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An interior penalty method for optimal control problems with state and input constraints of nonlinear systems. (English) Zbl 1336.49038
Summary: This paper exposes a methodology to solve state and input constrained optimal control problems for nonlinear systems. In the presented “interior penalty” approach, constraints are penalized in a way that guarantees the strict interiority of the approaching solutions. This property allows one to invoke simple (without constraints) stationarity conditions to characterize the unknowns. A constructive choice for the penalty functions is exhibited. The property of interiority is established, and practical guidelines for implementation are given. A numerical benchmark example is given for illustration.

MSC:
49M30 Other numerical methods in calculus of variations (MSC2010)
90C51 Interior-point methods
93C10 Nonlinear systems in control theory
93C35 Multivariable systems, multidimensional control systems
Software:
OPTRAGEN; Matlab; bvp4c
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References:
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