Switched state feedback control for continuous-time uncertain systems

This paper is concerned to design a switched state feedback robust control for continuous-time systems subject to norm bounded uncertainty. As important features of the proposed design method, we mention that it can handle a general LFT structure for the uncertainty and it is based on stability conditions that can be numerically solved by means of LMIs and a line search. Moreover, the switching rule as well as the state feedback gains are determined from the minimization of a guaranteed cost function derived from a multi-objective criterion. The theoretical results are illustrated with an academic example.     

A class of state observers for bilinear systems

By exploiting the fact that the output of the bilinear system is one-time differentiable whatever the input is, a new method of designing a state observer for bilinear system is proposed. The use of information on the derivative of y gives rise to a simple design procedure by which a wider class of bilinear systems has a state observer.     

Nonlinear bounded-error state estimation of continuous-time systems

This paper presents a first study on the application of interval analysis and consistency techniques to state estimation of continuous-time systems described by nonlinear ordinary differential equations. The approach is presented in a bounded-error context and the resulting methodology is illustrated by an example.     

不确定系统的不确定项观测器设计

为了克服常规用不确定项的界估计来设计控制器带来的保守性和动态性能差的弊端,本文就连续的和离散的不确定系统,分别提出了不确定项的观测器设计方案.通过引入分布和离散加权平均的概念,对这两种观测器的观测误差精度进行了分析估算,从数学上证明了所得的观测值在加权平均意义下是无偏的.此外,通过适当选择观测器反馈增益,可以得到满意的误差估计精度.把该方法应用到一个控制系统中,仿真结果表明所提出的观测器能很好的估计不确定项和改进闭环系统动态性能.     

Parameter and state estimation for uncertain linear systems by multiple observers

A parameter and state estimation problem is considered for uncertain linear time-invariant systems. Under a certain condition, it is shown that the state of the system can be asymptotically described by a linear combination of state estimates generated by suitable multiple observers, where the weights of the linear combination are the parameters to be estimated. Using this property, a computation method is proposed for simultaneous estimation of the parameters and the state from the output data of the plant and multiple observers.     

Cascade high-gain observers for a class of nonlinear systems with large delayed measurements

This paper proposes a cascade high-gain observer for a class of triangular nonlinear systems with large and diverse time delays at states and output equation. Compared with some existing results in the literature, the main contribution is to consider the simultaneous and diverse delays in both states and output and further, to propose a cascade observer in dealing with arbitrarily large delayed measurements. By choosing a suitable Lyapunov-Krasovskii functional, the sufficient condition is presented that guarantees the exponential convergence of observation error to the origin. Simulation results on a numerical example and a practical case study involving inverted pendulum are finally given to illustrate the effectiveness of the proposed approach.     

Trajectory-based design of robust non-fragile controllers for a class of uncertain linear continuous-time systems

This paper deals with a design problem of robust non-fragile stabilizing controllers for a class of uncertain linear continuous-time systems. The proposed design approach of robust non-fragile controllers is based on computation of the trajectory for the uncertain linear system and differs from the existing methods based on quadratic stabilization via Lyapunov criterion. In this paper, we show that sufficient conditions for asymptotical stability of the linear system with uncertainties and controller gain variations, and a LMI-based design algorithm of a robust non-fragile controller. Furthermore, we extend the result to the design problem of decentralized robust non-fragile controllers for a class of uncertain large-scale interconnected systems. Finally, the effectiveness of the proposed design scheme of robust non-fragile controllers is shown through illustrative examples.     

Robust state estimation for a class of uncertain time-delay systems

This paper considers a robust state estimation problem for a class of uncertain time-delay systems. In this problem, the noise and uncertainty are modelled deterministically via an integral quadratic constraint. The robust state estimation problem involves constructing the set of all possible states at the current time consistent with given output measurements and the integral quadratic constraint. This set is found to be an ellipsoid which is constructed via a linear state estimator.     

Discretization of cascaded continuous-time controllers for state and input delayed systems

This paper presents a new interpolation method that utilizes a Newton backward interpolation formula for the discretization of a continuous-time system with state and input delays. Also, a new output feedback state-matching digital redesign method, which utilizes the Newton extrapolation formula and the Chebyshev quadrature formula, enables the discretization of a cascaded continuous-time controller or filter for the continuous-time systems with delayed input and states, without employing a discrete time observer. The proposed method provides an alternative methodology for indirect digital design of a continuous-time unity-output feedback delayed system and enables us to implement accurately and effectively an existing or pre-designed cascaded analogue controller or filter via a digital controller.     

Using hybrid automata for set-membership state estimation with uncertain nonlinear continuous-time systems

This paper deals with set-membership state estimation for continuous-time systems from discrete-time measurements, in the unknown but bounded error framework. The classical predictor–corrector approach to state estimation uses interval Taylor methods for solving the prediction phase, which are known to have poor performance in presence of large model or input uncertainty. In this paper, we show how to derive more efficient predictors by using a nonlinear hybridization method which builds hybrid automata to characterize the boundaries of reachable sets. The derived continuous–discrete set-membership predictor–corrector estimator is then tested with simulated data from a bioreactor. Our method is compared to classical continuous-time interval observers and is shown to have promising performance.     

Robust adaptive backstepping control for a class of uncertain nonlinear systems based on disturbance observers

In this paper, a novel robust adaptive control scheme for a class of uncertain nonlinear systems is proposed using disturbance observer and backstepping method.Firstly, a disturbance observer is developed using radial basis function(RBF) neural network.The parameter updated law of the RBF neural network is given for monitoring subsystem disturbance well.The robust adaptive control scheme is then presented with backstepping method based on the designed disturbance observer.Semiglobal uniform ultimate bounded...     

一类不确定切换系统的鲁棒状态反馈镇定

研究了一类扰动项不满足匹配条件的不确定切换系统的鲁棒镇定问题.在每个子系统均不能镇定的情况下,利用完备性条件和多李雅普诺夫函数方法,分别得到了不确定切换系统可镇定的充分条件.状态矩阵和控制输入矩阵同时带有时变、未知且有界的不确定性,基于凸组合技术和LMI方法,设计出鲁棒状态反馈控制器及相应的切换策略,使得闭环系统在其平衡点处是渐近稳定的.最后仿真结果表明所设计的控制器及切换策略的正确有效性.     

Output feedback stabilization of a class of uncertain internally delayed systems

This paper is concerned with the problem of output feedback stabilization of a class of uncertain internally (i.e. in the state) delayed systems, in which only the upper bounds of nonlinear uncertainties are given. The designs of both static and dynamic output feedback controllers are considered. Some sufficient conditions for the stabilization of closed-loop systems are proposed, based upon the use of Lyapunov's stability criteria     

Construction of interval observers for continuous-time systems with discrete measurements

We consider continuous-time systems with input, output and additive disturbances in the particular case where the measurements are only available at discrete instants and have disturbances. To solve a state estimation problem, we construct continuous–discrete interval observers that are asymptotically stable in the absence of disturbances. These interval observers are composed of two copies of the studied system and of a framer, accompanied with appropriate outputs which give, componentwise, upper and lower bounds for the solutions of the studied system.     

Design of interval observers for uncertain dynamical systems

Interval state observers provide an estimate on the set of admissible values of the state vector at each instant of time. Ideally, the size of the evaluated set is proportional to the model uncertainty, thus interval observers generate the state estimates with estimation error bounds, similarly to Kalman filters, but in the deterministic framework. Main tools and techniques for design of interval observers are reviewed in this tutorial for continuous-time, discrete-time and time-delayed systems.     

Nonlinear observers for a class of biological systems: applicationto validation of a phytoplanktonic growth model

The authors construct nonlinear observers in order to discuss the validity of biological models. They consider a class of systems including many classical models used in biological modeling. They formulate the nonlinear observers corresponding to these systems and prove the conditions necessary for their exponential convergence. They apply these observers on the well-known Droop model which describes the growth of a population of phytoplanktonic cells. The validity of this model is discussed based on the performance of the observers working on experimental data     

Nonlinear robust H-infinity filtering for a class of uncertain systems via convex optimization

A new approach for robust H-infinity filtering for a class of Lipschitz nonlinear systems with time-varying uncertainties both in the linear and nonlinear parts of the system is proposed in an LMI framework. The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multi-objective optimization. The resulting H-infinity filter guarantees asymptotic stability of the estimation error dynamics with exponential convergence and is robust against nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit bounds on the nonlinear uncertainty are derived based on norm-wise and element-wise robustness analysis.     

Design of a class of new nonlinear disturbance observers based on tracking differentiators for uncertain dynamic systems

The main contribution of this paper is to present a general design method of new nonlinear disturbance observer (NDO) based on tracking differentiator (TD) for uncertain dynamic system. The stability and convergence of the proposed NDO can be guaranteed by TD. This new NDO can be used to estimate many types of uncertain disturbances, and can overcome the disadvantages of existing NDOs that need the priori information concerning the upper and lower bounds of the disturbance and its ith derivative’s Lipschitz upper bound. It can be also applied in uncertain dynamic system for various purposes such as disturbance estimate and compensation, solving the problem of control input constraint, and reducing even eliminating chattering of control input. Simulation results are presented to show the effectiveness of the developed NDO.