State Estimation of a Class of Hybrid Systems in the Presence of Unknown Mode Transitions

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 com- plicated 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 stochas- tic 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 in- formation,and the estimation of hybrid states is robust against the initial state.Simulation results illustrate the effectiveness of the proposed approach.     

线性连续时变系统的状态和输入混合估计:一种对策方法

The $H_\infty$ hybrid estimation problem for linear continuous time-varying systems is investigated in this paper, where estimated signals are linear combination of state and input. Design objective requires the worst-case energy gain from disturbance to estimation error be less than a prescribed level. Optimal solution of the hybrid estimation problem is the saddle point of a two-player zero sum differential game. Based on the differential game approach, necessary and sufficient solvable conditions for the hybrid estimation problem are provided in\hfill terms\hfill of\hfill solutions\hfill to\hfill a\hfill Riccati\hfill diffe-\\rential equation. Moreover, one possible estimator is proposed if the solvable conditions are satisfied. The estimator is characterized by a gain matrix and an output mapping matrix that reflects the internal relations between the unknown input and output estimation error. Both state and unknown inputs estimation are realized by the proposed estimator. Thus, the results in this paper are also capable of dealing with fault diagnosis problems of linear time-varying systems. At last, a numerical example is provided to illustrate the proposed approach.     

二维随机FM-II系统的状态估计

This paper is concerned with state estimation of two-dimensional (2-D) discrete stochastic systems. First, 2-D discrete stochastic system model is established by extending system matrices of the well-known Fornasini-Marchesini's second model into stochastic matrices. Each element of these stochastic matrices is second-order weakly stationary white noise sequences. Secondly, a linear and unbiased full-order state estimation problem for 2-D discrete linear stochastic model is formulated. Two estimation problems considered are the designs for the mean-square bounded estimation error and for the mean-square stochastic version of the suboptimal H∞ estimator, respectively. Our results can be seen as extensions of the 2-D linear deterministic case. Finally, illustrative examples are provided.     

Parametric estimation of interconnected nonlinear systems described by input-output mathematical models

In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems,which are composed of several interconnected nonlinear subsystems. Each subsystem can be described by an input-output nonlinear discrete-time mathematical model, with unknown, but constant or slowly time-varying parameters. Then, two recursive estimation methods are used to solve the parametric estimation problem for the considered class of the interconnected nonlinear systems. These methods are based on the recursive least squares techniques and the prediction error method. Convergence analysis is provided using the hyper-stability and positivity method and the differential equation approach. A numerical simulation example of the parametric estimation of a stochastic interconnected nonlinear hydraulic system is treated.     

Joint state and parameter estimation in particle filtering and stochastic optimization

In this paper, an adaptive estimation algorithm is proposed for non-linear dynamic systems with unknown static parameters based on combination of particle filtering and Simultaneous Perturbation Stochastic Approxi- mation （SPSA） technique. The estimations of parameters are obtained by maximum-likelihood estimation and sampling within particle filtering framework, and the SPSA is used for stochastic optimization and to approximate the gradient of the cost function. The proposed algorithm achieves combined estimation of dynamic state and static parameters of nonlinear systems. Simulation result demonstrates the feasibilitv and efficiency of the proposed algorithm     

Adaptive feedback control for nonlinear triangular systems subject to uncertain asymmetric dead-zone input

In this paper, an adaptive control strategy is proposed to investigate the issue of uncertain dead-zone input for nonlinear triangular systems with unknown nonlinearities. The considered system has no precise priori knowledge about the dead-zone feature and growth rate of nonlinearity. Firstly, a dynamic gain is introduced to deal with the unknown growth rate, and the dead-zone characteristic is processed by the adaptive estimation approach without constructing the dead-zone inverse. Then, by virtue of hyperbolic functions and sign functions, a new adaptive state feedback controller is proposed to guarantee the global boundedness of all signals in the closed-loop system. Moreover, the uncertain dead-zone input problem for nonlinear upper-triangular systems is solved by the similar control strategy. Finally, two simulation examples are given to verify the effectiveness of the control scheme.     

Nonlinear control and synchronization of a class of nonlinear coupled dynamical systems

In this paper, a control problem for a class of nonlinear coupled dynamical systems is proposed and a continuous nonlinear feedback control law is designed using direct Lyapunov method to solve the proposed control problem. Moreover, synchronization problem for a special case of this class nonlinear coupled dynamical systems is concerned. Numerical examples show the effectiveness and advantage of the designed continuous nonlinear control law and derived synchronization result.     

Uniform modeling of parameter dependent nonlinear systems

This paper addresses the problem of approximating parameter dependent nonlinear systems in a unified framework. This modeling has been presented for the first time in the form of parameter dependent piecewise affine systems. In this model, the matrices and vectors defining piecewise affine systems are affine functions of parameters. Modeling of the system is done based on distinct spaces of state and parameter, and the operating regions are partitioned into the sections that we call ’multiplied simplices’. It is proven that this method of partitioning leads to less complexity of the approximated model compared with the few existing methods for modeling of parameter dependent nonlinear systems. It is also proven that the approximation is continuous for continuous functions and can be arbitrarily close to the original one. Next, the approximation error is calculated for a special class of parameter dependent nonlinear systems. For this class of systems, by solving an optimization problem, the operating regions can be partitioned into the minimum number of hyper-rectangles such that the modeling error does not exceed a specified value. This modeling method can be the first step towards analyzing the parameter dependent nonlinear systems with a uniform method.     

Sliding mode control with disturbance observer for a class of nonlinear systems

This paper is concerned with the stabilization problem for a class of nonlinear systems with disturbance. The disturbance model is unknown and the first derivative of disturbance is bounded. Firstly, a general disturbance observer is proposed to estimate disturbance approximatively. Secondly, since the bound of the disturbance observer error is unknown, an adaptive sliding mode controller is designed to guarantee that the state of system asymptotically converges to zero and the unknown bound can be adjusted by an adaptive law. Finally, an example is given to illustrate the effectiveness of the proposed method.     

Global output feedback control of feedforward nonlinear time-delay systems with unknown growth rate and unknown measurement sensitivity

This paper discusses the problem of global state regulation via output feedback for a class of feedforward nonlinear time-delay systems with unknown measurement sensitivity. Different from previous works, the nonlinear terms are dominated by upper triangular linear unmeasured (delayed) states multiplied by unknown growth rate. The unknown growth rate is composed of an unknown constant, a power function of output, and an input function. Furthermore, due to the measurement uncertainty of the system output, it is more difficult to solve this problem. It is proved that the presented output feedback controller can globally regulate all states of the nonlinear systems using the dynamic gain scaling technique and choosing the appropriate Lyapunov–Krasovskii functionals.     

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.     

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.     

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.     

基于混合系统状态估计的故障诊断

如果将故障的发生视为一个离散事件,则存在故障可能的系统可以看作随机混合系 统,那么故障诊断问题就可转化为混合系统的离散状态估计问题.文中试图从这个角度研究 在非高斯噪声环境下非线性系统的故障诊断问题.在发生故障后的系统模型是已知的假定条 件下,使用随机混合自动机对系统建模,并利用基于粒子滤波的混合估计算法估计出混合状 态,从而完成故障诊断.仿真结果表明,所提的方法是可行的,可以处理某类故障诊断.     

State Estimation of Stochastic Impulsive System Via Stochastic Adaptive Impulsive Observer

This paper develops stochastic adaptive impulsive observer (SAIO) for state estimation of stochastic impulsive systems. Proposed observer is applicable to linear and a class of nonlinear stochastic impulsive systems. In addition to stochastic noises, the observer considers effect of parametric uncertainty and estimates unknown parameters by suitable adaptation laws. Interestingly, for certain impulsive systems, SAIO gives continuous state estimations from a discrete sequence of system output measurements. New theorems related to stochastic impulsive systems' boundedness are also developed and utilized to prove the boundedness of SAIO state estimation errors. Presented simulation results illustrate the effectiveness of the observer.     

State estimation in stochastic hybrid Systems with sparse observations

In this note we study the problem of state estimation for a class of sampled-measurement stochastic hybrid systems, where the continuous state x satisfies a linear stochastic differential equation, and noisy measurements y are taken at assigned discrete-time instants. The parameters of both the state and measurement equation depend on the discrete state q of a continuous-time finite Markov chain. Even in the fault detection setting we consider-at most one transition for q is admissible-the switch may occur between two observations, whence it turns out that the optimal estimates cannot be expressed in parametric form and time integrations are unavoidable, so that the known estimation techniques cannot be applied. We derive and implement an algorithm for the estimation of the states x, q and of the discrete-state switching time that is convenient for both recursive update and the eventual numerical quadrature. Numerical simulations are illustrated.     

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.