An analytic approach for computing pi-coefficients of continuous-time systems

The pi-sharing theory for continuous-time systems is discussed in this paper. An analytic approach is proposed for computing pi-coefficients of LTI systems. For the two scalar pi-coefficients, feasible regions are characterized graphically on a plane, and for the other two matrix pi-coefficients, the corresponding values are obtained by solving a Riccati equation. The results are applied in an example to determine the stability of a feedback system containing both linear and nonlinear subsystems.     

Near-optimal state estimation for interconnected systems

A new algorithm is proposed for estimating the state of a nonlinear stochastic system when only noisy observations of the state are available. The state estimation problem is formulated as a modal-trajectory, maximum likelihood estimation problem. The resulting minimization problem is analogous to the nonlinear tracking problem in optimal control theory. By viewing the system as an interconnection of lower-dimension subsystems and applying the so-called ε-coupling technqiue, which originated in the study of sensitivity of control systems to parameter variations, a near-optimal state estimation algorithm is derived which has the properties that all computations can be performed in parallel at the subsystem level and only linear equations need be solved. The principal attraction of the method is that significant reductions in the computational requirements relative to other approximate algorithms can be achieved when the system is large-dimensional.     

Two‐stage auxiliary model gradient‐based iterative algorithm for the input nonlinear controlled autoregressive system with variable‐gain nonlinearity

This article focuses on the parameter estimation problem of the input nonlinear system where an input variable‐gain nonlinear block is followed by a linear controlled autoregressive subsystem. The variable‐gain nonlinearity is described analytical by using an appropriate switching function. According to the gradient search technique and the auxiliary model identification idea, an auxiliary model‐based stochastic gradient algorithm with a forgetting factor is presented. For the sake of improving the parameter estimation accuracy, an auxiliary model gradient‐based iterative algorithm is proposed by utilizing the iterative identification theory. To further optimize the performance of the algorithm, we decompose the identification model of the system into two submodels and derive a two‐stage auxiliary model gradient‐based iterative (2S‐AM‐GI) algorithm by using the hierarchical identification principle. The simulation results confirm the effectiveness of the proposed algorithms and show that the 2S‐AM‐GI algorithm has higher identification efficiency compared with the other two algorithms.     

Robust fault diagnosis scheme in a class of nonlinear system based on UIO and fuzzy residual

In this study, a novel robust fault diagnosis scheme is developed for a class of nonlinear systems when both fault and disturbance are considered. The proposed scheme includes both component and sensor fault with nonlinear system that transferred to nonlinear Takagi-Sugeno (T-S) model. It considers a larger category of nonlinear system when fuzzification is used for only nonlinear distribution matrices. In fact the proposed method covers nonlinear systems could not transform to linear T-S model. This paper studies the problem of robust fault diagnosis based on two fuzzy nonlinear observers, the first one is a fuzzy nonlinear unknown input observer (FNUIO) and the other is a fuzzy nonlinear Luenberger observer (FNLO). This approach decouples the faulty subsystem from the rest of the system through a series of transformations. Then, the objective is to design FNUIO to guarantee the asymptotic stability of the error dynamic using the Lyapunov method; meanwhile, FNLO is designed for faulty subsystem to generate fuzzy residual signal based on a quadratic Lyapunov function and some matrices inequality convexification techniques. FNUIO affects only the fault free subsystem and completely removes any unknown inputs such as disturbances when residual signal is generated by FNLO is affected by component or sensor fault. This novelty and using nonlinear system in T-S model make the proposed method extremely effective from last decade literature. Sufficient conditions are established in order to guarantee the convergence of the state estimation error. Thus, a residual generator is determined on the basis of LMI conditions such that the estimation error is completely sensitive to fault vector and insensitive to the unknown inputs. Finally, an numerical example is given to show the highly effectiveness of the proposed fault diagnosis scheme.     

A 3-level autonomous mobile robot navigation system designed by using reasoning/search approaches

This paper describes how soft computing methodologies such as fuzzy logic, genetic algorithms and the Dempster–Shafer theory of evidence can be applied in a mobile robot navigation system. The navigation system that is considered has three navigation subsystems. The lower-level subsystem deals with the control of linear and angular volocities using a multivariable PI controller described with a full matrix. The position control of the mobile robot is at a medium level and is nonlinear. The nonlinear control design is implemented by a backstepping algorithm whose parameters are adjusted by a genetic algorithm. We propose a new extension of the controller mentioned, in order to rapidly decrease the control torques needed to achieve the desired position and orientation of the mobile robot. The high-level subsystem uses fuzzy logic and the Dempster–Shafer evidence theory to design a fusion of sensor data, map building, and path planning tasks. The fuzzy/evidence navigation based on the building of a local map, represented as an occupancy grid, with the time update is proven to be suitable for real-time applications. The path planning algorithm is based on a modified potential field method. In this algorithm, the fuzzy rules for selecting the relevant obstacles for robot motion are introduced. Also, suitable steps are taken to pull the robot out of the local minima. Particular attention is paid to detection of the robot’s trapped state and its avoidance. One of the main issues in this paper is to reduce the complexity of planning algorithms and minimize the cost of the search. The performance of the proposed system is investigated using a dynamic model of a mobile robot. Simulation results show a good quality of position tracking capabilities and obstacle avoidance behavior of the mobile robot.     

&thetas;-adaptive neural networks: a new approach to parameterestimation

A novel use of neural networks for parameter estimation in nonlinear systems is proposed. The approximating ability of the neural network is used to identify the relation between system variables and parameters of a dynamic system. Two different algorithms, a block estimation method and a recursive estimation method, are proposed. The block estimation method consists of the training of a neural network to approximate the mapping between the system response and the system parameters which in turn is used to identify the parameters of the nonlinear system. In the second method, the neural network is used to determine a recursive algorithm to update the parameter estimate. Both methods are useful for parameter estimation in systems where either the structure of the nonlinearities present are unknown or when the parameters occur nonlinearly. Analytical conditions under which successful estimation can be carried but and several illustrative examples verifying the behavior of the algorithms through simulations are presented.     

Stability and least-squares estimation

It is shown that the algorithms for the stability test of linear discrete systems and the algorithm for least-squares estimation are closely related.     

On the stability and convergence of self-tuning control–virtual equivalent system approach

This article presents a unified understanding and judgement of the stability and convergence of a general self-tuning control (STC) system, which consists of arbitrary control strategy, arbitrary parameter estimation algorithm and a deterministic/stochastic linear time-invariant (LTI) plant. The necessary conditions required for the global stability and convergence of a general STC system are relaxed, i.e. the convergence of parameter estimates is removed for both deterministic and stochastic STC schemes. To reach this goal, ‘virtual equivalent system (VES)’ concept and methodology is adopted. With the help of VES, the original nonlinear dominant (nonlinear in structure) problem is converted to a linear dominant (linear in structure) problem. The results developed in this article show that STC systems are stable and convergent for the abundance of control strategies and parameter estimation algorithms, which will provide great flexibility in the applications of STC.     

Fuzzy linear pulse-transfer function-based sliding-mode control fornonlinear discrete-time systems

In this paper, a nonlinear discrete-time system in the presence of input disturbance and measurement noise is approximated by N subsystems described by the linear pulse-transfer functions. Although the input disturbance and the measurement noise are unknown, they are modeled as known pulse-transfer functions. The approximation error between the nonlinear discrete-time system and the fuzzy linear pulse-transfer function system is represented by the linear time-invariant dynamic system in every subsystem, whose degree can be larger than that of the corresponding subsystem. Besides the input disturbance and the measurement noise, uncertainties are caused by the approximation error of the fuzzy-model and the interconnected dynamics resulting from the other subsystems. Owing to the presence of input disturbance, measurement noise, or uncertainties, a disadvantageous response occurs. Based on Lyapunov redesign, the switching control in every subsystem is designed to reinforce the system performance. Due to the time-invariant feature for a constant reference input, the operating point can approach the sliding surface in the manner of finite-time steps. The stability of the overall system is verified by Lyapunov stability theory     

A stochastic analysis of robust estimation algorithms in H∞ with rational basis functions

In this paper, a two‐stage nonlinear identification algorithm parameterized in terms of rational basis functions with fixed basis poles is studied when disturbances are subject to mild stochastic assumptions. The two‐stage algorithm is the archetype for robust estimation algorithms in H_∞ and its first stage is linear‐in‐data. Conditions for the consistency of both the stages are derived. It is shown that the two‐stage algorithm enjoys a better stochastic as well as deterministic performance than those of the linear algorithms. Copyright © 2001 John Wiley & Sons, Ltd.     

Continuous-time Hammerstein system identification

A continuous-time Hammerstein system, i.e., a system consisting of a nonlinear memoryless subsystem followed by a linear dynamic one, is identified. The system is driven and disturbed by white random signals. The a priori information about both subsystems is nonparametric, which means that functional forms of both the nonlinear characteristic and the impulse response of the dynamic subsystem are unknown. An algorithm to estimate the nonlinearity is presented and its pointwise convergence to the true characteristic is shown. The impulse response of the dynamic part is recovered with a correlation method. The algorithms are computationally independent. Results of a simulation example are given     

LANDING AN UNMANNED AIR VEHICLE: VISION BASED MOTION ESTIMATION AND NONLINEAR CONTROL

In this paper, we use computer vision as a feedback sensor in a control loop for landing an unmanned air vehicle (UAV) on a landing pad. The vision problem we address here is then a special case of the classic ego-motion estimation problem since all feature points lie on a planar surface (the landing pad). We study together the discrete and differential versions of the ego-motion estimation, in order to obtain both position and velocity of the UAV relative to the landing pad. After briefly reviewing existing algorithm for the discrete case, we present, in a unified geometric framework, a new estimation scheme for solving the differential case. We further show how the obtained algorithms enable the vision sensor to be placed in the feedback loop as a state observer for landing control. These algorithms are linear, numerically robust, and computationally inexpensive hence suitable for real-time implementation. We present a thorough performance evaluation of the motion estimation algorithms under varying levels of image measurement noise, altitudes of the camera above the landing pad, and different camera motions relative to the landing pad. A landing controller is then designed for a full dynamic model of the UAV. Using geometric nonlinear control theory, the dynamics of the UAV are decoupled into an inner system and outer system. The proposed control scheme is then based on the differential flatness of the outer system. For the overall closed-loop system, conditions are provided under which exponential stability can be guaranteed. In the closed-loop system, the controller is tightly coupled with the vision based state estimation and the only auxiliary sensor are accelerometers for measuring acceleration of the UAV. Finally, we show through simulation results that the designed vision-in-the-loop controller generates stable landing maneuvers even for large levels of image measurement noise. Experiments on a real UAV will be presented in future work.     

Stability of large-scale systems with saturating actuators

This paper is concerned with the stability problem of a large-scale system made of J subsystems. Each subsystem contains a saturating actuator, a linear time-invariant plant, and a linear time-invariant controller. A sufficient stability condition is given for the large-scale system with saturating actuators and an algorithm for synthesizing the stabilizing controllers is proposed. The plant of each subsystem is not constrainted to be stable and/or minimum-phase.     

基于交互容积卡尔曼的随机切换系统故障诊断

针对一类随机切换非线性系统的故障检测和故障估计问题,提出了一种基于交互式多模型和容积卡尔曼滤波（IMM CKF）的系统状态估计算法。该算法利用容积卡尔曼滤波（CKF）在不同时刻对每个子系统进行状态估计,把不同子系统状态估计结果融合得到最终的状态估计,实现对系统真实状态的估计。针对一类随机切换非线性系统发生执行器故障,采用IMM CKF估计系统状态;然后分析了IMM CKF算法的稳定性;根据状态估计结果,构造残差信号,设计残差评价函数,检测故障发生。当检测到故障发生时,设计增广系统,对故障幅值进行估计。通过仿真实验验证提出算法的有效性,结果表明该算法可以较为准确地诊断系统故障。     

Linear stabilization of nonlinear cascade systems

In this paper we consider the cascade connection of a nonlinear system and a system of integrators. Under suitable conditions we prove that if the nonlinear subsystem is stabilizable by means of a linear feedback, then a linear stabilizer exists for the overall system as well. In particular, we point out the role of the classical notion ofk-asymptotic stability.This work has been partially supported by the Ministero dell'Università e delia Ricerca Scientifica e Tecnologica (Italy).     

On the first-order estimation of multipliers from Kuhn–Tucker systems

The minimization of a nonlinear function with linear and nonlinear constraints and simple bounds can be performed by minimizing an augmented Lagrangian function that includes only the nonlinear constraints subject to the linear constraints and simple bounds. It is then necessary to estimate the multipliers of the nonlinear constraints and variable reduction techniques can be used to carry out the successive minimizations. The viability of estimating the multipliers of the nonlinear constraints from the Kuhn–Tucker system is analyzed and an acceptability test on the residual of the estimation is put forward. The computational performance of the procedure is compared with that of the inexpensive Hestenes–Powell multiplier update.Scope and purposeIt is possible to minimize a nonlinear function with linear and nonlinear constraints and simple bounds through the successive minimization of an augmented Lagrangian function including only the nonlinear constraints subject to the linear constraints and simple bounds. This method is particularly interesting when the linear constraints are flow conservation equations, as there are efficient techniques for solving nonlinear network problems. Regarding the successive estimation of the multipliers of the nonlinear constraints there is some doubt as to whether using the Kuhn–Tucker system could improve upon the inexpensive Hestenes–Powell update, especially considering that the Kuhn–Tucker system with partial augmented Lagrangians may not always lead to an acceptable multiplier estimation. Clarifying the computational efficiency of the multiplier update when there are linear or nonlinear side constraints is also a necessary previous step regarding the comparison between partial augmented Lagrangian techniques and either primal partitioning techniques for linear side constraints or projected Lagrangian methods in the case of nonlinear side constraints.     

Practical fusion algorithms for rotation matrices: A comparative study

Many computer vision, sensor fusion, and robotic applications require the estimation of a 3 × 3 rotation matrix from a set of measured or computed 3 × 3 noisy rotation matrices. This article classifies solution methods into three categories: nonlinear least squares, linear optimal, and linear suboptimal algorithms. Their performance is compared through simulation studies. It is shown that the linear suboptimal algorithms proposed in this article have an accuracy comparable to that of the optimal algorithms and are about five times faster. Furthermore, a particular nonlinear optimization algorithm is presented that has computational complexity similar to that of the linear optimal procedures. © 1992 John Wiley & Sons, Inc.     

ON THE STABILITY OF LARGE-SCALE POWER SYSTEMS

Abstract

This paper deals with the problem of transient stability of large-scale power systems by visting decomposition-aggregation techniques. In this approach based on a priori criteria, the system is decomposed to N-subsystems, the first (N— 1) subsystems described by linear model and the Nthdescribed by nonlinear model. Then each linear subsystem is reduced by aggregation techniques to an equivalent machine. Using this approach the problem of transient stability of large power systems is investigated. An algorithm for calculating the critical switching time based on this technique is proposed. The validity of this method is examined by studying large power systems of 11 machines, and the results obtained using IBM 370/165 digital computer of L.A-A.S. are reported.     

Distributed moving horizon state estimation for nonlinear systems with bounded uncertainties

In this work, we propose a distributed moving horizon state estimation (DMHE) design for a class of nonlinear systems with bounded output measurement noise and process disturbances. Specifically, we consider a class of nonlinear systems that are composed of several subsystems and the subsystems interact with each other via their subsystem states. First, a distributed estimation algorithm is designed which specifies the information exchange protocol between the subsystems and the implementation strategy of the DMHE. Subsequently, a local moving horizon estimation (MHE) scheme is designed for each subsystem. In the design of each subsystem MHE, an auxiliary nonlinear deterministic observer that can asymptotically track the corresponding nominal subsystem state when the subsystem interactions are absent is taken advantage of. For each subsystem, the nonlinear deterministic observer together with an error correction term is used to calculate a confidence region for the subsystem state every sampling time. Within the confidence region, the subsystem MHE is allowed to optimize its estimate. The proposed DMHE scheme is proved to give bounded estimation errors. It is also possible to tune the convergence rate of the state estimate given by the DMHE to the actual system state. The performance of the proposed DMHE is illustrated via the application to a reactor-separator process example.     

基于神经网络非线性系统的广义预测

为了对复杂的非线性系统进行广义预测控制 ,避免较长的离线训练 ,采用受控自回归积分滑动平均模型来描述线性子系统 ,用神经网络来逼近非线性子系统 ,利用递推最小二乘法和 Davidon最小二乘法分别作为线性子系统和非线性子系统的在线学习算法 ,建立了一种适合于广义预测控制的非线性系统控制模型。仿真结果证明 ,该模型在非线性系统的广义预测中的有效性 ,在实时控制中具有极其广阔的应用前景。