Identification of state-dependent parameter models with support vector regression

A support vector regression approach is presented for the identification of state-dependent parameter ARX models, whose parameters are described as functions of past inputs and outputs. The problem of identifying the state-dependent parameters reduces to a standard support vector regression problem with a kernel function which is defined in terms of the kernels used to represent the individual parameters. Numerical examples show that the support vector method gives accurate parameter estimates for systems which have a state-dependent parameter representation.     

Linear estimator stabilization of nonlinear sampled-data systems

It has been shown that the state of a linear system can be constructed from observations of its inputs and outputs. The observer which performs the construction is itself a linear system with time constants which may be chosen by the designer. This linear asymptotic estimator has been used previously to stabilize certain types of contimuous nonlinear systems. In this paper, a linear sampled-data estimator is developed. This estimator is used first to stabilize a linear sampled-data system and then it is used to stabilize a class of nonlinear sampled-data systems by the choice of the estimator's time constants and the feedback gain. Typical example applications are analyzed to illustrate the theoretical investigations.     

A clustering-based approach for the identification of a class of temporally switched linear systems

The behaviours of hybrid dynamic systems (HDS) are determined by combining continuous variables with discrete switching logic. The identification of a HDS aims to find an accurate model of the system’s dynamics based on its past inputs and outputs. In pattern recognition (PR) methods, each mode is represented by a set of similar patterns that form restricted regions in the feature space. These sets of patterns are called classes. A pattern is a vector built from past inputs and outputs. HDS identification is a challenging problem since it involves the estimation of different sets of parameters without knowing in advance which sections of the measured data correspond to the different modes of the system. Therefore, HDS identification can be achieved by combining two steps: clustering and parameter estimation. In the clustering step, the number of discrete modes (i.e., the classes that input-output data points belong) is estimated. The parameter estimation step finds the parameters of the models that govern the continuous dynamics in each mode. In this paper, an unsupervised PR method is proposed to achieve the clustering step of the identification of temporally switched linear HDS. The determination of the number of modes does not require prior information about the modes or their number.     

Regional stabilisation of polynomial non-linear systems using rational Lyapunov functions

In this article, we propose a new non-linear stabilisation approach based on the popular linear parameter-varying control techniques. The regional state-feedback control problem of polynomial non-linear systems will be studied using rational Lyapunov functions of states. By bounding the variation rates of each state, the domain of attraction will be embedded in the region specified by the non-linear vector field. As a result, the state-feedback stabilisation conditions will be formulated as a set of polynomial matrix inequalities and can be solved efficiently by sum-of-squares programming. The resulting Lyapunov matrix and state-feedback gains are typically state-dependent rational matrix functions. This approach is also extended to a class of output-dependent non-linear systems where the stabilising output-feedback controller can be synthesised using rational Lyapunov functions of outputs. Finally, several examples will be used to demonstrate the proposed stabilisation approach and clarify the effect of various choices of Lyapunov function forms and state constraints.     

Input-output representations of spectral systems and adaptive controls

In this paper two types of input-output representations (static ones and dynamic ones) are presented for the class of distributed parameter systems generated by spectral operators. The input-output equations can be expressed using filtered values generated from the inputs and outputs. Using the input-output representations, the design problem of an adaptive control system is also investigated for systems with unknown input and output distribution functions.     

A parametric frequency response method for non-linear time-varying systems

A new parametric frequency response algorithm is introduced to investigate linear and non-linear dynamic systems with time-varying parameters. In the new algorithm the time-varying parameters are regarded as additional inputs of the systems and the non-linear generalised frequency response functions for multi-input-single-output systems are then employed to obtain Zadeh's system functions from a differential equation representation. The parametric frequency response method reveals how the time-varying parameters affect the behaviour of the systems through a time-varying term. The new method can be applied to both linear and non-linear time-varying systems.     

一种非线性非高斯随机系统的故障诊断方法

针对非线性非高斯随机系统在线故障诊断的问题,运用粒子滤波器提出了一种基于方差自适应粒子滤波器的非线性非高斯随机系统的故障诊断方法,可以用来解决系统的参数偏差型故障诊断问题。通过对连续搅拌釜式反应器(CSTR)的仿真研究,可以看出,该算法实现简单,易于对系统进行在线估计,对于发生缓变和突变的参数偏差型故障的检测与估计均较为有效。     

Exponentially incremental dissipativity for nonlinear stochastic switched systems

ABSTRACT

In this paper, we investigate the exponentially incremental dissipativity for nonlinear stochastic switched systems by using the designed state-dependent switching law and multiple Lyapunov functions approach. Specifically, using incremental supply rate as well as a state dissipation inequality in expectation, a stochastic version of exponentially incremental dissipativity is presented. The sufficient conditions for nonlinear stochastic switched systems to be exponentially incrementally dissipative are given by the designed state-dependent switching law. Furthermore, the extended Kalman–Yakubovich–Popov conditions are derived by using two times continuously differentiable storage functions. Moreover, the incremental stability conditions in probability for nonlinear stochastic switched systems are derived based on exponentially incremental dissipativity. The exponentially incremental dissipativity is preserved for the feedback-interconnected nonlinear stochastic switched systems with the composite state-dependent switching law; meanwhile, the incremental stability in probability is preserved under some certain conditions. A numerical example is given to illustrate the validity of our results.     

On designing filters for uncertain sampled-data nonlinear systems

This paper is concerned with the problem of nonlinear filtering for sampled-data systems with nonlinear time-varying parameter uncertainty. The aim is to design a digital filter such that the ratio between the energy of the estimation errors and the energy of the exogenous inputs is minimised or guaranteed to be less or equal to a prescribed value for all admissible uncertainties. A nonlinear bounded real lemma for sampled-data systems with nonlinear time-varying parameter uncertainty is provided. Based on this nonlinear bounded real lemma, the robust filtering problem is solved in terms of both continuous and discrete Hamilton–Jacobi equations.     

Finite-time H∞ filtering for non-linear stochastic systems

This paper describes the robust H_∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H_∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton–Jacobi inequality. Based on this result, the existence of a finite-time H_∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.     

具有减少辨识参数的随机多变量极点配置自适应控制器

本文提出了一种新的限制输出个数减少随机多变量自适应控制中辨识参数的方法，并给出了减少辨识参数的极点配置自适应算法。虽然采用ｎ个输入１个输出的减少辨识参数的模型来设计控制器，但所提出的控制器能够保证被控系统的几个输出跟踪参考输入信号，仿真结果表明，所提出的方法是成功的。     

Wiener models of direction-dependent dynamic systems

Analysis of systems with direction-dependent dynamics is currently limited to cases in which the dynamics in the two directions of the output are first order; results for such systems have been published for both pseudo-random maximum-length binary (MLB) and inverse-repeat maximum-length binary (IR-MLB) inputs. These relatively limited analytical results make it useful to examine alternative ways of modelling such systems and in this paper, Wiener models are considered for this purpose. Methods for optimising the Wiener model parameters by matching the system and model cross-correlation functions, outputs, and discrete Fourier transforms of the outputs are considered, and the results are compared. These methods are also applied to a first-order direction-dependent system with a maximum-length ternary (MLT) input, for which no analytical results are currently available, and to a second-order system with an IR-MLB input.     

Representations of non-linear systems: the NARMAX model

Input-output representations of non-linear discrete-time systems are discussed. It is shown that the NARMAX (Non-linear AutoRegressive Moving Average with eXogenous inputs) model is a general and natural representation of non-linear systems and contains, as special cases, several existing non-linear models. The problem of approximating non-linear input-output systems is also addressed and several properties of non-linear models are highlighted using simple examples.     

Identification of multi-input systems based on correlation techniques

This article proposes a correlation analysis-based identification method for multi-input single-output systems. The basic idea is to estimate the equivalent FIR model parameters with the orders increasing, and to compute the parameter estimates of the original systems (i.e. each fictitious subsystem) using the system inputs and the outputs of the estimated FIR models and using the least squares optimisation. Simulation results indicate that the proposed algorithm can work well.     

Robust stability bounds for multi-delay networked control systems

In this paper, the robust stability of a perturbed linear continuous-time system is examined when controlled using a sampled-data networked control system (NCS) framework. Three new robust stability bounds on the time-invariant perturbations to the original continuous-time plant matrix are presented guaranteeing stability for the corresponding discrete closed-loop augmented delay-free system (ADFS) with multiple time-varying sensor and actuator delays. The bounds are differentiated from previous work by accounting for the sampled-data nature of the NCS and for separate communication delays for each sensor and actuator, not a single delay. Therefore, this paper expands the knowledge base in multiple inputs multiple outputs (MIMO) sampled-data time delay systems. Bounds are presented for unstructured, semi-structured, and structured perturbations.     

关于约束方差控制器的评估问题的研究

本文研究当系统的性能指标表现为系统输入及输出的方差约束时一类随机控制器的评价问题，给出了系统反馈输入及输出的辨识算法，该算法可用来评价反馈控制器能否使反馈系统满足既定的方差约束，以便在对实际系统实施控制之前及时调整控制器，从而达到设计目的。     

H ∞ control for non-linear stochastic systems: the output-feedback case

The H _∞ output-feedback control problem for non-linear stochastic systems is considered. A solution for a large class of non-linear stochastic systems is introduced (including non-linear diffusion systems as a subclass). This solution is based on a bounded real lemma for non-linear stochastic systems that was previously established via a stochastic dissipativity concept. The theory yields sufficient conditions for the closed-loop system to possess a prescribed L ₂-gain bound in terms of two Hamilton Jacobi inequalities: one that is associated with the state feedback part of the problem is n-dimensional (where n is the underlying system's state dimension) and the other inequality that stems from the estimation part is 2n-dimensional. Both stationary and non–stationary systems are considered. Stability of the closed-loop system is established, both in the mean-square and the in-probability senses. As the solution to the Hamilton Jacobi inequalities may, in general, lead to a non–realisable state estimator, a modification of the associated 2n-dimensional Hamilton Jacobi inequality is made in order to circumvent this realisation problem, while preserving the system's L ₂-gain bound. For time-invariant systems, the problem of robust output-feedback is considered in the case of norm-bounded uncertainties. A solution is then derived in terms of linear state-dependent matrix inequalities.     

Subspace identification of Bilinear and LPV systems for open- and closed-loop data

In this paper we present a novel algorithm to identify LPV systems with affine parameter dependence operating under open- and closed-loop conditions. A factorization is introduced which makes it possible to form a predictor that predicts the output, which is based on past inputs, outputs, and scheduling data. The predictor contains the LPV equivalent of the Markov parameters. Using this predictor, ideas from closed-loop LTI identification are developed to estimate the state sequence from which the LPV system matrices can be constructed. A numerically efficient implementation is presented using the kernel method. It turns out that if structure is present in the scheduling sequence the computational complexity reduces even more.