This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.

The sector bound approach to quantized feedback control | NOVA. The University of Newcastle's Digital Repository

Fixed-time cooperative control is currently a hot research topic in multiagent systems since it can provide a guaranteed settling time, which does not depend on initial conditions. Compared with asymptotic cooperative control algorithms, fixed-time cooperative control algorithms can achieve better closed-loop performance and disturbance rejection properties. Different from finite-time control, fixed-time cooperative control produces the faster rate of convergence and provides an explicit estimation of the settling time independent of initial conditions, which is desirable for multiagent systems. This paper aims at presenting an overview of recent advances in fixed-time cooperative control of multiagent systems. Some fundamental concepts about finite- and fixed-time stability and stabilization are first recalled with insight understanding. Then, recent results in finite- and fixed-time cooperative control are reviewed in detail and categorized according to different agent dynamics. Finally, this paper raises several challenging issues that need to be addressed in the near future.

An Overview of Recent Advances in Fixed-Time Cooperative Control of Multiagent Systems

This paper addresses the finite-time tracking issue for nonlinear quantized systems with unmeasurable states. Compared with the existing researches, the finite-time quantized feedback control is considered for the first time. By proposing a new finite-time stability criterion and designing a state observer, a novel adaptive neural output-feedback control strategy is raised by backstepping technique. Under the presented control scheme, the finite-time quantized feedback control problem is coped with without limiting assumption for nonlinear functions.

Adaptive Neural Network Finite-Time Output Feedback Control of Quantized Nonlinear Systems

This paper investigates the finite-time adaptive fuzzy control problem for a class of multi-input and multi-output (MIMO) nonlinear nonstrict feedback systems. During the control design process, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions, and fuzzy state observer is constructed to estimate the unmeasured states. By combining adaptive backstepping with the dynamic surface control (DSC) technique, a finite-time fuzzy adaptive control scheme is presented to overcome the “explosion of complexity” problem. The stability of the close-loop systems can be proved based on the finite-time Lyapunov stability theory. The presented control scheme demonstrates that the closed-loop systems are semiglobal practical finite-time stability, and tracking errors converge to a small neighborhood of the origin in a finite time. Finally, two simulation examples are provided to show the effectiveness of the presented control method.

Finite-Time Adaptive Fuzzy Output Feedback Dynamic Surface Control for MIMO Nonstrict Feedback Systems

This paper addresses the finite-time tracking problem of nonlinear pure-feedback systems. Unlike the literature on traditional finite-time stabilization, in this paper the nonlinear system functions, including the bounding functions, are all totally unknown. Fuzzy logic systems are used to model those unknown functions. To present a finite-time control strategy, a criterion of semiglobal practical stability in finite time is first developed. Based on this criterion, a novel adaptive fuzzy control scheme is proposed by a backstepping technique. It is shown that the presented controller can guarantee that the tracking error converges to a small neighborhood of the origin in a finite time, and the other closed-loop signals remain bounded. Finally, two examples are used to test the effectiveness of proposed control strategy.

Finite-Time Adaptive Fuzzy Tracking Control Design for Nonlinear Systems

The master–slave control design problem is considered for the networked teleoperation system with friction and external disturbances. A new finite-time synchronization control method is proposed with the help of adaptive fuzzy approximation. We develop a new nonsingular fast terminal sliding mode (NFTSM) to provide faster convergence and higher precision than the linear hyperplane-sliding mode and the classic terminal-sliding mode (TSM). Then, the adaptive fuzzy-logic system is employed to approximate the system uncertainties, and the corresponding adaptive fuzzy NFTSM controller is designed. By constructing Lyapunov function, the stability and finite-time synchronization performance are proved with the new controller in the presence of system uncertainties and external disturbances. Compared with the traditional teleoperation design method, the new control scheme achieves better transient-state performance and steady-state performance. Finally, the simulations are performed and the comparisons are shown among the proposed method, the P+d method, the PD+d method, the DFF method, and the classic TSM FTSM. The simulation results further demonstrate the effectiveness of the proposed method.

Adaptive Fuzzy Finite-Time Coordination Control for Networked Nonlinear Bilateral Teleoperation System

Due to the cognitive limitations of the human operator and lack of complete information about the remote environment, the work performance of such teleoperation systems cannot be guaranteed in most cases. However, some practical tasks conducted by the teleoperation system require high performances, such as tele-surgery needs satisfactory high speed and more precision control results to guarantee patient’ health status. To obtain some satisfactory performances, the error constrained control is employed by applying the barrier Lyapunov function (BLF). With the constrained synchronization errors, some high performances, such as, high convergence speed, small overshoot, and an arbitrarily predefined small residual constrained synchronization error can be achieved simultaneously. Nevertheless, like many classical control schemes only the asymptotic/exponential convergence, i.e., the synchronization errors converge to zero as time goes infinity can be achieved with the error constrained control. It is clear that finite time convergence is more desirable. To obtain a finite-time synchronization performance, the terminal sliding mode (TSM)-based finite time control method is developed for teleoperation system with position error constrained in this paper. First, a new nonsingular fast terminal sliding mode (NFTSM) surface with new transformed synchronization errors is proposed. Second, adaptive neural network system is applied for dealing with the system uncertainties and the external disturbances. Third, the BLF is applied to prove the stability and the nonviolation of the synchronization errors constraints. Finally, some comparisons are conducted in simulation and experiment results are also presented to show the effectiveness of the proposed method.

Finite Time Control Design for Bilateral Teleoperation System With Position Synchronization Error Constrained

The output-feedback based controller design problem is investigated for the networked teleoperation system in this paper. A new control scheme is proposed to guarantee the global asymptotic stability of the bilateral teleoperation system with time-varying delays and bounded inputs. First, a new fast terminal sliding-mode velocity observer is proposed to estimate the unknown velocity signals for the teleoperation system. Then, by considering the unknown gravity term, an adaptive SP+Sd-type (saturated proportion plus saturated damping) controller is designed based on the estimated velocity. In the new controllers, the specific sigmoidal function is not used, and any one on a set of saturation functions can be applied. Furthermore, by choosing Lypunov–Krasovskii functional, we show that the master–slave teleoperation system is stable under specific linear matrix inequality conditions. With the given controller design parameters and the upper bound of the input, the allowable maximal transmission delay can be computed by using the proposed stability criteria. Finally, both simulations and experiments are performed to show the effectiveness of the proposed methods.

Output-Feedback Adaptive Control of Networked Teleoperation System With Time-Varying Delay and Bounded Inputs

In this study, the state feedback fixed-time control problem is addressed for a class of high-order strict-feedback non-linear systems (SFNSs) with mismatching system uncertainties. Based on the fixed-time control technique and uniform exact difference method, a new fixed-time tracking control algorithm via the backstepping method in conjunction with a novel second-order sliding mode super-twisting-like structure adaptive fixed-time disturbance observer is proposed. Compared with many existing finite-time control results in which the convergence time grows unboundedly when the system initial conditions grow, the fixed-time control provides faster convergence rate by using high-degree terms and the settling time function derived only with controller parameters, is allowed to be adjusted independently of the system initial conditions. Moreover, to avoid the computation explosion, the singularity problem and to relax the assumption on the mismatching system uncertainties, the dynamics surface control method is employed based on a novel non-linear non-smooth first-order filter. Then the semi-globally uniformly fixed-time convergent performance of the high-order SFNSs is achieved. Finally, theoretical results are supported by simulation and experimental results.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-cta.2016.1143

Fixed-time backstepping control design for high-order strict-feedback non-linear systems via terminal sliding mode

This paper addresses the stability and position synchronization problems for bilateral nonlinear teleoperation system with asymmetric constant time delays under input saturation. Compared with previous work, not only the steady-state performance but also the transient-state performance is considered. In the presence of system uncertainties and external disturbances, the corresponding adaptive neural network (ANN) based prescribed performance control (PPC) scheme is designed. Moreover, the time-dependent stability conditions are derived by applying the linear matrix inequality (LMI). Finally, in simulation comparisons with P+d (proportion plus differential) controller are conducted, simulation results are presented to demonstrate the effectiveness of the proposed PPC approach.

Yana Yang

Papers

Adaptive Fuzzy Finite-Time Coordination Control for Networked Nonlinear Bilateral Teleoperation System

Finite Time Control Design for Bilateral Teleoperation System With Position Synchronization Error Constrained

Output-Feedback Adaptive Control of Networked Teleoperation System With Time-Varying Delay and Bounded Inputs

Fixed-time backstepping control design for high-order strict-feedback non-linear systems via terminal sliding mode

Adaptive neural network based prescribed performance control for teleoperation system under input saturation