Oscar A. Esquivel-Flores

On the Preconditioned Quasi-Monte Carlo Algorithm for Matrix Computations

In this paper we present a quasi-Monte Carlo Sparse Approximate Inverse (SPAI) preconditioner. In contrast to the standard deterministic SPAI preconditioners that use the Frobenius norm, Monte Carlo and quasi-Monte Carlo preconditioners rely on stochastic and hybrid algorithms to compute a rough matrix inverse (MI). The behaviour of the proposed algorithm is studied. Its performance is measured and compared with the standard deterministic SPAI and MSPAI (parallel SPAI) approaches and with the Monte Carlo approach. An analysis of the results is also provided.

Bounded communication between nodes of a networked control system as a strategy of scheduling

In a networked control system, several nodes exchange information through a network, to achieve specific control goals and thus increasing network traffic. This affects the overall system performance. Several approaches try to satisfy requirements of both control and communication performance. Particularly, some methodologies have been proposed to save bandwidth. One of such methodologies has been scheduling, which has been studied in depth through the last decade. Commonly, the objective of using scheduling to save bandwidth is to accurately use the computing resources. This paper shows two scheduling strategies, one performing static scheduling and the other carrying out dynamic scheduling, in order to expose the advantages of using dynamic scheduling in an ad hoc implementation. Both strategies execute on a real-time distributed system, and both are able to modify the frequency of transmission as well as the periods of tasks in individual components. Hence, both of them tend to impact on the quality of performance of the system, due to network use. The first scheduling strategy modifies the periods of task, and network access is assigned through a static scheduling algorithm. On the other hand, the second strategy, schedulability, is dynamically achieved by controlling the rate of frequency transmission into a frequency region, bounded by minimum and maximum transmission rates. Numerical simulations are used as implementations of both strategies.

Towards Monte Carlo preconditioning approach and hybrid Monte Carlo algorithms for Matrix Computations

An enhanced version of a stochastic SParse Approximate Inverse (SPAI) preconditioner for general matrices is presented in this paper. This method is used in contrast to the standard deterministic preconditioners computed by the Modified SParse Approximate Inverse Preconditioner (MSPAI). Thus we present a Monte Carlo preconditioner that relies on the use of Markov Chain Monte Carlo (MCMC) methods to compute a rough approximate matrix inverse first, which can further be optimized by an iterative filter process and a parallel refinement, to enhance the accuracy of the inverse and the preconditioner respectively. The advantage of the proposed approach is that finding the sparse Monte Carlo matrix inversion has a computational complexity linear of the size of the matrix, it is inherently parallel and thus can be obtained very efficiently for large matrices and can be used also as an efficient preconditioner while solving systems of linear algebraic equations. The behaviour of the proposed algorithm is studied and its performance measured, evaluated and compared with MSPAI.

Modelling of Networked Control Systems

This chapter shows models for time delays and others network imperfections generated into NCS and how they are integrated into control, scheduling or codesign algorithms. First, a time delay model is presented using a generalized exponential distribution based function with data collect from non-deterministic networks. After, three NCS models are presented, each incorporates information about the network imperfections with the ultimate aim of generating a corrective action. We present models based on control, communication and codesign methodologies. Finally, a neuro-fuzzy identification is presented to model the system states and estimate the parameters of the NCS based on multi-sampling periods.

Design of Networked Control System

This chapter presents the control strategies and codesign based on the NCS models presented in Chap. 2. Three methodologies are proposed focusing on vanishing the perturbations generated by the network, such as time delays larger than a sampling period and lost packets. First, an adaptive fuzzy control is developed according to the scheduling algorithm and the known and bounded time delay, the stategy us a fuzzy model and a LQR control design to modify the control input according to the time delay. A sampling frequency control is presented where the transmission frequiencies are modified into a region according the quality of services into the network. Finally, a codesign strategy is reviewed where the quality of service and the quality of control are trade-off with two fuzzy model, one fuzzy model modifies the input control based on the current sampling period and other fuzzy model modifies the next sampling period based on the time delays and lost packets in a time-lapse.

Introduction to Networked Control Systems

This chapter introduces a brief description of Networked Control Systems. A formal review of this book is given, describing the key issues within each chapter. A review of the strategies present in the literature is made to study and compensate for the network imperfections presenting three main methodologies. The control methodology focuses on generating control signals that counteract the effects of the network imperfections through modelling its dynamics or considering them as uncertainties. The communication methodology aims to improve the transmission of information and minimise imperfections through the scheduling and synchronisation of the nodes present in the network as a function of the system performance. The co-design methodology considers increasing the advantages of the various methodologies with the purpose of increasing system performance and minimising the effects of network imperfections. It is also presented the time delay modelling in nondeterministic networks, the main imperfection of the network. Finally, the maximum allowed transfer interval term is described which is the maximum bound for time imperfections of the network.

Control Strategies and Co-Design of Networked Control Systems: Considering Time Delay Effects

Introduction to Networked Control Systems -- Modelling of Networked Control Systems -- Distributed Systems Modelling -- Design of Networked Control System -- Control Design considering Mobile Computing -- Applications -- Conclusions. .

Control Design Considering Mobile Computing

In this chapter, an extension of distributed systems considering mobile computing is reviewed. First, A review of some scheduling algorithms is presented to get a good approximation to bounded time delays considering the spend time in all stages of communication and compute. A review of the most important algorithms in terms of consensus and routing is presented. A computer network design is presented from a selection of real-time features, scheduler, task handlers, priorities, precedencies and consensus. Finally, a brief review of control design for mobile conditions is presented with the most representative algorithms in the literature.

Distributed Systems Modelling

Distributed systems have a lot of applications, commonly with multitasks where the information exchange is high through a communication network, this exchange presents inherent time delays that degrade the system. For obtaining an acceptable performance in the distributed system, time delays need to be taken into consideration during design. This chapter is devoted to reviewing some representations of time delays in function of some features as the operative system, network, scheduling. These include the scalability, concurrency, feasibility and extensibility. Several situations are reviewed, such as aperiodic communications or consensus needs, among other situations. Finally, an introduction to a helicopter dynamic model is given, focusing on real-time representation with a relationship matrix of transmission frequencies through True-time simulation.

On Monte Carlo and Quasi-Monte Carlo for Matrix Computations.

This paper focuses on minimizing further the communications in Monte Carlo methods for Linear Algebra and thus improving the overall performance. The focus is on producing set of small number of covering Markov chains which are much longer that the usually produced ones. This approach allows a very efficient communication pattern that enables to transmit the sampled portion of the matrix in parallel case. The approach is further applied to quasi-Monte Carlo. A comparison of the efficiency of the new approach in case of Sparse Approximate Matrix Inversion and hybrid Monte Carlo and quasi-Monte Carlo methods for solving Systems of Linear Algebraic Equations is carried out. Experimental results showing the efficiency of our approach on a set of test matrices are presented. The numerical experiments have been executed on the MareNostrum III supercomputer at the Barcelona Supercomputing Center (BSC) and on the Avitohol supercomputer at the Institute of Information and Communication Technologies (IICT).