Delay-Dependent Robust Passive Control for Uncertain Discrete-Time Systems with Time Delays

This paper considers the problem of robust passive control for uncertain discrete systems with time-varying delays. We pay attention to designing a state feedback controller which guarantees the passivity of the closed-loop system for all admissible uncertainties. In terms of a linear matrix inequality, a sufficient condition for the solvability of this problem is presented and the explicit expression of the desired state feedback controller is given.

PASSIVE CONTROL FOR A CLASS OF UNCERTAIN TIME-DELAY SYSTEMS

This paper focuses on the passive control for a class of linear time delay system with norm bounded time varying parameter uncertainties by using a linear matrix inequality (LMI) approach. A sufficient condition under which the uncertain time delay system is quadratically stable and strictly passive for all admissible uncertainties was derived. It is shown that the solvability of problem of the robust passive controller design is implied by the feasibility of a linear matrix inequality.

Adaptive Robust Control for a Class of Uncertain MIMO Non-affine Nonlinear Systems

In this paper, the adaptive robust tracking control scheme is proposed for a class of multi-input and multi-output (MIMO) non-affine systems with uncertain structure and parameters, unknown control direction and unknown external disturbance based on backstepping technique. The MIMO non-affine system is first transformed into a time-varying system with strict feedback structure using the mean value theorem, and then the bounded time-varying parameters are estimated by adaptive algorithms with projection. To handle the possible 'controller singularity' problem caused by unknown control direction, a Nussbaum function is employed, and the dynamic surface control (DSC) method is applied to solve the problem of 'explosion of complexity' in backstepping control. It is proved that the proposed control scheme can guarantee that all signals of the closed-loop system are bounded through Lyapunov stability theorem and decoupled backstepping method. Simulation results are presented to illustrate the effectiveness of the proposed control scheme. © 2014 Chinese Association of Automation.

LMI-based robust control of uncertain discrete-time piecewise affine systems

The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties respectively.The basic idea of the proposed approaches is to construct piecewise-quadratic （PWQ） Lyapunov functions to guarantee the stability of the closed-loop systems.The partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid,then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities （LMIs）.Two examples are given to illustrate the proposed theoretical results.

Delay-dependent robust control for uncertain discrete singular systems with time-varying delay

The design problem of delay-dependent robust control for uncertain discrete singular systems with time-varying delay is addressed in this paper. The uncertainty is assumed to be norm-bounded. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent robust stability condition is derived and expressed in terms of linear matrix inequalities (LMIs). A suitable robust state feedback control law is presented, which guarantees that the resultant closed-loop system is regular, causal and stable for all admissible uncertainties. Numerical examples are given to demonstrate the applicability of the proposed method.

Adaptive Robust Control for A Class of Nonlinear Systems with Unknown Uncertainties

The problem of robust stabilization for nonlinear systems with partially known uncertainties is considered in this paper. The required information about uncertainties in the system is merely that the uncertainties are bounded, but the upper bounds are incompletely known. This paper can be viewed as an extension of the work in reference [1]. To compensate the uncertainties, an adaptive robust controller based on Lyapunov method is proposed and the design algorithm is also suggested. Compared with some previous controllers which can only ensure ultimate uniform boundedness of the systems, the controller given in the paper can make sure that the obtained closed-loop system is asymptotically stable in the large. Simulations show that the method presented is available and effective.

Switching Logic-based Adaptive Robust Control of Nonlinearly Parameterized Uncertain Systems

在这份报纸，切换基于逻辑的适应柔韧的控制为一个类被建议非线性地 parameterized 系统(NFS ) 。明确地，控制器主要由一项柔韧的类型条款组成探讨系统无常，和切换逻辑调节机制更新深奥控制获得。构造控制器完成全球一致地最终的固定(GUUB ) 系统错误的结果，和模拟结果被包括表明控制法律的有效性。

Robust passive control for discrete-time T-S fuzzy systems with delays

This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help of linear matrix inequality （LMI） method, robust passive controllers are designed so that the closed-loop system is robust stable and strictly passive. Furthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate. A numerical example illustrates the validity of the proposed method.

Multi-objective robust controller synthesis for discrete-time systems with convex polytopic uncertain domain

Multi-objective robust state-feedback controller synthesis problems for linear discrete-time uncertain systems are addressed. Based on parameter-dependent Lyapunov functions, the Gl2 and GH2 norm expressed in terms of LMI (Linear Matrix Inequality) characterizations are further generalized to cope with the robust analysis for convex polytopic uncertain system. Robust state-feedback controller synthesis conditions are also derived for this class of uncertain systems. Using the above results, multi-objective state-feedback controller synthesis procedures which involve the LMI optimization technique are developed and less conservative than the existing one. An illustrative example verified the validity of the approach.

Non-fragile observer-based passive control for descriptor systems with time-delay

This paper investigates the problem of non-fragile observer-based passive control for descriptor systems with time-delay. The perturbations in both the control gain and observer gain of the observer-based controller are considered. For the cases of the additive perturbations and multiplicative perturbations, sufficient conditions are given such that the closed-loop systems are admissible and passive with dissipation η. The observer-based controller gains could be obtained from the solutions of linear matrix inequalities （LMIs）. Moreover, the maximum dissipation of the system is provided. Simulation examples are given to show the effectiveness of the deign methods.

Adaptive Robust Control for a Lower Limbs Rehabilitation Robot Running Under Passive Training Mode

This paper focuses on the problem of the adaptive robust control of a lower limbs rehabilitation robot(LLRR) that is a nonlinear system running under passive training mode. In reality, uncertainties including modeling error, initial condition deviation, friction force and other unknown external disturbances always exist in a LLRR system. So, it is necessary to consider the uncertainties in the unilateral man-machine dynamical model of the LLRR we described. In the dynamical model, uncertainties are(possibly fast) time-varying and bounded. However, the bounds are unknown. Based on the dynamical model, we design an adaptive robust control with an adaptive law that is leakagetype based and on the framework of Udwadia-Kalaba theory to compensate for the uncertainties and to realize tracking control of the LLRR. Furthermore, the effectiveness of designed control is shown with numerical simulations.

Perturbation and robust controllability of singular distributed parameter control systems in Hilbert space

Perturbation and robust controllability of the singular distributed parameter control system are discussed via functional analysis and the theory of GE-semigroup in Hilbert space. The perturbation principle of GE-semigroup and the sufficient condition concerning the robust controllability of the singular distributed parameter control system are obtained, in which the controllability for singular distributed parameter control system is not destroyed, if we perturb the equation by small bounded linear operator.

DECENTRALIZED ROBUST CONTROL FOR UNCERTAIN FLEXIBLE SPACE STATION

A decentralized variable-structure robust control technique for uncertain large-scale systems is proposed and using the proposed technique. a decentralized robust control system for uncertain flexible space station is designed. The designed robust control system can guarantee the stability and safe operation of space station in a wide range of system parameters variations and highly intensive external disturbances. In addition. because decentralized adaptation laws for the upper bounds of system uncertainties are introduced, the control technique is particularly applicable to the uncertain flexible space station with complex structure whose bounds of system uncertainties can not be determined or vary with time.

Coordinated nonlinear robust control of TCSC and excitation for multi-machine systems

An advanced nonlinear robust control scheme is proposed for multi-machine power systems equipped with thyristor-controlled series compensation (TCSC). First, a decentralized nonlinear robust control approach based on the feedback linearization and H∞ theory is introduced to eliminate the nonlinearities and interconnections of the studied system, and to attenuate the exogenous disturbances that enter die system. Then, a system model is built up, which has considered all the generators’ and TCSC’s dynamics, and the effects of uncertainties such as disturbances. Next, a decentralized nonlinear robust coordinated control law is developed based on this model. Simulation results on a six-machine power system show that the transient stability of the power system is obviously improved and die power transfer capacity of long distance transmission lines is enhanced regardless of fault locations and system operation points. In addition, the control law has engineering practicality since all the variables in the expression of he control strategy can be measured locally.

Stabilization of nonlinear systems based on robust control Lyapunov function

This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization （robust practical stabilization） is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunnv function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.

Adaptive Robust Control of Multi-Machine Power Systems with Control Time Delay

The adaptive H_∞ control problem of multi-machine power system in the case of disturbances and uncertain parameters is discussed,based on a Hamiltonian model.Considered the effect of time delay during control and transmission,a Hamilton model with control time delay is established.Lyapunov-Krasovskii function is selected,and a controller which makes the system asymptotically stable is got.The controller not only achieves the stability control for nonlinear systems with time delay,but also has the ability to suppress the external disturbances and adaptive ability to system parameter perturbation.The simulation results show the effect of the controller.

Design of a Fixed-Order Robust Controller to Damp Inter-Area Oscillations in Power Systems

This paper presents the design of a robust fixed-order H∞ controller to damp out the inter-area oscillations and to enhance the stability of the power system. The proposed H∞ approach is based on shaping the open-loop transfer function in the Nyquist diagram through minimizing the quadratic error between the actual and the desired open loop transfer functions in the frequency domain under linear constraints that guarantee robustness and stability. The proposed approach is robust with respect to multi-model uncertainty closed-loop sensitivity functions in the Nyquist diagram through the constraints on their infinity norm. The H∞ constraints are linearized with the help of a desired open-loop transfer function. The controller is designed using the convex optimization techniques in which the difference between the open-loop transfer function and the desired one is minimized. The two-area four-machine test system is selected to evaluate the performance of the designed controller under different load conditions as well as different levels of wind penetrations.

Adaptive robust control of mobile satellite communication system with disturbance and model uncertainties

The tracking and stable control of a typical shipmounted mobile satellite communication system（MSCS） is studied.Unlike the former studies based on simplified single-axis models,a tri-axis nonlinear model including the kinematic and dynamic features of the MSCS is used as the control object.An adaptive robust controller with trajectory planning is designed to deal with large parametric uncertainties and uncertain nonlinearities of the system.A theoretic performance result is given and proved.The designed adaptive robust controller and other two traditional controllers are tested in the comparative simulations under three different situations.The simulation results show the tracking and stable validity of the proposed controller.