An online identification algorithm of unknown time-varying delay and internal multimodel control for discrete non-linear systems

In this paper, an online algorithm is proposed for the identification of unknown time-varying input delay in the case of discrete non-linear systems described by decoupled multimodel. This method relies on the minimization of a performance index based on the error between the real system and the partial internal models outputs. In addition, a decoupled internal multimodel control is proposed for the compensation of discrete non-linear systems with time-varying delay. This control scheme incorporates partial internal model controls. Each partial controller is associated to a specified operating zone of the non-linear system. The switching between these controllers is ensured by a supervisor that contains a set of local predictors. A simulation example is carried out to illustrate the significance of the proposed time-varying delay identification algorithm and the proposed internal multimodel control scheme.     

Model predictive control of nonlinear hybrid systems with discrete inputs employing a hybrid fuzzy model

The paper deals with model predictive control (MPC) of nonlinear hybrid systems with discrete inputs based on reachability analysis. In order to implement a MPC algorithm, a model of the process that we are dealing with is needed. In the paper, a hybrid fuzzy modelling approach is proposed. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for hybrid fuzzy modelling purposes is tackled. An efficient method of identification of the hybrid fuzzy model is also discussed.

An algorithm that is–due to its MPC nature–suitable for controlling a wide spectrum of systems (provided that they have discrete inputs only) is presented.

The benefits of the algorithm employing a hybrid fuzzy model are verified on a batch reactor example. The results suggest that by suitably determining the cost function, satisfactory control can be attained, even when dealing with complex hybrid–nonlinear–stiff systems such as the batch reactor.

Finally, a comparison between MPC employing a hybrid linear model and a hybrid fuzzy model is carried out. It has been established that the latter approach clearly outperforms the approach where a linear model is used.     

基于混合时滞观测器的混合反馈控制

对于一类具有状态和有限自动机输出时滞的离散混合系统,研究基于混合时滞观测器的混合反馈控制问题.通过系统线性部分和离散事件部分的Lyapunov函数构造了整个时滞系统的混合Lyapunov函数,进一步,给出混合反馈控制的设计方法且证明了闭环系统的稳定性.仿真例子说明该方法的有效性.     

Robust state estimation and fault diagnosis for uncertain hybrid nonlinear systems

Robust state estimation and fault diagnosis are challenging problems in the research of hybrid systems. In this paper, a novel robust hybrid observer is proposed for a class of uncertain hybrid nonlinear systems with unknown mode transition functions, model uncertainties and unknown disturbances. The observer consists of a mode observer for discrete mode estimation and a continuous observer for continuous state estimation. It is shown that the mode can be identified correctly and the continuous state estimation error is exponentially uniformly bounded. Robustness to unknown transition functions, model uncertainties and disturbances can be guaranteed by disturbance decoupling and selecting proper thresholds. The transition detectability and mode identifiability conditions are rigorously analyzed. Based on the robust hybrid observer, a robust fault diagnosis scheme is presented for faults modeled as discrete modes with unknown transition functions, and the analytical properties are investigated. Simulations of a hybrid three-tank system demonstrate that the proposed approach is effective.     

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 Event Occurrence Rules based Compact Modeling Formalism for a Class of Discrete Event Systems

The analysis, failure diagnosis and control of discrete event systems (DESs) requires an accurate model of the system. In this paper we present a methodology which makes the task of modeling DESs considerably less cumbersome, less error prone, and more user-friendly than it usually is. In doing so we simplify the modeling formalism of [4, 5], proposed for obtaining valid models of complex discrete event systems, by eliminating ‘precedence relations’, and capturing them as part of the ‘event occurrence rules’. Under the new modeling formalism the size of the system model is polynomial in the number of signals; whereas the number of states in the commonly used automata models is exponential in the number of signals. We present automated techniques for deriving an automaton model from the model in the proposed formalism. We illustrate the modeling formalism using examples drawn from manufacturing and process control systems.     

A randomized method for the identification of switched NARX systems

The identification of switched systems is a complex optimization problem that involves both continuous (parametrizations of the local models, a.k.a. modes) and discrete variables (model structures, switching signal). In particular, the combinatorial complexity associated with the estimation of the switching signal grows exponentially with the number of samples, which makes data segmentation (i.e. estimating the number and location of mode switchings, and the mode sequence) a challenging problem. In this work, we extend a previously developed randomized approach for the identification of switched systems to encompass the estimation of the switching locations. The method operates by extracting samples from a probability distribution of switched models, and gathering information from the associated model performances to update the distribution, until convergence to a limit distribution associated to a specific model. A suitable probability distribution is employed to represent the likelihood of a mode switching at a certain time, and the update process is designed to correct the switching locations and remove redundant switchings. The proposed algorithm has been compared to existing state-of-the-art methods and has been tested on various benchmark examples, to demonstrate its effectiveness.     

Hybrid dynamical systems with controlled discrete transitions

This invited survey focuses on a new class of systems–hybrid dynamical systems with controlled discrete transitions. A type of system behavior referred to as the controlled infinitesimal dynamics is shown to arise in systems with widely divergent dynamic structures and application domains. This type of behavior is demonstrated to give rise to a new dynamic mode in hybrid system evolution–a controlled discrete transition. Conceptual and analytical frameworks for modeling of and controller synthesis for such transitions are detailed for two systems classes: one requiring bumpless switching among controllers with different properties, and the other–exhibiting single controlled impacts and controlled impact sequences under collision with constraints. The machinery developed for the latter systems is also shown to be capable of analysing the behavior of difficult to model systems characterized by accumulation points, or Zeno-type behavior, and unique system motion extensions beyond them in the form of sliding modes along the constraint boundary. The examples considered demonstrate that dynamical systems with controlled discrete transitions constitute a general class of hybrid systems.     

Discrete quantity approach to continuous simulation modelling

Traditionally, simulation executives have been divided into discrete-event and continuous-time executives. Some systems require modelling using both discrete and continuous parts. Hybrid simulation executives have the drawback that they treat discrete and continuous parts of a system in completely different ways. Here it is shown how continuous models may be simulated using a discrete executive: the novel discrete quantity approach (DQA). The method could also be used to allow a continuous part to be added to a discrete model without the need for a hybrid executive.     

Modelling and Verification using Linear Hybrid Automata -- a Case Study

This paper discusses the use of hybrid automata to specify and verify embedded distributed systems, that consist of both discrete and continuous components. The basis of the evaluation is an automotive control system, which controls the height of an automobile by pneumatic suspension. It has been proposed by BMW AG as a case study taken from a current industrial development. Essential parts of the system have been modelled as hybrid automata and for appropiate ions several safety properties have been verified. The verification has been performed using HYTECH, a symbolic model checker for linear hybrid automata. The paper discusses the general appropiateness of hybrid automata to specify hybrid systems as well as advantages and drawbacks of the applied model-checking techniques.     

Balanced truncation for linear switched systems

We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians corresponding to each active discrete mode by solving systems of coupled Lyapunov equations. Depending on the type, each such Gramian corresponds to the energy associated to all possible switching scenarios that start or, respectively end, in a particular operational mode. In order to guarantee that hard to control and hard to observe states are simultaneously eliminated, we construct a transformed system, whose Gramians are equal and diagonal. Then, by truncation, directly construct reduced order models. One can show that these models preserve some properties of the original model, such as stability and that it is possible to obtain error bounds relating the observed output, the control input and the entries of the diagonal Gramians.     

Hybrid port–Hamiltonian systems: From parameterized incidence matrices to hybrid automata

This paper shows how to formally design a hybrid automaton model for a wide class of dissipative physical systems with sources and switching topology. This method is based on a mathematical representation of the dynamic network graph and of its dual graph, using the hybrid incidence matrix, and on a constructive method for analyzing admissible and constrained configurations. The port–Hamiltonian representation associated with the set of hybrid system configurations, parameterized by the discrete state of the switches, is synthesized to be part of the hybrid automaton of the system. This is a further step towards a generic control synthesis for physical switching systems.     

Recursive state estimation for hybrid systems

The paper deals with recursive state estimation for hybrid systems. An unobservable state of such systems is changed both in a continuous and a discrete way. Fast and efficient online estimation of hybrid system state is desired in many application areas. The presented paper proposes to look at this problem via Bayesian filtering in the factorized (decomposed) form. General recursive solution is proposed as the probability density function, updated entry-wise. The paper summarizes general factorized filter specialized for (i) normal state-space models; (ii) multinomial state-space models with discrete observations; and (iii) hybrid systems. Illustrative experiments and comparison with one of the counterparts are provided.     

Identification of Parameters of Nonlinear Dynamical Systems Simulated by Volterra Polynomials

We study the identification methods for the nonlinear dynamical systems described by Volterra series. One of the main problems in the dynamical system simulation is the problem of the choice of the parameters allowing the realization of a desired behavior of the system. If the structure of the model is identified in advance, then the solution to this problem closely resembles the identification problem of the system parameters. We also investigate the parameter identification of continuous and discrete nonlinear dynamical systems. The identification methods in the continuous case are based on application of the generalized Borel Theorem in combination with integral transformations. To investigate discrete systems, we use a discrete analog of the generalized Borel Theorem in conjunction with discrete transformations. Using model examples, we illustrate the application of the developed methods for simulation of systems with specified characteristics.     

Mixed model identification for linear time‐invariant systems with mixed noises in frequency domain

In this paper, we present a new method for frequency domain identification of discrete linear time‐invariant systems. We take consideration of the case where the output noises are mixed or unknown. In order to deal with this problem, a new mixed model structure is used correspondingly. The augmented Lagrangian method (ALM) is combined in selection of poles for the shifted Cauchy kernels to get solutions to the optimal problem. Simulations show the proposed method can get efficient approximation to the original systems.     

Problems with the estimation of stochastic differential equations using structural equations models

The present paper deals with the identification and maximum likelihood estimation of systems of linear stochastic differential equations using panel data. So we only have a sample of discrete observations over time of the relevant variables for each individual. A popular approach in the social sciences advocates the estimation of the “exact discrete model” after a reparameterization with LISREL or similar programs for structural equations models. The “exact discrete model” corresponds to the continuous time model in the sense that observations at equidistant points in time that are generated by the latter system also satisfy the former. In the LISREL approach the reparameterized discrete time model is estimated first without taking into account the nonlinear mapping from the continuous to the discrete time parameters. In a second step, using the inverse mapping, the fundamental system parameters of the continuous time system in which we are interested, are inferred. However, some severe problems arise with this “indirect approach”. First, an identification problem may arise in multiple equation systems, since the matrix exponential function denning some of the new parameters is in general not one‐to‐one, and hence the inverse mapping mentioned above does not exist. Second, usually some sort of approximation of the time paths of the exogenous variables is necessary before the structural parameters of the system can be estimated with discrete data. Two simple approximation methods are discussed. In both approximation methods the resulting new discrete time parameters are connected in a complicated way. So estimating the reparameterized discrete model by OLS without restrictions does not yield maximum likelihood estimates of the desired continuous time parameters as claimed by some authors. Third, a further limitation of estimating the reparameterized model with programs for structural equations models is that even simple restrictions on the original fundamental parameters of the continuous time system cannot be dealt with. This issue is also discussed in some detail. For these reasons the “indirect method” cannot be recommended. In many cases the approach leads to misleading inferences. We strongly advocate the direct estimation of the continuous time parameters. This approach is more involved, because the exact discrete model is nonlinear in the original parameters. A computer program by Hermann Singer that provides appropriate maximum likelihood estimates is described.     

Nonlinear parametric models from volterra kernels measurements

Methods for nonlinear system identification are often classified, based on the employed model form, into parametric (nonlinear differential or difference equations) and nonparametric (functional expansions). These methods exhibit distinct sets of advantages and disadvantages that have motivated comparative studies and point to potential benefits from combined use. Fundamental to these studies are the mathematical relations between nonlinear differential (or difference, in discrete time) equations (NDE) and Volterra functional expansions (VFE) of the class of nonlinear systems for which both model forms exist, in continuous or discrete time. Considerable work has been done in obtaining the VFE's of a broad class of NDE's, which can be used to make the transition from nonparametric models (obtained from experimental input-output data) to more compact parametric models. This paper presents a methodology by which this transition can be made in discrete time. Specifically, a method is proposed for obtaining a parametric NARMAX (Nonlinear Auto-Regressive Moving-Average with exogenous input) model from Volterra kernels estimated by use of input-output data.     

Hybrid control of a multicellular converter

In this paper a new switching scheme for modelling multicellular converters is proposed. We consider a converter with two cells which is represented as a hybrid system with four modes of operation. The operation modes of the system are governed by the adjustable reference voltage and a reference current, which are calculated by means of an energy balance principle. This study is justified by the hybrid behavior of the system considered, i.e., it presents discrete and continuous variables which represent the state of the switches and the evolution of the current and the terminal voltage of the floating condensers, respectively. The synthesis of the control is based on the determination of the switching sequences, ensuring the stability and the integrity of the switches.