State observers for a class of multi-output nonlinear dynamic systems

This note considers the problem of observer design for a class of multi-output nonlinear systems. A new state observer design methodology for linear time-varying multi-output systems is presented. Furthermore, we show that the same methodology can be extended to a class of multi-output nonlinear systems. Some sufficient conditions for the existence of the proposed observer are obtained, which guarantee that the error of state estimation converges asymptotically to zero. An example is given to demonstrate the effectiveness of the proposed methodology.     

Robust state estimation and fault diagnosis for uncertain hybrid nonlinear systems

Robust state estimation and fault diagnosis are challenging problems in the research of hybrid systems. In this paper, a novel robust hybrid observer is proposed for a class of uncertain hybrid nonlinear systems with unknown mode transition functions, model uncertainties and unknown disturbances. The observer consists of a mode observer for discrete mode estimation and a continuous observer for continuous state estimation. It is shown that the mode can be identified correctly and the continuous state estimation error is exponentially uniformly bounded. Robustness to unknown transition functions, model uncertainties and disturbances can be guaranteed by disturbance decoupling and selecting proper thresholds. The transition detectability and mode identifiability conditions are rigorously analyzed. Based on the robust hybrid observer, a robust fault diagnosis scheme is presented for faults modeled as discrete modes with unknown transition functions, and the analytical properties are investigated. Simulations of a hybrid three-tank system demonstrate that the proposed approach is effective.     

Boundary output feedback stabilization for a class of coupled parabolic systems

In this paper, the boundary output feedback stabilization problem is addressed for a class of coupled nonlinear parabolic systems. An output feedback controller is presented by introducing a Luenberger‐type observer based on the measured outputs. To determine observer gains, a backstepping transform is introduced by choosing a suitable target system with nonlinearity. Furthermore, based on the state observer, a backstepping boundary control scheme is presented. With rigorous analysis, it is proved that the states of nonlinear closed‐loop system including state estimation and estimation error of plant system are locally exponentially stable in the L²norm. Finally, a numerical example is proposed to illustrate the effectiveness of the presented scheme.     

Iterative learning control for MIMO nonlinear systems with arbitrary relative degree and no states measurement

This article presents a state observer based iterative learning control to solve the trajectory tracking problem of a class of time‐varying Multi‐Input‐Multi‐Output nonlinear systems with arbitrary relative degree. For this purpose, an asymptotically stable observer is derived for the system under consideration. There after, this observer is integrated with the iterative learning controller by replacing the state in the control law with its estimation yielded by the state observer. Hence, the stability of the whole control (nonlinear system plus controller plus observer) is guaranteed. Simulation result on nonlinear system shows that the trajectory tracking error decreases through the iterations. © 2013 Wiley Periodicals, Inc. Complexity 19: 37–45, 2013     

Design of observers for nonlinear systems with H ∞ performance analysis

This paper investigates the problem of observer design for nonlinear systems. By using differential mean value theorem, which allows transforming a nonlinear error dynamics into a linear parameter varying system, and based on Lyapunov stability theory, an approach of observer design for a class of nonlinear systems with time‐delay is proposed. The sufficient conditions, which guarantee the estimation error to asymptotically converge to zero, are given. Furthermore, an adaptive observer design for a class of nonlinear system with unknown parameter is considered. A method of H _∞ adaptive observer design is presented for this class of nonlinear systems; the sufficient conditions that guarantee the convergence of estimation error and the computing method for observer gain matrix are given. Finally, an example is given to show the effectiveness of our proposed approaches. Copyright © 2013 John Wiley & Sons, Ltd.     

Output feedback control for MIMO nonlinear systems using factorization

A new output feedback adaptive control scheme for multi-input and multi-output (MIMO) nonlinear systems is presented based on the high frequency gain matrix factorization and the backstepping approach with vector form. The only required prior knowledge about the high frequency gain matrix of the linear part of the system is the signs of its leading principal minors. The proposed controller is a dynamic one that only needs the measurement of the system output, and the observer and the filters are introduced in order to construct a virtual estimate of the unmeasured system states. The global stability of the closed-loop systems is guaranteed through this control scheme, and the tracking error converges to zero. Finally, the numerical simulation results illustrate the effectiveness of the proposed scheme.     

Robust state estimation and fault diagnosis for uncertain hybrid systems

Robust state estimation and fault diagnosis are challenging problems in the research into hybrid systems. In this paper a novel robust hybrid observer is proposed for a class of hybrid systems with unknown inputs and faults. Model uncertainties, disturbances and faults are represented as structured unknown inputs. The robust hybrid observer consists of a mode observer for mode identification and a continuous observer for continuous state estimation and mode transition detection. It is shown that the mode can be identified correctly and the continuous state estimation error is exponentially uniformly bounded. Robustness to model uncertainties and disturbances can be guaranteed for the hybrid observer by disturbance decoupling. Furthermore, the detectability and mode identifiability conditions are rigorously analyzed. On the basis of the robust hybrid observer, a robust fault detection and isolation scheme is presented also in the paper. Simulations of a hybrid four-tank system show the proposed approach is effective.     

基于中间观测器的非线性系统的故障估计

针对带有时滞和多故障的非线性系统,研究了基于中间观测器的故障估计问题.设计了中间变量和中间估计器,实现了多故障的故障估计,同时避免了观测器匹配条件的限制.根据Lyapunov稳定理论和线性矩阵不等式（LMI）方法,误差系统是渐近稳定的.最后,通过MATLAB仿真,验证了所提出方法的有效性.     

State and parameter estimation for nonlinear systems

State and parameter estimators are obtained for systems described by nonlinear evolution equations. Linear infinite dimensional observability theory together with a variety of fixed point theorems can be employed to obtain a finite time observer. Moreover, a nonlinear asymptotic observer is produced using stability results. The problem of joint state and parameter estimation is converted to the state estimation case, via an augmented state, so that these observer results can be utilised. Examples and remarks on the generality of the results are given.     

Disturbance-observer-based fuzzy terminal sliding mode control for MIMO uncertain nonlinear systems

This study is concerned with the design of a disturbance-observer-based fuzzy terminal sliding mode controller (FTSMC) for multi-input multi-output (MIMO) uncertain nonlinear systems by considering unknown non-symmetric input saturation and control singularity. The disturbance observer is proposed for the unmeasured external disturbance and guarantees the convergence of the disturbance estimation error to zero in a finite time. The terminal sliding mode controller (TSMC) is designed for MIMO uncertain nonlinear systems by utilizing the output of the proposed disturbance observer. This control scheme combines the disturbance-observer-based TSMC with a fuzzy logic system in the presence of unknown non-symmetric input saturation and control singularity in order to reduce chattering phenomena. Finite time asymptotic stability, convergence of the disturbance observer, and convergence of the closed-loop system are proved via Lyapunov stability theorem. In addition, a five-rotor unmanned aerial vehicle (UAV) is employed in the numerical simulations to demonstrate the effectiveness and performance of the proposed control scheme. Disturbance observer estimates the payload and flight endurance of the five-rotor UAV. Genetic algorithm (GA) optimization is used to specify the parameters of the disturbance-observer-based TSMC (GATSMC) to decrease chattering. Finally, the superior performance of FTSMC is investigated over TSMC and GATSMC.     

Sliding mode high-gain observers for a class of uncertain nonlinear systems

A robust high-gain observer for state and unknown input estimations for a special class of single-output nonlinear systems is developed in this article. Ensuring the observability of the unknown input with respect to the output, the disturbance can be estimated from the sliding surface. In the sliding mode, the convergence of the estimation error dynamics is proven similar to the analysis of high-gain observers.     

Global Convergence of a Control System by Means of an Observer

In this paper, we propose some sufficient conditions for the global stabilization of a class of nonlinear dynamic systems by using an estimated state feedback law given by an observer design.     

基于输出反馈的一类大型互联非线性系统的鲁棒全局指数稳定

研究基于输出反馈的一类新的大型互联非线性不确定系统的鲁棒全局指数稳定问题,通过构造每个子系统收敛的状态观测器,并对观测器的状态作线性变换,得到鲁棒分散输出反馈控制器.当该反馈控制律作用于该系统时,闭环系统是全局指数稳定的.     

Robust observer design for nonlinear uncertain switched systems under asynchronous switching

Switching between the system and the associated observer or controller is in fact asynchronous in switched control systems. However, many times we assume it synchronous, for simplicity. In this paper, the robust observer design problems for a class of nonlinear uncertain switched systems for synchronous and asynchronous switching are addressed. At first, a robust observer under synchronous switching is proposed based on average dwell time approach. After that, the results are extended to robust observer design in the asynchronous case. In this case, two working modes are adopted to facilitate the studies on the issue. Finally, an extension case covering more practical applications is investigated under asynchronous switching. The designed observer cannot maintain the asymptotical stability of error state, but the eventual boundness is guaranteed. At the end, a numerical design example is given to illustrate our results.     

Adjustable dimension descriptor observer based fault estimation for switched nonlinear systems with partially unknown nonlinear dynamics

This paper focuses on the fault estimation problem for switched systems with partially unknown nonlinear dynamics, actuator and sensor faults, simultaneously. The fault estimation observers are constructed, in which the observer dimension is not fixed and can be selected in a certain range. Both the disturbance decoupling and disturbance attenuation are considered, where the unknown nonlinear dynamics can be decoupled and the effect of modeling error and measurement disturbance is attenuated. Based on the average dwell time and the piecewise Lyapunov function, the observer parameter matrices can be calculated by solving LMIs and matrix equations. Finally, two examples are listed to verify the proposed fault estimation approach.     

Numerical computation of singular control problems with application to optimal heating and cooling by solar energy

The method presented here is an extension of the multiple shooting algorithm in order to handle multipoint boundary-value problems and problems of optimal control in the special situation of singular controls or constraints on the state variables. This generalization allows a direct treatment of (nonlinear) conditions at switching points. As an example a model of optimal heating and cooling by solar energy is considered. The model is given in the form of an optimal control problem with three control functions appearing linearly and a first order constraint on the state variables. Numerical solutions of this problem by multiple shooting techniques are presented.     

Output feedback regulation control for a class of cascade nonlinear systems and its application to fan speed control

The output feedback regulation problem is considered for a class of nonlinear systems with integral input-to-state stable (iISS) inverse dynamics and unknown control direction. The system output together with the complete unmeasured state components appears in the system uncertainties. A systematic output feedback control scheme is presented with the help of a dynamic observer, whose gain comes from an off-line time-varying Riccati matrix differential equation. The proposed scheme can be applied to the analysis of the speed tracking control of a fan. The simulation results demonstrate the validity of the presented algorithm.     

A counterexample for the global separation principle for discrete-time nonlinear systems

In the control systems literature, it is well known that a separation principle holds locally for nonlinear control systems, when exponential feedback stabilizers and exponential observers are used. In this paper, we present a counterexample to show that the global separation principle need not hold for nonlinear control systems. Our example demonstrates that global stability might be lost when an exponential observer is introduced into the nonlinear feedback loop associated with an exponentially stabilizing feedback control law.     

Dynamically stable control of articulated crowds

The synthesis of realistic complex body movements in real-time is a difficult problem in computer graphics and in robotics. High realism requires the accurate modeling of the details of the trajectories for a large number of degrees of freedom. At the same time, real-time animation necessitates flexible systems that can adapt and react in an online fashion to changing external constraints. Such behaviors can be modeled with nonlinear dynamical systems in combination with appropriate learning methods. The resulting mathematical models have manageable mathematical complexity, allowing to study and design the dynamics of multi-agent systems. We introduce Contraction Theory as a tool to treat the stability properties of such highly nonlinear systems. For a number of scenarios we derive conditions that guarantee the global stability and minimal convergence rates for the formation of coordinated behaviors of crowds. In this way we suggest a new approach for the analysis and design of stable collective behaviors in crowd simulation.     

Nonlinear adaptive output feedback robust control of hydraulic actuators with largely unknown modeling uncertainties

In this paper, a nonlinear adaptive output feedback robust controller is proposed for motion control of hydraulic servo systems in the presence of largely unknown matched and mismatched modeling uncertainties. Different from the existing control technologies, the presented hydraulic closed-loop controller which can deal with strong matched and mismatched parametric uncertainties is synthesized via the backstepping technique. Specially, a nonlinear disturbance observer which can estimate the largely mismatched disturbance is integrated into the design of the linear extended state observer to obtain estimation of unmeasurable system states, uncertain parameters and strong disturbances simultaneously. In addition, the projection-type adaptive law is synthesized into the design of the resulting controller. More importantly, the global stability of the whole closed-loop system is strictly guaranteed by the Lyapunov analysis. Furthermore, the effectiveness and practicability of the presented control strategy have been demonstrated by comparative experiments under different working conditions.