Uniformly ultimate boundedness for discontinuous systems with time-delay

The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed.Based on the Lyapunov-Krasovskii functional,the Lyapunov theorem for the globally strongly uniformly ultimate boundedness of retarded discontinuous systems is presented.Furthermore,the result is applied to a class of mechanical systems with a retarded discontinuous friction item.

Uniform Boundedness for Neutral Equations with Unbouned Delay

We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.

Robust adaptive control for interval time-delay systems

This paper focuses on the robust adaptive control problems for a class of interval time-delay systems and a class of large-scale interconnected systems. The nonlinear uncertainties of the systems under study are bounded by high- order polynomial functions with unknown gains. Firstly, the adaptive feedback controller which can guarantee the stability of the closed-loop system in the sense of uniform ultimate boundedness is proposed. Then the proposed adaptive idea is extended to robust stabilizing designing method for a class of large-scale interconnected systems. Here, another problem we address is to design a decentralized feedback adaptive controller such that the closed-loop system is stable in the sense of uniform ultimate boundedness for all admissible uncertainties and time-delay. Finally, an illustrative example is given to show the validity of the proposed approach.

Tracking Control of Uncertain Nonlinear Systems With Unknown Constant Input Delay

A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.

Adaptive fault-tolerant control of heavy lift launch vehicle via differential algebraic observer

A novel adaptive fault-tolerant control scheme in the differential algebraic framework was proposed for attitude control of a heavy lift launch vehicle （HLLV）. By using purely mathematical transformations, the decoupled input-output representations of HLLV were derived, rendering three decoupled second-order systems, i.e., pitch, yaw and roll channels. Based on a new type of numerical differentiator, a differential algebraic observer （DAO） was proposed for estimating the system states and the generalized disturbances, including various disturbances and additive fault torques. Driven by DAOs, three improved proportional-integral- differential （PID） controllers with disturbance compensation were designed for pitch, yaw and roll control. All signals in the closed-loop system were guaranteed to be ultimately uniformly bounded by utilization of Lyapunov＇s indirect method. The convincing numerical simulations indicate that the proposed control scheme is successful in achieving high performance in the presence of parametric perturbations, external disturbances, noisy corruptions, and actuator faults.

FLOATING QUANTIZATION EFFECTS ON MULTIRATE SAMPLED-DATA NONLINEAR CONTROL SYSTEMS

In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.

EXISTENCE OF THE UNIFORMLY ULTIMATE BOUNDED SOLUTIONS AND PERIODIC SOLUTIONS

In this paper, we study the existence of the uniformly ultimately bounded solutions and periodic solutions for a class of third order nonlinear control systemx …+F(r)x ¨+G(r)x ·+H(r)x=e(t).(1)Using analytic method of Liapunov Function, we established the sufficient conditions of the existence of the uniformly ultimately bounded solutions and periodic solutions of the system(1).

A New Robust Adaptive Neural Network Backstepping Control for Single Machine Infinite Power System With TCSC

For a single machine infinite power system with thyristor controlled series compensation(TCSC) device, which is affected by system model uncertainties, nonlinear time-delays and external unknown disturbances, we present a robust adaptive backstepping control scheme based on the radial basis function neural network(RBFNN). The RBFNN is introduced to approximate the complex nonlinear function involving uncertainties and external unknown disturbances, and meanwhile a new robust term is constructed to further estimate the system residual error,which removes the requirement of knowing the upper bound of the disturbances and uncertainty terms. The stability analysis of the power system is presented based on the Lyapunov function,which can guarantee the uniform ultimate boundedness(UUB) of all parameters and states of the whole closed-loop system. A comparison is made between the RBFNN-based robust adaptive control and the general backstepping control in the simulation part to verify the effectiveness of the proposed control scheme.

PERIODICITY IN FUNCTIONAL DIFFERENTIAL EQUATIONS

A criterion for the existence of T-periodic solutions of functional differential equations with finite delay is established, in which the uniform boundedness of solutions has been removed from the conditions. The obtained result is the counterpart of the one recently obtained for infinite delay equations, but the conditions in this work are simplified and much easier to verify. Also, the proof has been improved to be more clear and compact.

Characteristic model-based consensus of networked heterogeneous robotic manipulators with dynamic uncertainties

In this paper, we address the characteristic model-based discrete-time consensus problem of networked robotic manipulators with dynamic uncertainties. The research objective is to achieve joint-position consensus of multiple robotic agents interconnected on directed graphs containing a spanning tree. A novel characteristic model-based distributed adaptive control scenario is proposed with a state-relied projection estimation law and a characteristic model-based distributed controller. The performance analysis is also unfolded where the uniform ultimate boundedness(UUB) of consensus errors is derived by resorting to the discrete-time-domain stability analysis tool and the graph theory. Finally, numerical simulations illustrate the effectiveness of the proposed theoretical strategy.

Tracking control of the linear differential inclusion

The tracking control of linear differential inclusion is discussed. First, the definition of uniformly ultimate boundedness for linear differential inclusion is given. Then, a feedback law is constructed by using the convex hull Lyapunov function. The sufficient condition is given to guarantee the tracking error system uniformly ultimately bounded. Finally, a numerical example is simulated to illustrate the effectiveness of this control design.