模式转换未知的一类混杂系统的状态估计

Since the state of hybrid systems is determined by interacting continuous and discrete dynamics, the state estimation of hybrid systems becomes a challenging problem. It is more complicated when the discrete mode transition information is not available, and the modes of hybrid systems are nonlinear stochastic dynamic systems. To address this problem, this paper proposes a novel hybrid strong tracking filter (HSTF) for state estimation of a class of hybrid nonlinear stochastic systems with unknown mode transition, the method for designing HSTF is presented. The HSTF can estimate the continuous state and discrete mode accurately with unknown mode transition information, and the estimation of hybrid states is robust against the initial state. Simulation results illustrate the effectiveness of the proposed approach.     

A Novel Fuzzy Approach for State Estimation of Nonlinear Hybrid Systems Using Particle Filtering Method

Reliable state estimation is challenging for nonlinear hybrid systems. Particle filtering has emerged as an appealing approach for online hybrid state estimation. Mode detection in nonlinear hybrid systems is, however, a troublesome issue for the conventional particle filter mainly due to sample impoverishment. The problem is also exacerbated when dynamics that govern healthy or faulty modes are close together. False mode detection consequently leads to erroneous continuous state estimation. This paper proposes a novel fuzzy‐based particle filter to reduce continuous state estimation errors due to failures in mode detection. It is fulfilled by considering a fuzzified contribution of each feasible mode in overall estimation. In addition, two new resampling strategies are presented to tackle the degeneracy problem. A set of simulation test studies are conducted to extract the characteristic features and evaluate the performance of the proposed algorithm compared to observation and transition‐based most likely modes tracking particle filter (OTPF) as one of the most meticulous proposed estimation algorithms. The simulation results demonstrate the superior efficiency of the algorithm in dealing with the considered potential estimation problems.     

Partially‐observable stochastic hybrid systems (poshss) state estimation and optimal control

This paper discusses the state estimation and optimal control problem of a class of partially‐observable stochastic hybrid systems (POSHS). The POSHS has interacting continuous and discrete dynamics with uncertainties. The continuous dynamics are given by a Markov‐jump linear system and the discrete dynamics are defined by a Markov chain whose transition probabilities are dependent on the continuous state via guard conditions. The only information available to the controller are noisy measurements of the continuous state. To solve the optimal control problem, a separable control scheme is applied: the controller estimates the continuous and discrete states of the POSHS using noisy measurements and computes the optimal control input from the state estimates. Since computing both optimal state estimates and optimal control inputs are intractable, this paper proposes computationally efficient algorithms to solve this problem numerically. The proposed hybrid estimation algorithm is able to handle state‐dependent Markov transitions and compute Gaussian‐ mixture distributions as the state estimates. With the computed state estimates, a reinforcement learning algorithm defined on a function space is proposed. This approach is based on Monte Carlo sampling and integration on a function space containing all the probability distributions of the hybrid state estimates. Finally, the proposed algorithm is tested via numerical simulations.     

Fault-tolerant control for a class of hybrid systems with uncontrollable switching

This article focuses on the fault-tolerant control (FTC) problem for a class of hybrid systems modelled by hybrid automata. An observer-based FTC framework is proposed for the hybrid system with uncontrollable state-dependent switching and without full continuous state measurements. Two kinds of faults are considered: continuous faults that affect each mode and discrete faults that affect the mode transition. Sufficient conditions are given such that the hybrid system can be stabilised in the sense of LaSalle invariance principle. Simulation results of example of CPU processing control show the efficiency of the proposed method.     

Moving horizon estimation for switching nonlinear systems

This paper is concerned with moving horizon estimation for a class of constrained switching nonlinear systems, where the system mode is regarded as an unknown discrete state to be estimated together with the continuous state. In this work, we establish the observability framework of switching nonlinear systems by proposing a series of concepts about observability and analyzing the properties of such concepts. By fully applying the observability properties, we prove the stability of the proposed moving horizon estimators. Simulation results are reported to verify the derived results.     

基于迁移系统分析的线性混成系统安全验证

混成自动机行为中既包含离散行为又包含连续行为,非常复杂。其安全性验证问题难以解决,即使是线性混成自动机,它的可达性问题也被证明是不可判定的。现有工具大都使用多面体计算来计算线性混成自动机的可达状态空间集,复杂度高,可处理问题规模非常有限。为了避免这类问题,实现了一种新的工具。该工具将线性混成自动机表达为等价的迁移系统,并利用迁移系统上不变式生成相关工作对混成自动机进行验证。实验数据表明,方法有效可行,工具具有良好的性能。     

State estimation for linear hybrid systems with periodic jumps and unknown inputs

In order to solve the state estimation problem for linear hybrid systems with periodic jumps and unknown inputs, some hybrid observers are proposed. The proposed observers admit a Luenberger‐like structure and the synthesis is given in terms of linear matrix inequalities (LMIs). Therefore, the proposed observer designs are completely constructive and provide some input‐to‐state stability properties with respect to unknown inputs. It is worth mentioning that the structure of the hybrid observers, as well as the structure of the LMIs, depends on some observability properties of the flow and jump dynamics, respectively. Then, in order to compensate the effect of the unknown inputs, a hybrid sliding‐mode observer is added to the Luenberger‐like observer structure, providing exponential convergence to zero of the state estimation error despite certain class of unknown inputs. The existence of the hybrid observers and the unknown input hybrid observer is guaranteed if and only if the hybrid system is observable and strongly observable, respectively. Some numerical examples illustrate the feasibility of the proposed estimation approach.     

Robust discrete‐time nonlinear sliding mode state estimation of uncertain nonlinear systems

In this paper, we propose a discrete‐time nonlinear sliding mode observer for state and unknown input estimations of a class of single‐input/single‐output nonlinear uncertain systems. The uncertainties are characterized by a state‐dependent vector and a scalar disturbance/unknown input. The discrete‐time model is derived through Taylor series expansion together with nonlinear state transformation. A design methodology that combines the discrete‐time sliding mode (DSM) and a nonlinear observer design is adopted, and a strategy is developed to guarantee the convergence of the estimation error to a bound within the specified boundary layer. A relation between sliding mode gain and boundary layer is established for the existence of DSM, and the estimation is made robust to external disturbances and uncertainties. The unknown input or disturbance can also be estimated through the sliding mode. The conditions for the asymptotical stability of the estimation error are analysed. Application to a bioreactor is given and the simulation results demonstrate the effectiveness of the proposed scheme. Copyright © 2006 John Wiley & Sons, Ltd.     

Analysis of Hybrid Systems Based on Hybrid Net Condition/Event System Model

In thispaper, hybrid net condition /event systems are introducedas a model for hybrid systems. The model consists of a discretetimed Petri net and a continuous Petri net which interact eachother through condition and event signals. By introducing timeddiscrete places in the model, timing constraints in hybrid systemscan be easily described. For a class of hybrid systems that canbe described as linear hybrid net condition /eventsystems whose continuous part is a constant continuous Petrinet, two methods are developed for their state reachability analysis.One is the predicate-transformation method, which is an extensionof a state reachability analysis method for linear hybrid automata.The other is the path-based method, which enumerates all possiblefiring seqenences of discrete transitions and verifies if a givenset of states can be reached from another set by firing a sequenceof discrete transitions. The verification is performed by solvinga constraint satisfaction problem. A technique that adds additionalconstraints to the problem when a discrete state is revisitedalong the sequence is developed and used to prevent the methodfrom infinite enumeration. These methods provide a basis foralgorithmic analysis of this class of hybrid systems.     

Active Estimation for Jump Markov Linear Systems

Jump Markov Linear Systems are convenient models for systems that exhibit both continuous dynamics and discrete mode changes. Estimating the hybrid discrete-continuous state of these systems is important for control and fault detection. Existing solutions for hybrid estimation approximate the belief state by maintaining a subset of the possible discrete mode sequences. This approximation can cause the estimator to lose track of the true mode sequence when the effects of discrete mode changes are subtle.      

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.     

Observer‐based fault‐tolerant control for a class of hybrid impulsive systems

This paper investigates the fault‐tolerant control (FTC) problem for a class of hybrid nonlinear impulsive systems. Two kinds of faults are considered: continuous faults that affect each mode and discrete faults that affect the impulsive switching. The FTC strategy is based on the trade‐off between the frequency of switching and the decreasing rate of Lyapunov functions along the solution of the system, which maintains the stability of overall hybrid impulsive systems in spite of these two kinds of faults. A switched reluctance motor example is taken to illustrate the applicability of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

一类混杂系统建模和优化控制的研究

为解决混杂系统优化控制的计算复杂性问题,针对结合逻辑规则的工业过程混杂模型,采用结合约束程序的混合整数非线性规划算法,求解这种混杂模型的优化控制。计算实例表明,通过混杂建模方法,可以充分利用工业对象的机理模型以及操作工经验或专家经验,建立系统的更精确模型;结合约束程序混合整数非线性规划算法可以较迅速地求解混杂模型优化控制问题,从而使该方法可以用于工业过程实时控制中。     

A benchmark for optimal control problem solvers for hybrid nonlinear systems

In this paper, a benchmark problem is proposed in order to assess comparisons between different optimal control problem solvers for hybrid nonlinear systems. The model is nonlinear with 20 states, 4 continuous controls, 1 discrete binary control and 4 configurations. Transitions between configurations lead to state jumps. The system is inspired by the simulated moving bed, a counter-current separation process.     

混合系统剖析,描述与建模

混合系统是一种离散和连续构件交织的系统。通常以微分方程为连续模型，以离散事件系统或自动机为离散模型。通过分析混合系统的微观结构，文中提出了面向系统设计的描述语言ＤＤＬ。它能直观、精确刻画混合现象，方便设计决策描述，而且通过控制器符号与系统指称约束的延迟，为系统设计带来很大的灵活性。由ＤＤＬ描述的混合系统，经内部通信隐藏和系统单步协调积，可转换为混合变迁系统。     

基于粒子滤波算法的混合系统监测与诊断

利用粒子滤波算法具有同时估计连续状态和离散状态的特点,提出一种可用于混合系 统状态监测与诊断的新方法.给出了该方法的理论推导和设计步骤,讨论了在诊断应用中粒子滤 波器所遇到的问题,并给出了改善的措施.仿真结果证明用粒子滤波器对混合系统进行监测与诊 断是可行的,所提的方法对估计结果有比较好的改善.     

Hybrid state estimation: a target tracking application

In this paper we present a framework in which the general hybrid filtering or state estimation problem can be formulated. The problem of joint tracking and classification can be formulated in this framework as well as the problem of multiple model filtering with additional mode observations. In this formulation the state vector is decomposed into a continuous (kinematic) component and a discrete (mode and/or class) component. We also suppose that there are two types of measurements. Measurements that are related to the continuous part of the state (e.g. bearing and range measurements in a radar application) and measurements that are related to the discrete part of the state (e.g. radar cross-section measurements). We will derive an optimal filter for this problem and will show how this filter can be implemented numerically.     

基于混合信号的状态估计方法

传统的系统状态估计方法只用到连续信号,而离散测量信号所包含的信息没有得到利用.提出一种基于混合信号(包括连续和离散)的系统状态估计方法,既利用了连续信号,也用到离散信号的信息.该方法将离散信号的变化视作系统的离散事件,提取其准确的信息并参与系统状态估计,构成具有混合系统特性的新型状态估计器.还讨论了该估计器的稳定性条件和设计方法.仿真实验证明这种所提出的状态估计方法可以有效地改善系统的状态估计性能.     

Assume–guarantee verification of nonlinear hybrid systems with Ariadne

In many applicative fields, there is the need to model and design complex systems having a mixed discrete and continuous behavior that cannot be characterized faithfully using either discrete or continuous models only. Such systems consist of a discrete control part that operates in a continuous environment and are named hybrid systems because of their mixed nature. Unfortunately, most of the verification problems for hybrid systems, like reachability analysis, turn out to be undecidable. Because of this, many approximation techniques and tools to estimate the reachable set have been proposed in the literature. However, most of the tools are unable to handle nonlinear dynamics and constraints and have restrictive licenses. To overcome these limitations, we recently proposed an open‐source framework for hybrid system verification, called Ariadne , which exploits approximation techniques based on the theory of computable analysis for implementing formal verification algorithms. In this paper, we will show how the approximation capabilities of Ariadne can be used to verify complex hybrid systems, adopting an assume–guarantee reasoning approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Receding-horizon estimation for switching discrete-time linear systems

Receding-horizon state estimation is addressed for a class of discrete-time systems that may switch among different modes taken from a finite set. The system and measurement equations for each mode are assumed to be linear and perfectly known, but the current mode of the system is unknown, the state variables are not perfectly measurable and are affected by disturbances. The system mode is regarded as an unknown discrete state to be estimated together with the continuous state vector. Observability conditions are found to distinguish the system mode in the presence of bounded system and measurement noises. These results allow one to construct an estimator that relies on the combination of the identification of the discrete state with the estimation of the state variables by minimizing a receding-horizon quadratic cost function. The convergence properties of such an estimator are studied, and simulation results are reported to show the effectiveness of the proposed approach.