On construction of asymptotically stable iterated function system with probabilities

We consider a Markov chain generated by random iterations of a family of mappings indexed by elements of an arbitrary measurable space. Under sufficiently weak assumptions we construct a family of place-dependent probability measures such that considered Markov chain converges to a stationary distribution. We also prove some sufficient condition for asymptotic stability of a family of i.i.d. mappings and we apply obtained result for discrete white noise random dynamical systems showing analogous probabilistic long-time behavior.     

Chaotification via system immersion

By introducing a definition of partially chaotic for a kind of generalized chaotic system, this paper discusses the chaotification problem with a new approach based on (system) immersion and (manifold) invariance. The basic idea is to immerse the plant system into a reduced-order chaotic system. The proposed approach is also applied to chaotify systems with uncertain parameters. Illustrative examples with simulation results are presented to validate the proposed chaotification schemes.     

Linear programming formulation of MDPs in countable state space: The multichain case

We present an Linear Programming formulation of MDPs with countable state and action spaces and no unichain assumption. This is an extension of the Hordijk and Kallenberg (1979) formulation in finite state and action spaces. We provide sufficient conditions for both existence of optimal solutions to the primal LP program and absence of duality gap. Then, existence of a (possibly randomized) average optimal policy is also guaranteed. Existence of a stationary average optimal deterministic policy is also investigated.     

Modelling and system identification of active magnetic bearing systems

Active magnetic bearing (AMB) systems have recently attracted much attention in the rotating machinery industry due to their advantages over traditional bearings such as fluid film and rolling element bearings. The AMB control system must provide robust performance over a wide range of machine operating conditions and over the machine lifetime in order to make this technology commercially viable. An accurate plant model for AMB systems is essential for the aggressive design of control systems. In this paper, we propose two approaches to obtain accurate AMB plant models for the purpose of control design: physical modelling and system identification. The former derives a model based upon the underlying physical principles. The latter uses input – output data without explicitly resorting to physical principles. For each problem, a brief summary of the theoretical derivation and assumptions is given. Experimental results based on data collected from an AMB test facility at the United Technologies Research Center provide a vehicle for a comparison of the two approaches.     

A low-order active fault-tolerant state space self-tuner for the unknown sampled-data nonlinear singular system using OKID and modified ARMAX model-based system identification

In this paper, we present two control schemes for the unknown sampled-data nonlinear singular system. One is an observer-based digital redesign tracker with the state-feedback gain and the feed-forward gain based on off-line observer/Kalman filter identification (OKID) method. The presented control scheme is able to make the unknown sampled-data nonlinear singular system to well track the desired reference signal. The other is an active fault tolerance state-space self-tuner using the OKID method and modified autoregressive moving average with exogenous inputs (ARMAX) model-based system identification for unknown sampled-data nonlinear singular system with input faults. First, one can apply the off-line OKID method to determine the appropriate (low-) order of the unknown system order and good initial parameters of the modified ARMAX model to improve the convergent speed of recursive extended-least-squares (RELS) method. Then, based on modified ARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown sampled-data nonlinear singular system with immeasurable system state. Moreover, in order to overcome the interference of input fault, one can use a fault-tolerant control scheme for unknown sampled-data nonlinear singular system by modifying the conventional self-tuner control (STC). The presented method can effectively cope with partially abrupt and/or gradual system input faults. Finally, some illustrative examples including a real circuit system are given to demonstrate the effectiveness of the presented design methodologies.     

Real-coded genetic algorithm for system identification and controller tuning

This paper presents an application of real-coded genetic algorithm (RGA) for system identification and controller tuning in process plants. The genetic algorithm is applied sequentially for system identification and controller tuning. First GA is applied to identify the changes in system parameters. Once the process parameters are identified, the optimal controller parameters are identified using GA. In the proposed genetic algorithm, the optimization variables are represented as floating point numbers. Also, cross over and mutation operators that can directly deal with the floating point numbers are used. The proposed approach has been applied for system identification and controller tuning in nonlinear pH process. The simulation results show that the GA based approach is effective in identifying the parameters of the system and the nonlinearity at various operating points in the nonlinear system.     

Modelling and system identification of an experimental apparatus for anomaly detection in mechanical systems

This paper presents design, modelling and system identification of a laboratory test apparatus that has been constructed to experimentally validate the concepts of anomaly detection in complex mechanical systems. The test apparatus is designed to be complex in itself due to partially correlated interactions amongst its individual components and functional modules. The experiments are conducted on the test apparatus to represent operations of mechanical systems where both dynamic performance and structural durability are critical.     

Parametric solution to the joint system identification and optimization problem

This study is concerned with the simultaneous identification and optimization of static systems. The necessity and the advantages of an integrated approach to the identification and optimization of the system model is established theoretically as well as computationally. A parametric approach to the integrated problem is proven to converge to the integrated problem solution. The general methodology of decomposition of large-scale systems is extended by implementingfeasible decomposition of the joint problem. A multilevel approach is then utilized to successfully solve example problems. Handling the system constraints via a penalty-function technique is shown to be an efficient approach when using the parametric formulation of the joint problem. Numerical results for two example problems are presented using the Univac 1108 digital computer, revealing the economic advantages and disadvantages of the integrated approach to the identification and optimization problems.The authors wish to thank Messieurs I. Lefkowitz, L. S. Lasdon, F. Gembicki, and O. B. Olagundoye for their critique, comments, and suggestions during the course of this study.     

Analysis for the identification of an unknown diffusion coefficient via semigroup approach

This paper presents a semigroup approach for the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient k(u_x) in the inhomogenenous quasi‐linear parabolic equation u_t(x, t)=(k(u_x)u_x(x, t))_x +F(u), with the Dirichlet boundary conditions u(0, t)=ψ₀, u(1, t)=ψ₁ and source function F(u). The main purpose of this paper is to investigate the distinguishability of the input–output mappings Φ[·]:??→C¹[0, T], Ψ[·]:??→C¹[0, T] via semigroup theory. Copyright © 2009 John Wiley & Sons, Ltd.     

Dynamic analysis and system identification of an LCD glass-handling robot driven by a PMSM

In this paper, Hamilton’s principle is employed to derive Lagrange’s equations of an liquid crystal display (LCD) glass-handling robot driven by a permanent magnet synchronous motor (PMSM). The robot has three arms driven by two timing belts. The dynamic formulations can be expressed by one and four independent variables, which are named as the rigid and flexible models, respectively. In order to verify the dynamic formulation is correct, we reduce the flexible model to the rigid one under some assumptions. In this paper, we adopt the real-coded genetic algorithm (RGA) to identify all the parameters of the robot and PMSM simultaneously. It is found that the RGA can identify system parameters which are difficult to be measured in practical problems, for examples, the inductance, stator resistance, motor torque constant, damping coefficient of the motor and timing belts. In numerical simulations, vibrations due to flexibility of the timing belts are investigated for the angular displacements, speeds, accelerations of arms, and the horizontal and vertical displacements of the robot. The angular displacements of the robot arm and the translational positions of the robot end are obtained in the numerical simulations and experimental results. From their comparisons, it is demonstrated that identification results of the dynamic model with four independent variables present the better matching with experimental results of the system.     

Real-coded Genetic Algorithm for system identification and tuning of a modified Model Reference Adaptive Controller for a hybrid tank system

Modeling and controlling of level process is one of the most common problems in the process industry. As the level process is nonlinear, Model Reference Adaptive Control (MRAC) strategy is employed in this paper. To design an MRAC with equally good transient and steady state performance is a challenging task. The main objective of this paper is to design an MRAC with very good steady-state and transient performance for a nonlinear process such as the hybrid tank process. A modification to the MRAC scheme is proposed in this study. Real-coded Genetic Algorithm (RGA) is used to tune off-line the controller parameters. Three different versions of MRAC and also a Proportional Integral Derivative (PID) controller are employed, and their performances are compared by using MATLAB. Input–output data of a coupled tank setup of the hybrid tank process are obtained by using Lab VIEW and a system identification procedure is carried out. The accuracy of the resultant model is further improved by parameter tuning using RGA. The simulation results shows that the proposed controller gives better transient performance than the well-designed PID controller or the MRAC does; while giving equally good steady-state performance. It is concluded that the proposed controllers can be used to achieve very good transient and steady state performance during the control of any nonlinear process.     

Combining evolutionary and stochastic gradient techniques for system identification

In the present contribution, a novel method combining evolutionary and stochastic gradient techniques for system identification is presented. The method attempts to solve the AutoRegressive Moving Average (ARMA) system identification problem using a hybrid evolutionary algorithm which combines Genetic Algorithms (GAs) and the Least Mean Squares LMS algorithm. More precisely, LMS is used in the step of the evaluation of the fitness function in order to enhance the chromosomes produced by the GA. Experimental results demonstrate that the proposed method manages to identify unknown systems, even in cases with high additive noise. Furthermore, it is observed that, in most cases, the proposed method finds the correct order of the unknown system without using a lot of a priori information, compared to other system identification methods presented in the literature. So, the proposed hybrid evolutionary algorithm builds models that not only have small MSE, but also are very similar to the real systems. Except for that, all models derived from the proposed algorithm are stable.     

A novel 2D partial unwinding adaptive Fourier decomposition method with application to frequency domain system identification

This paper proposes a two‐dimensional (2D) partial unwinding adaptive Fourier decomposition method to identify 2D system functions. Starting from Coifman in 2000, one‐dimensional (1D) unwinding adaptive Fourier decomposition and later a type called unwinding AFD have been being studied. They are based on the Nevanlinna factorization and a maximal selection. This method provides fast‐converging rational approximations to 1D system functions. However, in the 2D case, there is no genuine unwinding decomposition. This paper proposes a 2D partial unwinding adaptive Fourier decomposition algorithm that is based on algebraic transforms reducing a 2D case to the 1D case. The proposed algorithm enables rational approximations of real coefficients to 2D system functions of real coefficients. Its fast convergence offers efficient system identification. Numerical experiments are provided, and the advantages of the proposed method are demonstrated.     

The auxiliary principle and an algorithm for a system of generalized set-valued mixed variational-like inequality problems in Banach spaces

In this paper, we introduce and study a new system of generalized set-valued mixed variational-like inequality problems (SGSMVLIP) and its related auxiliary problems in reflexive Banach spaces. The auxiliary principle technique is applied to study the existence and an iterative algorithm of solutions for the system of generalized set-valued mixed variational-like inequality problems. At first, the existence and uniqueness of solutions of the auxiliary problems for (SGSMVLIP) is shown. Next, an iterative algorithm for solving (SGSMVLIP) is constructed by using the existence and uniqueness result. Finally, we prove the existence of solutions of (SGSMVLIP) and discuss the convergence analysis of the algorithm. These results improve, unify and generalize many corresponding known results given in the literature.     

A queueing system with random server capacity and multiple control

The authors study queueing, input and output processes in a queueing system with bulk service and state dependent service delay. The input flow of customers, modulated by a semi-Markov process, is served by a single server that takes batches of a certain fixed size if available or waits until the queue accumulates enough customers for service. In the latter case, the batch taken for service is of random size dependent on the state of the system, while service duration depends both on the state of the system and on the batch size taken. The authors establish a necessary and sufficient condition for equilibrium of the system and obtain the following results: Explicit formulas for steady state distribution of the queueing process, intensity of the input and output processes, and mean values of idle and busy periods. They employ theory of semi-regenerative processes and illustrate the results by a number of examples. In one of them an optimization problem is discussed.     

On the Stokes system and on the biharmonic equation in the half‐space: an approach via weighted Sobolev spaces

In this paper, we investigate the Stokes system and the biharmonic equation in a half‐space of ?ⁿ. Our approach rests on the use of a family of weighted Sobolev spaces as a framework for describing the behaviour at infinity. A complete class of existence, uniqueness and regularity results for both the problems is proved. The proofs are mainly based on the principle of reflection. Copyright © 2002 John Wiley & Sons, Ltd.