Nonlinear system identification under missing observations: The case of unknown model structure

This article presents an algorithm for identification of nonlinear state-space models when the “true” model structure of a process is unknown. In order to estimate the parameters in a state-space model, one needs to know the model structure and have an estimate of states. An approximation of the model structure is obtained using radial basis functions centered around a maximum a posteriori estimate of the state trajectory. A particle filter approximation of smoothed states is then used in conjunction with expectation maximization algorithm for estimating the parameters. The proposed approach is extended to handle missing observations and illustrated through a real application.     

Nonlinear tracking in a diffusion process with a Bayesian filter and the finite element method

A new approach to nonlinear state estimation and object tracking from indirect observations of a continuous time process is examined. Stochastic differential equations (SDEs) are employed to model the dynamics of the unobservable state. Tracking problems in the plane subject to boundaries on the state-space do not in general provide analytical solutions. A widely used numerical approach is the sequential Monte Carlo (SMC) method which relies on stochastic simulations to approximate state densities. For off-line analysis, however, accurate smoothed state density and parameter estimation can become complicated using SMC because Monte Carlo randomness is introduced. The finite element (FE) method solves the Kolmogorov equations of the SDE numerically on a triangular unstructured mesh for which boundary conditions to the state-space are simple to incorporate. The FE approach to nonlinear state estimation is suited for off-line data analysis because the computed smoothed state densities, maximum a posteriori parameter estimates and state sequence are deterministic conditional on the finite element mesh and the observations. The proposed method is conceptually similar to existing point-mass filtering methods, but is computationally more advanced and generally applicable. The performance of the FE estimators in relation to SMC and to the resolution of the spatial discretization is examined empirically through simulation. A real-data case study involving fish tracking is also analysed.     

零点配置与一类非线性广义系统的状态反馈控制

针对状态空间实现为非最小相位的非线性广义系统的控制问题,提出一种非线性广义系统的状态空间实现算法,构建了一个等价于原输出函数的综合输出函数,能任意配置状态空间实现的传输零点,使该状态空间实现为最小相位的.所构建的最小相位输出函数能直接用于构造状态反馈控制器,实现对非线性广义系统状态反馈控制.将所得结论应用于Logistic增长的SIR传染病模型,仿真结果表明了所提方法的有效性和可行性.     

基于状态延迟动态递归神经网络的机器人动态自适应跟踪辨识

对一种在Elman动态递归网络基础上发展而来的复合输入动态递归网络(CIDRNN)作 了改进,提出一种新的动态递归神经网络结构,称为状态延迟动态递归神经网络(State Delay Input Dynamical Recurrent Neural Network).具有这种新的拓扑结构和学习规则的动态递归网 络,不仅明确了各权值矩阵的意义,而且使权值的训练过程更为简洁,意义更为明确.仿真实验 表明,这种结构的网络由于增加了网络输入输出的前一步信息,提高了收敛速度,增强了实时 控制的可能性.然后将该网络用于机器人未知非线性动力学的辨识中,使用辨识实际输出与机理 模型输出之间的偏差,来识别机理模型或简化模型所丢失的信息,既利用了机器人现有的建模 方法,又可以减小网络运算量,提高辨识速度.仿真结果表明了这种改进的有效性.     

Estimating a state-space model from point process observations

A widely used signal processing paradigm is the state-space model. The state-space model is defined by two equations: an observation equation that describes how the hidden state or latent process is observed and a state equation that defines the evolution of the process through time. Inspired by neurophysiology experiments in which neural spiking activity is induced by an implicit (latent) stimulus, we develop an algorithm to estimate a state-space model observed through point process measurements. We represent the latent process modulating the neural spiking activity as a gaussian autoregressive model driven by an external stimulus. Given the latent process, neural spiking activity is characterized as a general point process defined by its conditional intensity function. We develop an approximate expectation-maximization (EM) algorithm to estimate the unobservable state-space process, its parameters, and the parameters of the point process. The EM algorithm combines a point process recursive nonlinear filter algorithm, the fixed interval smoothing algorithm, and the state-space covariance algorithm to compute the complete data log likelihood efficiently. We use a Kolmogorov-Smirnov test based on the time-rescaling theorem to evaluate agreement between the model and point process data. We illustrate the model with two simulated data examples: an ensemble of Poisson neurons driven by a common stimulus and a single neuron whose conditional intensity function is approximated as a local Bernoulli process.     

Online variational inference for state-space models with point-process observations

We present a variational Bayesian (VB) approach for the state and parameter inference of a state-space model with point-process observations, a physiologically plausible model for signal processing of spike data. We also give the derivation of a variational smoother, as well as an efficient online filtering algorithm, which can also be used to track changes in physiological parameters. The methods are assessed on simulated data, and results are compared to expectation-maximization, as well as Monte Carlo estimation techniques, in order to evaluate the accuracy of the proposed approach. The VB filter is further assessed on a data set of taste-response neural cells, showing that the proposed approach can effectively capture dynamical changes in neural responses in real time.     

Stability of controllers with on-line computations

The dynamical systems theory developed by Zufiria [1], Zufiria and Guttalu [2, 3], and Guttalu and Zufiria [4] is applied to the stability analysis of control systems in which the feedback control law requires in real time the solution of a set of nonlinear algebraic equations. Since a small sampling period is assumed, the stability and performance of the controlled process can be studied with a continuous-time formulation. A singularly perturbed system is used to model both the dynamics of the system being controlled and a numerical iterative algorithm required to compute the control law. An updating control procedure has been proposed based on the iterative nature of the control algorithm. The results obtained by Zufiria [1] regarding the behavior of a dynamical system that models the numerical algorithms lead to a considerable simplification in the analysis. For the case of a control problem involving inverse kinematics, the numerical algorithm that solves for inverse kinematics can be considered as an observer (or an estimator) of the state-space variables. The study provides an estimate of the required speed of computations to preserve the stability of the controller.Recommended by E .P. Ryan     

Fault coverage modeling in nonlinear dynamical systems

In this paper, we propose an approach for modeling fault coverage in nonlinear dynamical systems. Fault coverage gives a measure of the likelihood that a system will be able to recover after a fault occurrence. In our setup, the system dynamics are described by a standard state-space model. The system input (disturbance) is considered to be unknown but bounded at all times. Before any fault occurrence, the vector field governing the system dynamics is such that, for any possible input signal, the corresponding system reach set is contained in some region of the state space defined by the system performance requirements. When a fault occurs, the vector field that governs the system dynamics might be altered. Fault coverage is defined as the probability that, given a fault has occurred, the system trajectories remain, at all times, within the region of the state-space defined by the performance requirements. Input-to-state stability (ISS) concepts are used to compute estimates of the proposed coverage model. Several examples are discussed in order to illustrate the proposed modeling approach.     

Use of multiple models and qualitative knowledge for on-line moving horizon disturbance estimation and fault diagnosis

An integrated fault detection, fault isolation, and parameter estimation technique is presented in this paper. Process model parameters are treated as disturbances that dynamically affect the process outputs. A moving horizon estimation technique minimizes the error between process and model measurements over a finite horizon by calculating model parameter values across the estimation horizon. To implement qualitative process knowledge, this minimization is constrained such that only a limited number of different faults (parameters) may change during a specific horizon window. Multiple linear models are used to capture nonlinear process characteristics such as asymmetric response, variable dynamics, and changing gains. Problems of solution multiplicity and computational time are addressed. Results from a nonlinear chemical reactor simulation are presented.     

State-space approach to nonlinear predictive generalised minimum variance control

A nonlinear predictive generalised minimum variance control algorithm is introduced for the control of nonlinear discrete-time multivariable systems. The plant model is represented by the combination of a very general nonlinear operator and also a linear subsystem which can be open-loop unstable and is represented in state-space model form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The solution for the control law is derived in the time domain using a general operator representation of the process. The controller includes an internal model of the nonlinear process, but because of the assumed structure of the system, the state observer is only required to be linear. In the asymptotic case, where the plant is linear, the controller reduces to a state-space version of the well-known GPC controller.     

A novel neural internal model control for multi-input multi-output nonlinear discrete-time processes

An internal model-based neural network control is proposed for unknown non-affine discrete-time multi-input multi-output (MIMO) processes in nonlinear state space form under model mismatch and disturbances. Based on the neural state-space model built for an unknown nonlinear MIMO state space process, an approximate internal model and approximate decoupling controllers are derived simultaneously. Thus, the learning of the inverse process dynamics is not required. A neural network model-based extended Kalman observer is used to estimate the states of a nonlinear process as not all states are accessible. The proposed neural internal model control can work for open-loop unstable processes with its closed-loop stability derived analytically. The application to a distributed thermal process shows the effectiveness of the proposed approach for suppressing nonlinear coupling and external disturbances and its feasibility for the control of unknown non-affine nonlinear discrete-time MIMO state space processes.     

Learning and classification of complex dynamics

Standard, exact techniques based on likelihood maximization are available for learning auto-regressive process models of dynamical processes. The uncertainty of observations obtained from real sensors means that dynamics can be observed only approximately. Learning can still be achieved via “EM-K”-expectation-maximization (EM) based on Kalman filtering. This cannot handle more complex dynamics, however, involving multiple classes of motion. A problem arises also in the case of dynamical processes observed visually: background clutter arising for example, in camouflage, produces non-Gaussian observation noise. Even with a single dynamical class, non-Gaussian observations put the learning problem beyond the scope of EM-K. For those cases, we show here how “EM-C”-based on the CONDENSATION algorithm which propagates random “particle-sets,” can solve the learning problem. Here, learning in clutter is studied experimentally using visual observations of a hand moving over a desktop. The resulting learned dynamical model is shown to have considerable predictive value: when used as a prior for estimation of motion, the burden of computation in visual observation is significantly reduced. Multiclass dynamics are studied via visually observed juggling; plausible dynamical models have been found to emerge from the learning process, and accurate classification of motion has resulted. In practice, EM-C learning is computationally burdensome and the paper concludes with some discussion of computational complexity     

Nonlinear characterization of the performance of production and logistics networks

Today’s networks of production and logistics are often characterized by large structural and dynamical complexity. As a consequence of their nonlinear and potentially unstable dynamics, efficient planning and control is hardly possible, resulting in economic risks. The solution of the corresponding problems requires an overall understanding of the complex behavior of such systems. This paper uses discrete-event simulation to study networks that consist of a low number of cooperating manufacturers. The dynamics of the logistic parameters in the model are analyzed using methods originated in the theory of nonlinear dynamical systems. The results allow evaluation and potential improvement of the performance of different concepts and strategies that may be applied for the control of the dynamics of manufacturing networks.     

改进的频域辨识方法及其在直升机建模中的应用

本文提出了一种改进的直升机状态空间模型的频域系统辨识方法.该方法根据飞行扫频数据,得到包含直升机动力学模型耦合特性的非参数频率响应.将模式识别中的K平均理论应用到搜索状态空间模型代价函数的最小值中,根据机理建模结果拟合频率响应得到线性的六自由度直升机状态空间模型中的待辨参数.频率响应的计算中应用了一种复合窗函数方法,该方法综合不同窗口长度的频率响应得到一组优化的结果,显著增加了动力学模型频带和频率响应的精度.比较辨识得到的模型和飞行试验数据响应结果表明,辨识得到的模型较好地反映了该型无人直升机在悬停状态下的动力学特性.     

A RBF-ARX model-based robust MPC for tracking control without steady state knowledge

A RBF-ARX modeling and robust model predictive control (MPC) approach to achieving output-tracking control of the nonlinear system with unknown steady-state knowledge is proposed. On the basis of the RBF-ARX model with considering the system time delay, a local linearization state-space model is obtained to represent the current behavior of the nonlinear system, and a polytopic uncertain linear parameter varying (LPV) state-space model is built to represent the future system’s nonlinear behavior. Based on the two models, a quasi-min–max MPC algorithm with constraint is designed for output-tracking control of the nonlinear system with unknown steady state knowledge. The optimization problem of the quasi-min–max MPC algorithm is finally converted to the convex linear matrix inequalities (LMIs) optimization problem. Closed-loop stability of the MPC strategy is guaranteed by the use of parameter-dependent Lyapunov function and feasibility of the LMIs. Two examples, i.e. the modeling and control of a continuously stirred tank reactor (CSTR) and a two tank system demonstrate the effectiveness of the RBF-ARX modeling and robust MPC approach.     

An approximation algorithm for box abstraction of transition systems on real state spaces

Predicate abstraction is a powerful technique for extracting finite-state models from infinite-state systems such as computer software, and is applied to verification of safety properties. Predicate abstraction is also applied to verification of dynamical systems on real state spaces such as hybrid dynamical systems. In this paper, we propose a fast algorithm for computing entire abstract state spaces of transition systems on real state spaces. The method is based on the box abstraction of state spaces, and requires a relatively smaller number of reachability checks and Boolean operations. We also propose a fast method for computing the set of boxes that intersect a given convex polyhedron. This computation is a part of the proposed state-space generation algorithm. Effectiveness of the algorithm is evaluated by the computation time and by the difference of the approximated state space from the exact state space.