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A gradient algorithm for solution of the optimal control problem for hybrid switching systems
Author(s) -
Salehi Hojat Allah,
Tavassoli Babak
Publication year - 2020
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2673
Subject(s) - convergence (economics) , optimal control , extension (predicate logic) , gradient descent , control theory (sociology) , function (biology) , switching time , set (abstract data type) , computer science , mathematical optimization , hybrid system , algebraic equation , mathematics , descent (aeronautics) , algorithm , control (management) , engineering , artificial neural network , nonlinear system , physics , quantum mechanics , machine learning , artificial intelligence , evolutionary biology , aerospace engineering , electrical engineering , economics , biology , programming language , economic growth
Summary In this article, an algorithm is presented for solving the optimal control problem for the general form of a hybrid switching system. The cost function comprises terminal, running and switching costs. The controlled system is an autonomous hybrid switching system with jumps either at some switching times or some time varying switching manifolds. The proposed algorithm is an extension of the first‐order gradient method for the conventional optimal control problem. The algorithm requires a low computational effort. The system's dynamical equations together with a set of algebraic equations are solved at each iteration in order to find the descent direction. The convergence of algorithm is proved and examples are provided to demonstrate the efficiency of the algorithm for different types of hybrid switching system optimal control problems.