ISSN:
1573-8698
Keywords:
49K
;
49L
;
93
;
Chained systems
;
optimal control problems
;
Pontryagin maximum principle
;
extremals
;
switching structure
;
second-order optimality conditions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract To study a time-optimal control problem with bounded controls and an optimal control problem with a quadratic functional for the so-called 2-chained control system $$\dot x_1 = u_1 , \dot x_2 = u_{2,} \dot x_3 = \dot x_2 u_{1,} ... ,\dot x_n = \dot x_{n - 1} u_{1,} $$ we start with the first-order optimality condition, the Pontryagin maximum principle, determine normal, singular, and abnormal extremals, provide a complete description of the switching structure for bang-bang extremals of the time-optimal problem, describe their branchings, and derive Jacobi-type second-order optimality conditions for the problem with the quadratic functional. Finally we discuss the relations between 2-chained and power form systems.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02254700
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