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Linear quadratic optimal control via Fourier-based state parametrization. (English) Zbl 0765.49022
Calculating the control which solves the linear quadratic optimal control problem with constraints is the problem addressed. The idea is to approximate the state and output trajectory of a time-dependent linear system by a polynomial and a finite Fourier series. Since the input matrix is assumed to be invertible, the approximated control follows from the approximated state trajectory. The constraints on the control are then translated to algebraic constraints on the coefficients of the polynomial and the Fourier series. Next one obtains an (approximate) solution for the optimal control problem by solving it for the approximated system. By means of some examples the authors show how this approximated optimal control is a good candidate for the optimal control of the original system, when the constraints can be well expressed in Fourier series. In the case of bang-bang control the approximation is rather poor. The authors present some methods for improving the convergence speed for this case.
Reviewer: H.Zwart (Enschede)

MSC:
49N05 Linear optimal control problems
93B40 Computational methods in systems theory (MSC2010)
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