Dynamic Optimization of Path-Constrained Switched Systems

[LeeAndro]

English | 2023 | ISBN: 3031234278 | 113 pages | True PDF,EPUB | 10.82 MB​

This book provides a series of systematic theoretical results and numerical solution algorithms for dynamic optimization problems of switched systems within infinite-dimensional inequality path constraints. Dynamic optimization of path-constrained switched systems is a challeg task due to the complexity from seeking the best combinatorial optimization among the system input, switch s and switching sequences. Meanwhile, to ensure safety and guarantee product quality, path constraints are required to be rigorously satisfied (i.e., at an infinite number of points) within a finite number of iterations. Several novel methodologies are presented by using dynamic optimization and semi-infinite programming techniques. The core advantages of our new approaches lie in two folds: i) The system input, switch s and the switching sequence can be optimized simultaneously. ii) The proposed algorithms teate within finite iterations while coming with a certification of feasibility for the path constraints. In this book, first, we provide brief surveys on dynamic optimization of path-constrained systems and switched systems. For switched systems with a fixed switching sequence, we propose a bi-level algorithm, in which the input is optimized at the inner level, and the switch s are updated at the outer level by using the gradient information of the optimal value function calculated at the optimal input. We then propose an efficient single-level algorithm by optimizing the input and switch s simultaneously, which greatly reduces the number of nonlinear programs and the computational burden. For switched systems with free switching sequences, we propose a solution framework for dynamic optimization of path-constrained switched systems by employing the variant 2 of generalized Benders decomposition technique. In this framework, we adopt two different system formulations in the primal and master problem construction and explicitly characterize the switching sequences by introducing a binary variable. Finally, we propose a multi-objective dynamic optimization algorithm for locating approximated local Pareto solutions and quantitatively analyze the approximation optimality of the obtained solutions. This book provides a unified framework of dynamic optimization of path-constrained switched systems. It can therefore serve as a useful book for researchers and graduate students who are interested in knowing the state of the art of dynamic optimization of switched systems, as well as recent advances in path-constrained optimization problems. It is a useful source of up-to-date optimization methods and algorithms for researchers who study switched systems and graduate students of control theory and control eeering. In addition, it is also a useful source for eeers who work in the control and optimization fields such as robotics, chal eeering and industrial processes.



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