Stability analysis of neural-network interconnected systems

This paper is concerned with the stability problem of a neural-network (NN) interconnected system which consists of a set of NN models. First, a linear difference inclusion (LDI) state-space representation is established for the dynamics of each NN model. Subsequently, based on the LDI state-space representation, a stability criterion in terms of Lyapunov's direct method is derived to guarantee the asymptotic stability of NN interconnected systems. Finally, a numerical example with simulations is given to demonstrate the results.     

结构化状态空间中的递阶再励学习方法

在状态空间满足结构化条件的前提下,通过状态空间的维度划分直接将复杂的原始MDP问题递阶分解为一组简单的MDP或SMDP子问题,并在线对递阶结构进行完善.递阶结构中嵌入不同的再励学习方法可以形成不同的递阶学习.所提出的方法在具备递阶再励学习速度快、易于共享等优点的同时,降低了对先验知识的依赖程度,缓解了学习初期回报值稀少的问题.     

A state-space formulation for optimal Hankel-norm approximations

The optimal Hankel-norm approximation problem studied in [1] is reformulated in a state-space setting. The crucial extension theorem is reestablished in this framework. The minimal degree optimal approximation is then derived in terms of state-space parameters     

Robust stability of state-space models with structureduncertainties

A method for robust eigenvalue location analysis of linear state-space models affected by structured real parametric perturbations is proposed. The approach, based on algebraic matrix properties, deals with state-space models in which system matrix entries are perturbed by polynomial functions of a set of uncertain physical parameters. A method converting the robust stability problem into nonsingularity analysis of a suitable matrix is proposed. The method requires a check of the positivity of a multinomial form over a hyperrectangular domain in parameter space. This problem, which can be reduced to finding the real solutions of a system of polynomial equations, simplifies considerably when cases with one or two uncertain parameters are considered. For these cases, necessary and sufficient conditions for stability are given in terms of the solution of suitable real eigenvalue problems     

Robustness design of fuzzy control for nonlinear multiple time-delay large-scale systems via neural-network-based approach

The stabilization problem is considered in this correspondence for a nonlinear multiple time-delay large-scale system. First, the neural-network (NN) model is employed to approximate each subsystem. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of each NN model. According to the LDI state-space representation, a robustness design of fuzzy control is proposed to overcome the effect of modeling errors between subsystems and NN models. Next, in terms of Lyapunov's direct method, a delay-dependent stability criterion is derived to guarantee the asymptotic stability of nonlinear multiple time-delay large-scale systems. Finally, based on this criterion and the decentralized control scheme, a set of fuzzy controllers is synthesized to stabilize the nonlinear multiple time-delay large-scale system.     

自适应鲁棒控制器设计新方法在电液伺服系统中的应用

提出了一种自适应鲁棒控制器设计新方法, 并运用在阀控缸电液位置伺服系统中.首先, 将含有确定、不确定、已知、未知、线性和非线性项的电液伺服系统进行完整地数学建模, 以状态空间的形式表出.然后利用本文所提的新方法设计自适应鲁棒控制器和相应的自适应律来处理所建模型中的各项元素.该控制器通过设计一个带有虚拟控制量的控制状态空间表达式并结合状态观测器来获得.设计合适的虚拟控制量, 可在任意给定条件下, 使所有的系统状态都收敛到所设计的理想状态.接着设计李亚普诺夫函数来证明闭环系统的稳定性.最后建立硬件实验平台与经典自适应鲁棒控制方法进行对比实验验证此自适应鲁棒控制器设计新方法的有效性和优势.     

Realization and performance evaluation of a class of image models for recursive restoration problems

A new class or causal and semicausal image models is defined on the basis of the spatial scheme assumed to explain the correlation between adjacent pixels. Each model is realized in terms of a state-space representation suitable for recursive strip filtering. Numerical experiments arc performed to test the applicability of the proposed method and to evaluate the influence of the spatial scheme on the corresponding filter performance.     

Interval frequency negative imaginary systems

This paper studies interval frequency negative imaginary (IFNI) systems based on minimal state-space realisations. Firstly, the concept of the IFNI transfer functions is introduced, and the relationship between the IFNI transfer functions and the interval frequency positive real transfer functions is established. Secondly, based on the generalised KYP lemma, a necessary and sufficient condition is derived for IFNI transfer functions with minimal state-space realisation in terms of linear matrix inequalities. Our results coincide with the existing negative imaginary lemma when the interval frequency set becomes the positive frequency set. Also, a time domain interpretation of the IFNI property is provided in terms of the system input, output and state. Finally, two examples are used to illustrate the developed theory.     

A connection between normalized coprime factorizations and linear quadratic regulator theory

Given a transfer matrix described by a minimal state-space triple, a method is given for computing state-space realizations for the numerator and denominator of a normalized, stable, right coprime factorization for the transfer matrix. The method involves the solution of an algebraic Riccati equation. It allows the use of existing computational state-space algorithms in finding normalized stable right coprime factorizations, and avoids explicit calculations of spectral factors.     

Note on ‘ On the definition of transfer function ’

An algorithm for directly obtaining the canonical state-space model corresponding to the Cauer third form of continued fraction expansion (CFE) from a given general state-space model is presented. The algorithm can be used to determine the transfer function of linear time-invariant system from its state-space model as well as to obtain the reduced order models..Two new similarity matrices, one transforms a state-space equation from a general form to a Cauer third CFE canonical form, and the other transforms a state-space model in phase-variable form to a state-space model in a Cauer third CFE canonical form, are derived. Using these matrices an approximate relationship between the original state vector and the state-vector of reduced model obtained by the method of Cauer third CFE is established     

Cauer continued-fraction expansion about s = 0 and s = a for biased reduced-order state-space models

A method of linear-system reduction is presented which produces biased state-space models such that combinations of retained time-moments and weighted time-moments may be varied. The method is based on the concept of representing the system transfer function in a biased Cauer form of continued-fraction expansion (CFE) about s = 0 and s = a. A new algorithm for obtaining the continued-fraction expansion of the transfer function of a linear time-invariant system from its state-space model directly, without first determining the corresponding transfer function, is derived. A realization which uses only integrators for the biased Cauer continued-fraction expansion about s = 0 and s = a is presented. The corresponding canonical state-space model is established, which allows the reduced-order state-space model to be formed by directly partitioning the system matrices. Also presented are two new similarity transformation matrices; one is used to transform a state-space model from a general form to a state-space model in the biased CFE canonical form, and the other is used to transform a state-space model from phase-variable canonical form to the biased CFE canonical form.     

A new parametrization of H∞ suboptimal controllers

Elementary state-space concepts are used to derive a transparent solution to the H _∞ control problem on an infinite horizon. The main contribution of this solution is a novel representation of suboptimal controllers in terms of a pair of parametric Riccati equations with a coupling constraint. Unlike the classical parametrization in terms of linear fractional transformation, this state-space representation has a homogeneous Riccati formulation which should help to make the most of the suboptimal controller diversity. Potential applications include the design of reduced-order controllers and, more generally, the selection of suboptimal controllers to meet or optimize additional constraints.     

Identification of continuous-time models for nonlinear dynamic systems from discrete data

A new iOFR-MF (iterative orthogonal forward regression--modulating function) algorithm is proposed to identify continuous-time models from noisy data by combining the MF method and the iOFR algorithm. In the new method, a set of candidate terms, which describe different dynamic relationships among the system states or between the input and output, are first constructed. These terms are then modulated using the MF method to generate the data matrix. The iOFR algorithm is next applied to build the relationships between these modulated terms, which include detecting the model structure and estimating the associated parameters. The relationships between the original variables are finally recovered from the model of the modulated terms. Both nonlinear state-space models and a class of higher order nonlinear input–output models are considered. The new direct method is compared with the traditional finite difference method and results show that the new method performs much better than the finite difference method. The new method works well even when the measurements are severely corrupted by noise. The selection of appropriate MFs is also discussed.     

J-inner-outer factorization, J-spectral factorization, and robustcontrol for nonlinear systems

The problem of expressing a given nonlinear state-space system as the cascade connection of a lossless system and a stable, minimum-phase system (inner-outer factorization) is solved for the case of a stable system having state-space equations affine in the inputs. The solution is given in terms of the stabilizing solution of a certain Hamilton-Jacobi equation. The stable, minimum-phase factor is obtained as the solution of an associated nonlinear spectral factorization problem. As an application, one can arrive at the solution of the nonlinear H_∞-control problem for the disturbance feedforward case     

The structure of nonlinear control systems possessing symmetries

A concept of symmetry is defined for general nonlinear control systems. It is shown, under various technical conditions, that nonlinear control systems with symmetries admit local and/or global decompositions in terms of lower dimensional subsystems and feedback loops. The structure of the individual subsystems is dependent on the structure of the symmetry group; for example, if the symmetry group is Abelian, one of the subsystems is a quadrature. An additional feature of the decomposition is that the state-space dimensions of the subsystems sum to the state-space dimension of the original system.     

Dedicated microprocessors for realtime identification of multivariable systems

In this paper, an algorithm is proposed for identifying multivariable systems in state-space form from noisy data, which is suitable for implementation on dedicated microprocessor systems. The proposed algorithm uses the normalized stochastic approximation criterion which reduces the computational complexity and memory requirements. It is shown that the overall performance of the proposed stochastic approximation algorithm when using a dedicated microprocessor with fixed point arithmetic is superior to the extended least-squares method in terms of memory requirements, execution speed per iteration, and the estimation results.