A new decentralized implicit adaptive regulator for large-scale systems described by discrete-time state-space mathematical models

In this paper, we treat the problem of decentralized implicit adaptive regulation for large-scale stochastic systems composed into a set of interconnected systems that are described by discrete-time state-space mathematical models with unknown parameters. The key idea in the decentralized regulation method is to design local regulator using only local information such that the state of each interconnected system is regulated to a certain constant reference signal. The main contribution is the proposition of a decentralized implicit adaptive regulator based on state-feedback strategy that can be applied to stochastic interconnected systems with unknown parameters. Furthermore, the practical implementation of the proposed decentralized implicit adaptive regulator can be made easily (low-cost implementation of the electronic components, short computation of the decentralized control law, etc.). A theorem is established and proved which gives sufficient stability conditions of the resulting closed-loop interconnected systems by using the Lyapunov method. An example of numerical simulation is treated to test the performance of the proposed decentralized implicit adaptive regulator.     

Error models for stable hybrid adaptive systems

This paper presents several stable adaptive algorithms for the control of hybrid and discrete systems in which the control parameters are adjusted at rates slower than those at which the systems operate. Continuous algorithms of an integral type, recently suggested in the literature [5] are also shown to belong to this class. From a practical standpoint, the infrequent adjustment of the control parameters makes for more robust adaptive control while from a theoretical point of view, the algorithms are attractive since they provide a unified framework for the design of continuous, hybrid, and discrete adaptive systems. Simulation results are included to indicate the type of responses that can be expected using the different algorithms.     

On mathematical models of the service networks

Queueing theory, as a part of probability theory, has classical problems and well-established mathematical apparatus. In this short review we follow queueing theory relations with other mathematical disciplines and different applied problems.     

Parametric models of linear multivariable systems for adaptive control

This paper presents a parametrization method for direct adaptive control of linear multivariable systems with strictly proper discrete-time or continuous-time transfer functions. The necessary a priori information is shown to be a diagonal matrix with the noninvertible zeros of the Smith form and appropriate polynomial degrees.     

Decentralized adaptive control of interconnected systems with reduced-order models

The adaptive control of interconnected systems whose subsystems possess slow and fast modes is investigated in the presence of external disturbances. A simple example is first used to show that a decentralized adaptive controller can become unstable due to the unmodeled interconnections and/or neglected parasitics. An approach is then developed for stabilization and tracking using decentralized adaptive controllers with modified adaptive laws. Sufficient conditions are obtained under which a region of attraction exists for boundedness and exponential convergence of the state/parameter errors to a small residual set. The size of the region of attraction depends on the frequency range of the local parasitics in such a way that if all the local parasitics become infinitely fast, the region of attraction becomes the whole space.     

Coupling control and human factors in mathematical models of complex systems

It is known that with the increasing complexity of technological systems that operate in dynamically changing environments and require human supervision or a human operator, the relative share of human errors is increasing across all modern applications. This indicates that in the analysis and control of such systems, human factors should not be eliminated by conventional formal mathematical methodologies. Instead, they must be incorporated into the modelling framework.In this paper we analyse mathematically how such factors can be effectively incorporated into the analysis and control of complex systems. As an example, we focus our discussion around one of the key problems in the intelligent transportation systems (ITS) theory and practice, the problem of speed control, considered here as a decision making with limited information available. The problem is cast mathematically in the general framework of control problems and is treated in the context of dynamically changing environments where control is coupled to human factors. Since in this case control might not be limited to a small number of control settings, as it is often assumed in the control literature, serious difficulties arise in the solution of this problem. We demonstrate that the problem can be reduced to a set of Hamilton–Jacobi–Bellman equations where human factors are incorporated via estimations of the system Hamiltonian. In the ITS context, these estimations can be obtained with the use of on-board equipment like sensors/receivers/actuators, in-vehicle communication devices, etc. The proposed methodology provides a way to integrate human factors into the solving process of the models for other complex dynamic systems.     

Parametric estimation of interconnected nonlinear systems described by input-output mathematical models

In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems,which are composed of several interconnected nonlinear subsystems. Each subsystem can be described by an input-output nonlinear discrete-time mathematical model, with unknown, but constant or slowly time-varying parameters. Then, two recursive estimation methods are used to solve the parametric estimation problem for the considered class of the interconnected nonlinear systems. These methods are based on the recursive least squares techniques and the prediction error method. Convergence analysis is provided using the hyper-stability and positivity method and the differential equation approach. A numerical simulation example of the parametric estimation of a stochastic interconnected nonlinear hydraulic system is treated.     

Analytic models of adaptive load sharing schemes in distributedreal-time systems

In a distributed real-time system, nonuniform task arrivals may temporarily overload some nodes while leaving some other nodes idle. As a result, some of the tasks on an overloaded node may miss their deadlines even if the overall system has the capacity to meet the deadlines of all tasks. A decentralized, dynamic load sharing (LS) scheme has been proposed as a solution to this problem. Analytic queuing models to comparatively evaluate this LS scheme as well as three other schemes-no LS, LS with random selection of a receiver node, and LS with perfect information- are developed. The evolution of a node's load state is modeled as a continuous-time semi-Markov process, where cumulative execution time (CET), rather than the commonly-used queue length (QL), is employed to describe the workload of a node. The proposed scheme is compared against other LS schemes. The validity of analytic models is checked with simulations. Both analytic and simulation results indicate that by using judicious exchange/use of state information and Bayesian decision mechanism, the proposed scheme makes a significant improvement over other existing LS schemes in minimizing the probability of dynamic failure     

多变量周期系统的多模型二阶段自适应控制

对于一类参数未知的多变量周期系统,传统自适应控制方法存在参数收敛慢的问题,导致系统暂态响应差、控制效果不理想.因此,本文针对多变量周期系统设计了多模型二阶段自适应控制器.首先根据先验知识,确定不确定区域范围,并在不确定区域内建立多个自适应模型.然后根据李雅普诺夫理论得到第一阶段辨识方程;在第二阶段中,充分考虑辨识误差并...     

Robust adaptive control of nonlinear systems represented by input-output models

A robust adaptive control scheme is proposed for a class of nonlinear systems represented by input-output models with unmodeled dynamics. The scheme does not require the unknown parameters to satisfy the linear dependence condition and parameter estimation is not needed. With the proposed control scheme, all the variables in the closed-loop system are bounded in the presence of unmodeled dynamics and bounded disturbances. Moreover, the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriately.     

Particle systems for adaptive, isotropic meshing of CAD models

We present a particle-based approach for generating adaptive triangular surface and tetrahedral volume meshes from computer-aided design models. Input shapes are treated as a collection of smooth, parametric surface patches that can meet non-smoothly on boundaries. Our approach uses a hierarchical sampling scheme that places particles on features in order of increasing dimensionality. These particles reach a good distribution by minimizing an energy computed in 3D world space, with movements occurring in the parametric space of each surface patch. Rather than using a pre-computed measure of feature size, our system automatically adapts to both curvature as well as a notion of topological separation. It also enforces a measure of smoothness on these constraints to construct a sizing field that acts as a proxy to piecewise-smooth feature size. We evaluate our technique with comparisons against other popular triangular meshing techniques for this domain.     

On the adaptive stabilization of linear systems

The problem of adaptively stabilizing a linear system to zero is addressed. A new result is presented, showing that a finite family of linear systems is adaptively stabilizable if and only if the family is simultaneously stabilizable in the wellknown algebraic sense. This result is all the more surprising as the observations available consist of the signal corrupted by additive white Gaussian noise.     

Qualitative modelling for automatic identification of mathematical models of chemical reaction systems

Mathematical modelling and identification of systems, where the structure of some equations is unknown, is a difficult task. As this is usually done manually by a human expert, it is associated with terms such as experience and intuition. However, an experienced modeller will have a clear procedure to deduce a model. In a first step he or she will analyse experimental data on a qualitative level. Only those models are then tested in a quantitative identification which pass the qualitative check. In this contribution this efficient procedure is translated into methods. A tool TAM-C is introduced which automatically finds structures and parameters of formal kinetics. The main part of the contribution is dedicated to the qualitative preselection of possible model candidates and the application to an industrial process.     

Evolution of mathematical models of chaotic systems based on multiobjective genetic programming

This work is concerned with the identification of models for nonlinear dynamical systems using multiobjective evolutionary algorithms. Systems modelling involves the processes of structure selection, parameter estimation, model performance and model validation and involves a complex solution space. Evolutionary Algorithms (EAs) are search and optimisation tools founded on the principles of natural evolution and genetics, which are suitable for a wide range of application areas. Due to the versatility of these tools and motivated by the versatility of genetic programming (GP), this evolutionary paradigm is proposed for this modelling problem. GP is then combined with a multiobjective function definition scheme. Multiobjective genetic programming (MOGP) is applied to multiple, conflicting objectives and yields a set of candidate parsimonious and valid models, which reproduce the original system behaviour. The MOGP approach is then demonstrated as being applicable for system modelling with chaotic dynamics. The circuit introduced by Chua, being one of the most popular benchmarks for studying nonlinear oscillations, and the Duffing–Holmes oscillator are the systems to test the evolutionary-based modelling approach introduced in this paper.     

Improving transient response of adaptive control systems usingmultiple models and switching

A well-known problem in adaptive control is the poor transient response which is observed when adaptation is initiated. In this paper we develop a stable strategy for improving the transient response by using multiple models of the plant to be controlled and switching between them. The models are identical except for initial estimates of the unknown plant parameters. The control to be applied is determined at every instant by the model which best approximates the plant. Simulation results are presented to indicate the improvement in performance that can be achieved     

Deriving software architectural models from requirements models for adaptive systems: the STREAM-A approach

Some quality attributes are known to have an impact on the overall architecture of a system, so that they are required to be properly handled from the early beginning of the software development. For example, adaptability is a key concern for autonomic and adaptive systems, which brings to them the capability to alter their behavior in response to changes on their surrounding environments. In this paper, we propose a Strategy for Transition between Requirements and Architectural Models for Adaptive systems (STREAM-A). In particular, we use goal models based on the i* (i-Star) framework to support the design and evolution of systems that require adaptability. To obtain software architectures for such systems, the STREAM-A approach uses model transformations from i* models to architectural models expressed in Acme. Both the requirements and the architectural model are refined to accomplish the adaptability requirement.     

On passivity and adaptive stabilization of nonlinear systems

This paper is about the adaptive stabilization of nonlinear systems which are feedback equivalent to passive systems. A calculation is provided showing that the matching condition assumed by Ortega-Rodriguez (1990) is not necessary. Examples are also discussed of adaptively stabilizable systems for which known conditions are not verified     

On sampled-data models for nonlinear systems

Models for deterministic continuous-time nonlinear systems typically take the form of ordinary differential equations. To utilize these models in practice invariably requires discretization. In this paper, we show how an approximate sampled-data model can be obtained for deterministic nonlinear systems such that the local truncation error between the output of this model and the true system is of order /spl Delta//sup r+1/, where /spl Delta/ is the sampling period and r is the system relative degree. The resulting model includes extra zero dynamics which have no counterpart in the underlying continuous-time system. The ideas presented here generalize well-known results for the linear case. We also explore the implications of these results in nonlinear system identification.