A behavioral approach to the control of discrete linear repetitive processes

This paper formulates the theory of linear discrete time repetitive processes in the setting of behavioral systems theory. A behavioral, latent variable model for repetitive processes is developed and for the physically defined inputs and outputs as manifest variables, a kernel representation of their behavior is determined. Conditions for external stability and controllability of the behavior are then obtained. A sufficient condition for stabilizability is also developed for the behavior and it is shown under a mild restriction that, whenever the repetitive system is stabilizable, a regular constant output feedback stabilizing controller exists. Next, a notion of eigenvalues is defined for the repetitive process under an action of a closed-loop controller. It is then shown how under controllability of the original repetitive process, an arbitrary assignment of eigenvalues for the closed-loop response can be achieved by a constant gain output feedback controller under the above restriction. These results on the existence of constant gain output feedback controllers are among the most striking properties enjoyed by repetitive systems, discovered in this paper. Results of this paper utilize the behavioral model of the repetitive process which is an analogue of the 1D equivalent model of the dynamics studied in earlier work on these processes.     

Polynomial equation approach to exact model matching problem in multivariable linear systems

A new procedure for solving exact model matching problems in multivariable linear systems is presented. The procedure consists of solving a linear polynomial matrix equation. Conditions for existing dynamical, stable and least order solutions of the problem are given. It is a generalization for multivariable linear systems of Kucera's (1981) approach for single-input-single-output (SISO) systems.     

A piecewise switched linear approach for traffic flow modeling

Traffic modeling is a key step in several intelligent transportation systems (ITS) applications. This paper regards the traffic modeling through the enhancement of the cell transmission model. It considers the traffic flow as a hybrid dynamic system and proposes a piecewise switched linear traffic model. The latter allows an accurate modeling of the traffic flow in a given section by considering its geometry. On the other hand, the piecewise switched linear traffic model handles more than one congestion wave and has the advantage to be modular. The measurements at upstream and downstream boundaries are also used in this model in order to decouple the traffic flow dynamics of successive road portions. Finally, real magnetic sensor data, provided by the performance measurement system on a portion of the Californian SR60-E highway are used to validate the proposed model.     

A new modeling approach for the biobjective exact optimization of satellite payload configuration

Communication satellites have the crucial role to forward signals to customers. They filter and amplify uplink signals coming from Earth stations to improve the signal quality before reaching customers. These operations are performed by the payload component of the satellite that embeds reconfigurable components (e.g., switches). These components route signals to appropriate signal processing components (e.g., amplifiers, filters) and lead amplified signals to the output antenna. In order to route the channels that compose signals, satellite engineers can remotely modify switch states. These are typically updated when one or more new channels must be connected or when failures occur. However, satellites embed always more switches to answer customer demands, which makes their reconfiguration time consuming and error prone without appropriate decision aid tools. Power transmission is a crucial objective to ensure a maximum quality of service at reasonable cost. This is why satellite operators aim at minimizing incoming power signals while guaranteeing a maximum factor of amplification at the output antenna. This problem is referred to as the “satellite payload power problem.” Previous works have outlined the difficulty to solve exactly large instances of this problem. This work proposes to improve the existing mathematical formulation of the switch network. We show that it can be modeled as a static network and switch states can be deduced after optimization, thus limiting the combinatorial explosion. Computational experiments on different sizes of realistic instances using the adaptive ε‐constraint method demonstrate the computational time gain with this new model and the possibility to solve larger instances.     

A variational integrators approach to second order modeling and identification of linear mechanical systems

The theory of variational integration provides a systematic procedure to discretize the equations of motion of a mechanical system, preserving key properties of the continuous time flow. The discrete-time model obtained by variational integration theory inherits structural conditions which in general are not guaranteed under general discretization procedures. We discuss a simple class of variational integrators for linear second order mechanical systems and propose a constrained identification technique which employs simple linear transformation formulas to recover the continuous time parameters of the system from the discrete-time identified model. We test this approach on a simulated eight degrees of freedom system and show that the new procedure leads to an accurate identification of the continuous-time parameters of second-order mechanical systems starting from discrete measured data.     

A linear algebra approach to OLAP

Inspired by the relational algebra of data processing, this paper addresses the foundations of data analytical processing from a linear algebra perspective. The paper investigates, in particular, how aggregation operations such as cross tabulations and data cubes essential to quantitative analysis of data can be expressed solely in terms of matrix multiplication, transposition and the Khatri–Rao variant of the Kronecker product. The approach offers a basis for deriving an algebraic theory of data consolidation, handling the quantitative as well as qualitative sides of data science in a natural, elegant and typed way. It also shows potential for parallel analytical processing, as the parallelization theory of such matrix operations is well acknowledged.     

A systemic approach to process modeling

This article presents a system's view of a common sense management model for systems (COSMOS) [1]. Salient features of COSMOS are introduced through the unfolding story of process development of a hypothetical corporation called IM Co. This systemic view models the dynamic complexity of a system or organization so that inerrelationships, rather than things, patterns of changes, rather than snapshots, are captured. COSMOS views changes as an ongoing opportunity and provides guidance for system changes to be performed in small steps. However, these small steps can build a long lever that is capable of producing dramatic effects. When performing changes, essential trade-offs have to be considered. COSMOS provides three perspectives—activity, communication, and infrastructure—of a process to assist managers in dealing with these trade-offs. The model also includes a generic two-level hierarchy—control and execution levels—to keep balance among the three perspectives.Small Is Beautiful — Ernst Fredrich Schumacher Give me a lever long enough ... and single-handed I can move the world — Archimedes     

A new approach to fuzzy modeling

This paper proposes a new approach to fuzzy modeling. The suggested fuzzy model can express a given unknown system with a few fuzzy rules as well as Takagi and Sugeno's model (1985), because it has the same structure as that of Takagi and Sugeno's model. It is also as easy to implement as Sugeno and Yasukawa's model (1993) because its identification mimics the simple identification procedure of Sugeno and Yasukawa's model. The suggested algorithm is composed of two steps: coarse tuning and fine tuning. In coarse tuning, fuzzy C-regression model (FCRM) clustering is used, which is a modified version of fuzzy C-means (FCM). In fine tuning, gradient descent algorithm is used to precisely adjust parameters of the fuzzy model instead of nonlinear optimization methods used in other models. Finally, some examples are given to demonstrate the validity of this algorithm     

A simple approach to system modeling

This paper describes an approach to system modeling based on heuristic mean value analysis. The virtues of the approach are conceptual simplicity and computational efficiency. The approach can be applied to a large variety of systems, and can handle features such as resource constraints, tightly and loosely coupled multiprocessors, distributed processing, and certain types of CPU priorities. Extensive validation results are presented, including truly predictive situations. The paper is intended primarily as a tutorial on the method and its applications, rather than as an exposition of research results.     

A simple approach to system modeling

This paper describes an approach to system modeling based on heuristic mean value analysis. The virtues of the approach are conceptual simplicity and computational efficiency. The approach can be applied to a large variety of systems, and can handle features such as resource constraints, tightly and loosely coupled multiprocessors, distributed processing, and certain types of CPU priorities. Extensive validation results are presented, including truly predictive situations. The paper is intended primarily as a tutorial on the method and its applications, rather than as an exposition of research results.     

A formal approach to fuzzy modeling

A formalism for coding fuzzy models of dynamical systems is presented. It is shown that the formalism is rich enough to capture the performance of arbitrary conventional discrete time dynamical systems whose transition maps are polynomials with rational coefficients. The proof of this fact provides a constructive algorithm for generating fuzzy models to arbitrarily closely approximate an arbitrary map on a compact set. Our modeling formalism highlights the similarities between fuzzy systems and hybrid control systems. We hope to be able to exploit these similarities by extending results from the area of hybrid systems to the fuzzy domain and vice versa     

A knowledge-based approach to CIM modeling

This paper discusses issues in building a conceptual modeling approach that has sufficient semantic power to represent the complexities of decision making in CIM systems. To express the information in a conceptual model we make use of an amalgam of powerful paradigms: a hybrid methodology, that integrates the concepts of object-oriented programming, messagepassing semantics, and temporal logic. We further illustrate an example incorporating some of these concepts.     

The exact model-matching problem for linear time-varying systems: an algebraic approach

The exact model-matching problem is formulated and solved for linear time-varying systems. The condition for the existence of a proper solution, which is well known in the time-invariant case, is proven here to still be valid in the time-varying case. The properness is characterized using the Smith-MacMillan form at infinity, recently defined by the authors for the transfer matrices with time-varying coefficients.     

A new approach to fuzzy-neural system modeling

We develop simple but effective fuzzy-rule based models of complex systems from input-output data. We introduce a simple fuzzy-neural network for modeling systems, and we prove that it can represent any continuous function over a compact set. We introduce “fuzzy curves” and use them to: 1) identify significant input variables, 2) determine model structure, and 3) set the initial weights in the fuzzy-neural network model. Our method for input identification is computationally simple and, since we determine the proper network structure and initial weights in advance, we can train the network rapidly. Viewing the network as a fuzzy model gives insight into the real system, and it provides a method to simplify the neural network     

A hierarchical/relational approach to modeling

We describe a hierarchical/relational approach to math programming modeling. The approach transforms free-form generic modeling constructs into linear and nonlinear models which are independent of end-user data structures. The underlying relationships with graph-based interfaces and the inherent aggregation/disaggregation capabilities of the approach are also discussed.The modeling approach will be illustrated with several process industry applications including distribution planning, operations planning, and production scheduling.     

A transformed input-domain approach to fuzzy modeling

This paper presents an explanation of a fuzzy model considering the correlation among components of input data. Generally, fuzzy models have a capability of dividing an input space into several subspaces compared to a linear model. But hitherto suggested fuzzy modeling algorithms have not taken into consideration the correlation among components of sample data and have addressed them independently, which results in an ineffective partition of the input space. In order to solve this problem, this paper proposes a new fuzzy modeling algorithm, which partitions the input space more effectively than conventional fuzzy modeling algorithms by taking into consideration the correlation among components of sample data. As a way to use the correlation and divide the input space, the method of principal component is used. Finally, the results of the computer simulation are given to demonstrate the validity of this algorithm     

A computational approach to modeling commodity markets

We build an agent based computational framework to study large commodity markets. A detailed representation of the consumers, producers and the market is used to study the micro level behavior of the market and its participants. The user can control players’ preferences, their strategies, assumptions of the model, its initial conditions, market elements and trading mechanisms. The first part of the paper describes the computational framework and its three main modules. The later part describes a case study that examines the decentralized market in detail, specifically the computational options available for matching the buyers and suppliers in a synthetic market. The study illustrates the sensitivity of the outcome of various economic variables, such as clearing price, quantity, profits and social welfare, to different matching schemes in a bilateral computational setting. Based on seven different matching orders for the buyers and suppliers, our study shows that the results can vary dramatically for different pairing orders.