Optimal Control of Switched Systems

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Farahbakhsh-Tooli, Elena | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46045 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi-Amiri, Nezam
Abstract:
We consider the problem of optimal control of switched systems. In order to solve this problem, by using the Lagrange interpolation, we transform it into an equivalent nonlocal optimal control problem, and then by applying several conditions we transform it into a moment problem. This way, a nonlinear and non-convex optimal control problem is converted to an equivalent optimal control problem with linear and convex structure, which allows us to obtain an equivalent convex formulation of the problem. So we obtain an approximation of the unknown function by using the Lagrange interpolation, and an approximation of the integral term by using the trapezoidal method. Finally, we solve the problem by applying the Euler Forward method. We apply the approach to solve several optimal control problems
Keywords:
Optimal Control ; Semidefinite Optimization ; Moment Method ; Sum of Squares (SOS) ; Switched Optimal Control Problom ; Positive Polynomials