In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems - in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) - whose solutions converge to the exact solution of the NP-hard problem.
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- Mechanical Engineering
- Convex Optimization
- Lyapunov theory
- Optimal energy storage
- Parallel Computing
- Polynomial optimization
- stability analysis
- Control Theory
- Parallel processing (Electronic computers)
- Mathematical optimization
- Stability--Mathematical models.
- Partial requirement for: Ph.D., Arizona State University, 2016Note typethesis
- Includes bibliographical references (pages 198-208)Note typebibliography
- Field of study: Mechanical engineering