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Chebyshev inclusion functions based symplectic algorithm for solving non-linear optimal control problem with interval uncertainty. (English) Zbl 1418.49014

Summary: This article proposes a non-probabilistic interval analysis algorithm to obtain the influence domain of non-linear optimal control problem with interval uncertain parameter. The proposed non-probabilistic interval analysis algorithm is mainly constructed based on the symplectic algorithm and Chebyshev interval method. Firstly, the interval model is used to descript the uncertainties arising in optimal control problem. These uncertainties are the uncertain-but-bounded initial conditions or parameter variables. Thus, they are expressed based on the lower and upper bounds of variables without probability distributions. Then the Chebyshev inclusion function is employed to represent the relation between input uncertain parameters and responses of optimal control evaluation. By doing this, the optimal control problem with interval variables is transformed into a new set of optimal control problems with deterministic variables. So, the symplectic algorithm can be directly applied to the solving of the deterministic optimal control problems. Finally with the solutions of deterministic optimal control problems, the interval operation is used to obtain the influence domain, i.e., the bounds of the responses to the states and control inputs. The effectiveness of the proposed method is verified by a simple uncertain optimal control problem and an optimal orbital rendezvous problem with uncertainties in astrodynamics.

MSC:

49K05 Optimality conditions for free problems in one independent variable
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