Optimal design of decentralized large-scale systems with low sensitivity to non-linearity

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Alshaban, Esmail M
Lu, Tianshi
Sawan, M. Edwin
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The optimal design of complex systems with low sensitivity to nonlinear subsystems is an important problem in engineering and science. When talking about non-linearity, linearization of non-linear control systems is an important technique used in control engineering to analyze the behavior of complex nonlinear systems. The process involves approximating a nonlinear system around an operating point by a linear system that can be analyzed using conventional linear control theory. This technique is particularly useful in control system design since it allows the use of well-established techniques such as state feedback, and linear quadratic regulator (LQR) to design controllers for nonlinear systems. Linearization is a powerful tool that can help researchers understand the behavior of nonlinear systems and design effective control strategies to achieve desired performance objectives. This paper proposes the single perturbation method as a model reduction technique to reduce the order of the system. The singular perturbation approach identifies the slow and fast dynamics of a complex system and develops reduced-order models that represent the system’s core characteristics. The reduced-order models are then used to design optimal controllers for the complex system that are insensitive to the nonlinear subsystems. Game theory is a branch of mathematics that looks at how people make strategic decisions when the results of their choices depend on the decisions made by others. It can be used in a lot of different ways in control systems, especially in the design of systems with more than one person making decisions and interacting with each other. Game theory may be used to control systems to evaluate agent behavior and create controller designs that maximize system performance. The reduced order model was optimized using Nash strategy of game theory.

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Thesis (Ph.D.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics
Wichita State University
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