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System availability is the probability of the system being operable at instant t. Markov chains are a model used for system availability analysis. The exact analytical solution in terms of component failure rates and repair rates for steady-state system availability is complex to find solving the large numbers of simultaneous linear equations that result from the model. Although exact analytical solutions have been developed for series and parallel systems and for some other small size systems, they have not been developed for large scale general systems with n distinct components. Some methods for approximate analytical solutions have been suggested, but limitations on network types, over simplified states merge conditions and lack of predictions of approximation errors make these methods difficult to use. Markov state transition graphs can be classified as symmetric or asymmetric. A symmetric Markov graph has two-way transitions between each pair of communicating nodes. An asymmetric Markov graph has some pair(s) of communicating nodes with only one-way transitions. In this research, failure rates and repair rates are assumed to be component dependent only. Exact analytical solutions are developed for systems with symmetric Markov graphs. Pure series systems, pure parallel systems and general k out of n systems are examples of systems with symmetric Markov graphs. Instead of solving a large number of linear equations from the Markov model to find the steady-state system availability, it is shown that only algebraic operations on component failure rates and repair rates are necessary. In fact, for the above class of systems, the exact analytical solutions are relatively easy to obtain. Approximate analytical solutions for systems with asymmetric Markov graphs are also developed based on the exact solutions for the corresponding symmetric Markov graphs. The approximate solutions are shown to be close to the exact solutions for large scale and complex systems. Also, they are shown to be lower bounds for the exact solutions. Design principles to improve systems availability are derived from the analytical solutions for systems availability. Important components can be found easily with the iteration procedure and computer programs provided in this research.

No description available.

The main objectives of this dissertation are the following. The first objective is concerned with the stabilization of large-scale systems by a decentralized control. The fundamental idea behind this type of control is the stabilization of the isolated subsystems of a large-scale system in such a way that the global stability requirement is also satisfied. For this purpose, a new stability criterion is introduced to identify a class of interconnected systems that can be stabilized by local state feedback. In addition to this, two specific classes of interconnections are presented for which the overall system stability can be ensured by a decentralized approach. A new constructive procedure for the design of decentralized controllers for the identified classes of large-scale systems is discussed. The principal advantages of this design procedure are that it requires a minimal amount of computation and is a systematic procedure eliminating the trial and error arguments as in the earlier methods. The second objective of the dissertation is to investigate the problem of the stabilization of a class of large-scale systems which are composed of identical subsystems and identical interconnections. For this class of systems, certain significant theorems, concerning the qualitative properties are introduced. Following the guidelines set forth by the above theorems, a few different schemes for the decentralized and multilevel control of the aforementioned class of large-scale interconnected systems are presented. The third objective concerns the development of a few different schemes for the design of an asymptotic state estimator for large-scale systems described as interconnections of several low-order subsystems. The most attractive feature of the present schemes is that the majority of the necessary computations are performed at the subsystem level only, thereby leading to a simple and practicable estimator design. Finally, all the above results are illustrated by numerical examples. Further, a comparison study is conducted to show the advantages of the methods and the results in this dissertation in comparison with some results available in the literature.

In the design of large-scale systems the problem is often too large to be approached by a single group. Then the system design problem must be resolved into component subproblems with different groups assigned to work on each subproblem. A. Wayne Wymore's "Tricotyledon Theory of Systems Design" (T3SD) provides a general system theoretic framework for the statement of large-scale system design problems. In this paper some results are developed for the extension of T3SD to the problem of the resolution of system design problems into system component design problems. Initially resolutions with respect to I/O specifications and technologies are defined and examined. Following this, resolutions with respect to merit orderings in which the merit orderings on the component problems have a specified relation with the merit orderings on the original problem are discussed. Ideal, strong and perfect resolutions with respect to merit orderings are defined and relationships among these types of resolutions are discussed. It is shown that trivial strong and ideal resolutions can always be developed from simple resolutions. Perfect resolutions are always ideal resolutions and ideal resolutions are always strong resolutions. Finally it is shown that given a class of simple resolutions there always exists a maximal ideal resolution for that class.

A novel design methodology of a decentralized adaptive sliding mode control scheme for a class of large-scale systems with mismatched disturbances and uncertainties in each subsystem and interconnections is proposed in this thesis. The main idea of this new method is that the design of the switching surface of each subsystem is through the design of a pseudo-feedback controller which can stabilize the dynamics when system is in the sliding mode. The feedback gain of the pseudo controller then becomes a important parameter of switching surface. The proposed controllers of each subsystem contain three parts. The first part is measurable feedback signals, and the second part is an adaptive control mechanism, which is used for overcoming the disturbances and uncertainties of each subsystem and interconnections among subsystems. The information of upper bound of those disturbances and uncertainties are not required. The third part of the decentralized controllers is used for adjusting the convergent rate of state variables of the controlled system. The asymptotical stability is guaranteed for each subsystem even if the mismatched perturbations exist when employing the proposed control scheme. An example is demonstrated for showing the feasibility of the proposed methodology.

Thesis (M.S.)--Ohio University, August, 2000. / Title from PDF t.p.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 44-48). Also available via the Internet.

We develop a data-driven approach to Pareto optimal control of large-scale systems, where decision makers know only their local dynamics. Using reinforcement learning, we design a control strategy that optimally balances multiple objectives. The proposed method achieves near-optimal performance and scales well with the total dimension of the system. Experimental results demonstrate the effectiveness of our approach in managing multi-area power systems. / Master of Science / We have developed a new way to manage complex systems—like power networks—where each part only knows about its own behavior. By using a type of artificial intelligence known as reinforcement learning, we've designed a method that can handle multiple goals at once, ensuring that the entire system remains stable and works efficiently, no matter how large it gets. Our tests show that this method is particularly effective in coordinating different sections of power systems to work together smoothly. This could lead to more efficient and reliable power distribution in large networks.

There is an emerging need to develop new techniques for control system design that better address the challenges posed by modern large-scale cyber-physical systems. These systems are often massive networks of interconnected and interoperating subsystems that fuse physical processes, embedded computation, automation technologies, and communication. The resulting problems are dimensionally large, exhibit significant time-varying structural variations during operation, and feature complex dynamics, constraints and objectives across local and global-system scales. These properties are difficult to address using traditional control theoretic methods without substantial loss of performance and robustness. To overcome these limitations, this dissertation presents new concepts and methods for control of modern large-scale variably-structured systems through self-assembling and self-configuring control constructs that allow for fundamental restructuring of the control system’s topology in response to the current system structure. We present the System Component Graph (SCG) formulation as a mathematical framework that generalizes and extends directed graph methods from decentralized control. We present algorithms, methods, and metrics for real-time decentralization and control-structure optimization, utilizing the inclusion principle for addressing interconnected overlapping dynamics and optimal linear-quadratic (LQ) methods for local decentralized subsystem control. Global system control and performance is achieved through a centralized planner that provides continuous real-time optimized trajectories as guidance command inputs to each subsystem. We present the method of Random Subcomplement Trees (RST) for pseudo-optimal real-time trajectory planning of large-scale systems which formalizes and extends the method of rapidly-exploring random trees in a control optimization framework. The RST method defines transformations from the higher-dimension state space into an intermediate lower-dimensional search space, where optimal transitions between subspace states are defined. In the context of this approach, the resulting decentralized topology found within the SCG framework provides the RST subspace definition and requisite transformations, and optimal transitions in the search space are found through forward evaluation of the closed-loop decentralized subsystem dynamics. The methods developed in this thesis are applied to a set of real-world problems spanning various domains and demonstrate the application of these methods from first-principle modeling through control system analysis, design, implementation, and evaluation in experimental tests and simulation.