Analysis of Large-Scale Asynchronous Switched Dynamical Systems

This dissertation addresses research problems related to the switched system as well as its application to large-scale asynchronous dynamical systems. For decades, this switched system has been widely studied in depth, owing to the broad applicability of the switched system framework. For example, the switched system can be adopted for modeling the dynamics of numerous systems including power systems, manufacturing systems, aerospace systems, networked control systems, etc. Despite considerable research works that have been developed during last several decades, there are still remaining yet important and unsolved problems for the switched systems. In the first part of this dissertation, new methods are developed for uncertainty propagation of stochastic switched systems in the presence of the state uncertainty, represented by probability density functions(PDFs). The main difficulty of this problem is that the number of PDF components in the state increases exponentially under the stochastic switching, incurring the curse of dimensionality. This dissertation provides a novel method that circumvents the issue regarding the curse of dimensionality. As an extension of this research, the new method for the switching synthesis is presented in the second part, to achieve the optimal performance of the switched system. This research is relevant to developing the switching synthesis on how to switch between different switching modes. In the following chapters, some interesting applications that emerges as today's leading-edge technology in high-performance computing (HPC) will be introduced. Generally, the massive parallel computing entails idle process time in multi-core processors or distributed computing devices as up to 80% of total computation time, owing to the synchronization of the data. Thus, there is a trend toward relaxing such a restriction on synchronization penalty to overcome this bottleneck problem. This dissertation presents a synchronous computing algorithms as a key solution to Leverage the computing performance to the maximum capabilities. The price to Pay for adopting the asynchronous computing algorithms is, however, unpredictability of the solution due to the randomness in the behavior of asynchrony. In this dissertation, the switched system is employed to model the characteristics of the asynchrony in parallel computing, enabling analysis of the asynchronous algorithm. Particularly, the analysis will be performed for massively parallel asynchronous numerical algorithms implemented on 1D heat equation and large-scale asynchronous distributed quadratic programming problems. As another case study, this switched system is also implemented on the stability analysis of large-scaled is tribute networked control systems (DNCS) having random communication delays. For these problems, the convergence or stability analysis is carried out by the switched system framework. One of major concerns when adopting the switched system framework for analysis of these systems is the scalability issues associated with extremely large switching mode numbers. Due to the massive parallelism or large-scale distributed nodes, the switching mode numbers are beyond counting, leading to the computational intractability. The proposed methods are developed targeting the settlement of this scalability issue, which inevitably takes place in adopting the switched system framework. Thus, the primary emphasis of this dissertation is placed on the mathematical development of computationally efficient tools, particularly for analysis of the large-scale asynchronous switched dynamical system, which has broad applications including massively parallel asynchronous numerical algorithms to solve ODE/PDE problems, distributed optimization problems, and large-scale DNCS with random communication delays

Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance

Issued as Progress report, and Final report, Project no. E-21-67