to an arbitrarily small region at any settling time and all the signals in the closed-loop system are semi-globally practical finite-time stable (SGPF-stable). Two simulation examples are given to exhibit the effectiveness and superiority of the presented technique.

Finite time thermodynamic analysis of quantum Otto heat engine with squeezed thermal bath

We investigate the finite time performance of reciprocating quantum Otto heat engine coupled to squeezed hot reservoir. We emphasize the converged limit cycle where each stroke is performed in finite time. To fully exploit the quantum availability provided by the squeezed bath, an optimal frequency protocol in the work extraction stroke is explicitly proposed. The power output is optimized with respect to the hot and cold isochore times. Thermodynamic analysis shows that for a wide range of squeezing parameters, efficiency at maximum power exceeds the generalized Curzon–Ahlborn efficiency defined by the effective temperature of the squeezed bath.

Design, verification and robotic application of a novel recurrent neural network for computing dynamic Sylvester equation

To solve dynamic Sylvester equation in the presence of additive noises, a novel recurrent neural network (NRNN) with finite-time convergence and excellent robustness is proposed and analyzed in this paper. As compared with the design process of Zhang neural network (ZNN), the proposed NRNN is based on an ingenious integral design formula activated by nonlinear functions, which are able to expedite the convergence speed and suppress unknown additive noises during the solving process of dynamic Sylvester equation. In addition, the global stability, finite-time convergence and denoising property of the NRNN model are theoretically proved. The upper bound of the finite convergence time for the NRNN model is also estimated in theory. Simulative results further verify the efficiency of the NRNN model, as well as its superior robust and finite-time performance to the conventional ZNN model for dynamic Sylvester equation in front of additive noises. At last, the proposed design method for establishing the NRNN model is successfully applied to kinematical control of robotic manipulator in front of additive noises.

Chattering-free full-order recursive sliding mode control for finite-time attitude synchronization of rigid spacecraft

This paper investigates a quaternion-based finite-time cooperative attitude synchronization and tracking of multiple rigid spacecraft with a virtual leader subject to bounded external disturbances. Firstly, the communication network between followers is assumed to be an undirected graph and every follower can get a direct access to the virtual leader, by using two neighborhood attitude error signals, a novel chattering-free recursive full-order sliding mode control algorithm is proposed such that all follower spacecraft synchronize to the virtual leader in finite time. In the proposed algorithm, the sliding mode surface is constructed by two layers of sliding mode surfaces, which are called as the outer and the inner sliding mode surfaces. To achieve finite-time performance of sliding mode dynamics, the outer sliding mode surface is designed as a terminal sliding mode manifold, and the inner one is designed as a fast nonsingular terminal sliding mode manifold, respectively. Then, to reduce the heavy communication burden, a distributed recursive full-order sliding mode control law is designed by introducing a distributed finite-time sliding mode estimator such that only a subset of the group members has access to the virtual leader. Finally, a numerical example is illustrated to demonstrate the validity of the proposed results.

Finite-Time LPV Analysis of a Vision Based Landing System with Anti-Windup Augmentation

Abstract In contrast to standard ILS-based landing control systems, vision-based strategies rely on specific measures that introduce non-linearities into the control laws. Moreover, during the landing phase high gains are often used to improve performances at the expense of stability which is then degraded. This is not much an issue since both final approach and flare segments are short-time maneuvers. However, high gains induce saturations which in turn lead to performances degradation. For these reasons, vision-based landing systems design and tuning require a specific attention which generally involves a time-consuming trial-and-error process. The latter could certainly be fasten and improved with the help of adapted analysis tools providing a reliable estimate of the finite-time performance level of the aforementioned saturated nonlinear closed-loop system. As observed in Biannic and Burlion (2017), it can be rewritten as a saturated Linear Parameter Varying (LPV) system for which many tools exist or can be extended. In this contribution, original discrete-time extensions are then proposed to characterize finite-time performance indexes for a vision-based landing system including an anti-windup device.

MSO: a framework for bound-constrained black-box global optimization algorithms

This paper addresses a class of algorithms for solving bound-constrained black-box global optimization problems. These algorithms partition the objective function domain over multiple scales in search for the global optimum. For such algorithms, we provide a generic procedure and refer to as multi-scale optimization (MSO). Furthermore, we propose a theoretical methodology to study the convergence of MSO algorithms based on three basic assumptions: (a) local Holder continuity of the objective function f, (b) partitions boundedness, and (c) partitions sphericity. Moreover, the worst-case finite-time performance and convergence rate of several leading MSO algorithms, namely, Lipschitzian optimization methods, multi-level coordinate search, dividing rectangles, and optimistic optimization methods have been presented.

A novel approach for stability and transparency control of nonlinear bilateral teleoperation system with time delays

In this paper, a novel control approach is presented to improve the stability and transparency of the nonlinear bilateral teleoperation system with time delays, where a four-channel (4-CH) architecture using modified wave reflection reduction transformation is explored in order to guarantee the passivity of the communication channels in the nonlinear bilateral teleoperation system; a sliding-mode controller is proposed to compensate for the dynamic uncertainties and enhance the system synchronization performance in finite time. The system stability has been analyzed using Lyapunov functions. The proposed method is validated through experimental work based on a 3-DOF bilateral teleoperation platform in the presence of time delays. The experimental results clearly demonstrate that the proposed control algorithm has superiority on system transparency over other wave-based systems.

Linear matrix inequalities design approach for robust stabilization of uncertain nonlinear systems with perturbation based on optimally-tuned global sliding mode control

This paper presents a novel global sliding mode control technique for the stabilization of a class of uncertain and nonlinear dynamic systems with perturbation. Using the Lyapunov stability theory and linear matrix inequality, some sufficient conditions are deduced to guarantee the asymptotic stabilization of the system states and to modify the robustness of the system. To improve the robust performance, an innovative reaching control law is designed to guarantee a chattering-free finite time performance under the uncertainty and nonlinearities and is optimally tuned using a modified random search algorithm. Simulation results are provided to show the effectiveness of the suggested technique.

Efficiency at maximum power of a quantum heat engine based on two coupled oscillators.

We propose and theoretically investigate a system of two coupled harmonic oscillators as a heat engine. We show how these two coupled oscillators within undamped regime can be controlled to realize an Otto cycle that consists of two adiabatic and two isochoric processes. During the two isochores the harmonic system is embedded in two heat reservoirs at constant temperatures T(h) and T(c)(<T(h)), respectively, and it is tuned slowly along a protocol to realize an adiabatic process. To illustrate the performance in finite time of the quantum heat engine, we adopt the semigroup approach to model the thermal relaxation dynamics along the two isochoric processes, and we find the upper bound of efficiency at maximum power (EMP) η* to be a function of the Carnot efficiency η(C)(=1-T(c)/T(h)): η*≤η(+)≡η(C)(2)/[η(C)-(1-η(C))ln(1-η(C))], identical to those previously derived from ideal (noninteracting) microscopic, mesoscopic, and macroscopic systems.

Bandits with Budgets

We investigate multi-armed bandits with budgets, a natural model for ad-display optimization encountered in search engines. We provide asymptotic regret lower bounds satisfied by any algorithm, and propose algorithms which match those lower bounds. We consider different types of budgets: scenarios where the advertiser has a fixed budget over a time horizon, and scenarios where the amount of money that is available to spend is incremented in each time slot. Further, we consider two different pricing models, one in which an advertiser is charged for each time her ad is shown (i.e., for each impression) and one in which the advertiser is charged only if a user clicks on the ad. For all of these cases, we show that it is possible to achieve O(log(T)) regret. For both the cost-per-impression and cost-per-click models, with a fixed budget, we provide regret lower bounds that apply to any uniformly good algorithm. Further, we show that B-KL-UCB, a natural variant of KL-UCB, is asymptotically optimal for these cases. Numerical experiments (based on a real-world data set) further suggest that B-KL-UCB also has the same or better finite-time performance when compared to various previously proposed (UCB-like) algorithms, which is important when applying such algorithms to a real-world problem.