System identification of nonlinear state-space models

This paper is concerned with the parameter estimation of a general class of nonlinear dynamic systems in state-space form. More specifically, a Maximum Likelihood (ML) framework is employed and an Expectation Maximisation (EM) algorithm is derived to compute these ML estimates. The Expectation (E) step involves solving a nonlinear state estimation problem, where the smoothed estimates of the states are required. This problem lends itself perfectly to the particle smoother, which provides arbitrarily good estimates. The maximisation (M) step is solved using standard techniques from numerical optimisation theory. Simulation examples demonstrate the efficacy of our proposed solution.     

Networked recursive filtering for time-delayed nonlinear stochastic systems with uniform quantisation under Round-Robin protocol

In this paper, the design of networked recursive filter is investigated for a kind of nonlinear stochastic systems subject to missing measurements, fixed time-delay and uniform quantisation under the Round-Robin protocol. In a digital platform, the information coming from multi-sensors could be subject to missing measurements due to the environment effect and then need to be transformed into digital signals via uniform quantizers. In addition, the Round-Robin protocol is adopted to govern the token accessing to channel media so as to both save energy and mitigate the data congestion. A novel extended Kalman-type recursive filter is constructed that firstly combines the Round-Robin protocol, namely, in the form of the augmentation of the plant system dynamics and the protocol-induced periodic measurements. In the simultaneous consideration of system delays, missing measurements, uniform quantisation, as well as the Round-Robin protocol, the purpose for the discussed filtering problem is to obtain a set of filter parameters over a finite-horizon to minimise the upper bound of filtering error covariance as far as possible. Via elaborate mathematical analysis, the desired filter parameter is obtained by virtue of solving two Riccati-type optimisation equations, which are dependent on the latest estimation states. The genetic algorithm has been introduced to optimise the dynamic parameter selections. In addition, it is revealed in theory that the trace of the upper bound of filtering error covariance is non-decreasing as the quantisation level increases. Finally, the effectiveness of the proposed design scheme is inspected by a discretised maneuvering target tracking system.     

Quantised polynomial filtering for nonlinear systems with missing measurements

This paper is concerned with the polynomial filtering problem for a class of nonlinear systems with quantisations and missing measurements. The nonlinear functions are approximated with polynomials of a chosen degree and the approximation errors are described as low-order polynomial terms with norm-bounded coefficients. The transmitted outputs are quantised by a logarithmic quantiser and are also subject to randomly missing measurements governed by a Bernoulli distributed sequence taking values on 0 or 1. Dedicated efforts are made to derive an upper bound of the filtering error covariance in the simultaneous presence of the polynomial approximation errors, the quantisations as well as the missing measurements at each time instant. Such an upper bound is then minimised through designing a suitable filter gain by solving a set of matrix equations. The filter design algorithm is recursive and therefore applicable for online computation. An illustrative example is exploited to show the effectiveness of the proposed algorithm.     

Simultaneous input and state estimation for nonlinear systems with applications to flow field estimation

This paper studies the problem of simultaneous input and state estimation (SISE) for nonlinear dynamical systems with and without direct input–output feedthrough. We take a Bayesian perspective to develop a sequential joint input and state estimation approach. Our scheme gives rise to a nonlinear Maximum a Posteriori optimization problem, which we solve using the classical Gauss–Newton method. The proposed approach generalizes a number of SISE methods presented in the literature. We illustrate the effectiveness of the proposed scheme for nonlinear systems with direct feedthrough in an oceanographic flow field estimation problem involving submersible drogues that measure position intermittently and acceleration continuously.     

在JSP中使用递归算法生成目录树

由于JSP开发环境没有TreeView控件,因此在JSP中生成目录树比较困难。针对这一问题,提出了一个用于生成目录树的有效方法,并详细讲述了如何在JSP中利用递归算法将该方法与数据库技术相结合来生成目录树。     

Variational Bayesian learning of nonlinear hidden state-space models for model predictive control

This paper studies the identification and model predictive control in nonlinear hidden state-space models. Nonlinearities are modelled with neural networks and system identification is done with variational Bayesian learning. In addition to the robustness of control, the stochastic approach allows for various control schemes, including combinations of direct and indirect controls, as well as using probabilistic inference for control. We study the noise-robustness, speed, and accuracy of three different control schemes as well as the effect of changing horizon lengths and initialisation methods using a simulated cart–pole system. The simulations indicate that the proposed method is able to find a representation of the system state that makes control easier especially under high noise.     

An ergodic theorem for filtering with applications to stability

Ergodic properties of the signal–filtering pair are studied for continuous time finite Markov chains, observed in white noise. The obtained law of large numbers is applied to the stability problem of the nonlinear filter with respect to initial conditions. The Furstenberg–Khasminskii formula is derived for the top Lyapunov exponent of the Zakai equation and is used to estimate the stability index of the filter.     

Adaptive discrete-time sliding-mode control of nonlinear systems described by Wiener models

In this paper, we propose an adaptive control scheme that can be applied to nonlinear systems with unknown parameters. The considered class of nonlinear systems is described by the block-oriented models, specifically, the Wiener models. These models consist of dynamic linear blocks in series with static nonlinear blocks. The proposed adaptive control method is based on the inverse of the nonlinear function block and on the discrete-time sliding-mode controller. The parameters adaptation are performed using a new recursive parametric estimation algorithm. This algorithm is developed using the adjustable model method and the least squares technique. A recursive least squares (RLS) algorithm is used to estimate the inverse nonlinear function. A time-varying gain is proposed, in the discrete-time sliding mode controller, to reduce the chattering problem. The stability of the closed-loop nonlinear system, with the proposed adaptive control scheme, has been proved. An application to a pH neutralisation process has been carried out and the simulation results clearly show the effectiveness of the proposed adaptive control scheme.     

Multigradient recursive reinforcement learning NN control for affine nonlinear systems with unmodeled dynamics

In this paper, an adaptive reinforcement learning approach is developed for a class of discrete‐time affine nonlinear systems with unmodeled dynamics. The multigradient recursive (MGR) algorithm is employed to solve the local optimal problem, which is inherent in gradient descent method. The MGR radial basis function neural network approximates the utility functions and unmodeled dynamics, which has a faster rate of convergence than that of the gradient descent method. A novel strategic utility function and cost function are defined for the affine systems. Finally, it concludes that all the signals in the closed‐loop system are semiglobal uniformly ultimately bounded through differential Lyapunov function method, and two simulation examples are presented to demonstrate the effectiveness of the proposed scheme.     

A feasible directions algorithm for nonlinear complementarity problems and applications in mechanics

Complementarity problems are involved in mathematical models of several applications in engineering, economy and different branches of physics. We mention contact problems and dynamics of multiple bodies systems in solid mechanics. In this paper we present a new feasible direction algorithm for nonlinear complementarity problems. This one begins at an interior point, strictly satisfying the inequality conditions, and generates a sequence of interior points that converges to a solution of the problem. At each iteration, a feasible direction is obtained and a line search performed, looking for a new interior point with a lower value of an appropriate potential function. We prove global convergence of the present algorithm and present a theoretical study about the asymptotic convergence. Results obtained with several numerical test problems, and also application in mechanics, are described and compared with other well known techniques. All the examples were solved very efficiently with the present algorithm, employing always the same set of parameters.     

Efficient estimation of hybrid systems with applications to tracking

Particle filtering has been recognised as a superior alternative to the traditional estimation methods as it is applicable to nonlinear/non-Gaussian system. A central issue in real-time applications of particle filtering is its high computational cost. This problem is compounded when it is used in hybrid system estimation. A new particle filtering method for nonlinear/non-Gaussian hybrid system estimation is proposed in this article. The new method integrates the high-accuracy interacting multiple model particle filtering algorithm with the computationally efficient observation and transition-based most likely modes tracking particle filtering algorithm to get high-accuracy estimation with reduced computational load. The algorithm is applied to a manoeuvring target tracking application to demonstrate its efficiency.     

A recursive algorithm for estimating multiple models continuous transfer function with non-uniform sampling

A multiple model recursive least squares algorithm combined with a first-order low-pass filter transformation method, named λ-transform, is proposed for the simultaneous identification of multiple model orders continuous transfer functions from non-uniformly sampled input–output data. The λ-transformation is shown to be equivalent to a canonical transformation between discrete z-domain and δ-domain using the negative value of the λ-transform filter time-constant instead of the sampling interval parameter. The proposed algorithm deals with oversampling, sampling jitter or non-uniform sample intervals without the need for extra digital anti-aliasing pre-filtering, downsampling or interpolation algorithms, producing multiple models with a cost function that facilitates automatic selection of best-fitted models. Besides, measurement noise is noted as beneficial, bringing up an inherent bias toward low-order models. Simulated examples and a drum-boiler level experimental result exhibiting non-minimum phase behaviour illustrate the application of the proposed method.     

GSM全速率语音编码中Schur递归算法的FPGA实现

Schur递归算法是GSM全速率语音编码算法中计算短期滤波参数的一个关键部分。由于它是一个典型的双循环结构,所以在算法的FPGA实现中也具有代表意义,本文对Schur递归算法的特点进行了详细的分析,提出了一种利用FPGA实现Schur递归算法的方案,并对其实现过程中各模块的设计方法进行了详细的分析。     

On some finite dimensional nonlinear filters for certain diffusions observed in correlated noise

An extension of the one dimensional Bene nonlinear filter to the case of correlated process and observation noises is presented. Conditions are derived so that the optimal nonlinear filter is finite dimensional.     

Identification of an additive nonlinear system and its applications in generalized Hammerstein models

An identification algorithm is developed for a class of nonlinear systems that are multi-input and multi-output in an additive form. The convergence results are achieved and its applications to identification of a generalized Hammerstein system is also discussed.     

递归收缩算法中支点的处理策略研究

为了确保生成无向图割集的递归收缩算法的正确性和稳定性,对算法中种子顶点是支点的情形进行了分析,并采取了新的处理策略。分析了支点具有一个非可吸簇的情形,引进附加吸入的概念,修正了种子顶点的BFSO值取值规则,解决了现有算法可能遗漏割集的问题。针对支点没有非可吸簇的情形,给出了一个新的处理策略,解决了现有算法在某些特殊输入条件下效率不高的问题,在理论上分析了新处理策略的有效性,并做了相应的实验比较,理论分析和实验比较均表明：新的处理策略采用提高了递归收缩算法的稳定性。     

Filtering of systems with nonlinear measurements with an application to target tracking

This paper studies the problem of recursive state estimation of stochastic linear systems with nonlinear measurements. The main idea is to rewrite the measurement map in a linear form by considering, as system output, a vector of “virtual” measurements. The result is a linear system with a non‐Gaussian and nonstationary output noise. State estimation is therefore obtained using a Kalman filter or, alternatively, a quadratic filter, suitably designed for non‐Gaussian systems. This work provides two sufficient conditions for the application of the virtual measurement approach and shows its effectiveness in the case of the maneuvering target tracking problem.     

Changing supply rates for input-output to state stable discrete-time nonlinear systems with applications

We present results on changing supply rates for input-output to state stable discrete-time nonlinear systems. Our results can be used to combine two Lyapunov functions, none of which can be used to verify that the system has a certain property, into a new composite Lyapunov function from which the property of interest can be concluded. The results are stated for parameterized families of discrete-time systems that naturally arise when an approximate discrete-time model is used to design a controller for a sampled-data system. We present several applications of our results: (i) a LaSalle criterion for input to state stability (ISS) of discrete-time systems; (ii) constructing ISS Lyapunov functions for time-varying discrete-time cascaded systems; (iii) testing ISS of discrete-time systems using positive semidefinite Lyapunov functions; (iv) observer-based input to state stabilization of discrete-time systems. Our results are exploited in a case study of a two-link manipulator and some simulation results that illustrate advantages of our approach are presented.