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Optimal control of hybrid systems with sliding modes. (English) Zbl 1447.93044

Awrejcewicz, Jan (ed.), Dynamical systems in theoretical perspective. Łódź, Poland, December 11–14, 2017. Based on the 14th international conference on dynamical systems: theory and applications (DSTA). Cham: Springer. Springer Proc. Math. Stat. 248, 283-293 (2018).
Summary: This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguish it from the other procedures for the problem. First of all a sliding mode is coped with differential-algebraic equations (DAEs) and that guarantees accurate tracking of the sliding motion surface. The second important feature is the calculation of cost and constraints functions gradients with the help of adjoint equations. The adjoint equations presented in the paper take into account sliding motion. The third feature is the integration of the presented procedure with the interactive dynamic optimization server (IDOS) which is a computing environment dedicated to optimal control problems. IDOS user interface relies on dynamic optimization modeling language (DOML) which is an extension of Modelica language. In the paper we discuss the elements of DOML which help defining hybrid optimal control problems. The paper presents the application of the proposed procedure to an optimal control problem related to a mechanical system with dry friction.
For the entire collection see [Zbl 1403.37005].

MSC:

93B12 Variable structure systems
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C15 Control/observation systems governed by ordinary differential equations
49J15 Existence theories for optimal control problems involving ordinary differential equations

Software:

Modelica; OOQP; DOML
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Full Text: DOI

References:

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