On the Hybrid Minimum Principle: The Hamiltonian and Adjoint Boundary Conditions

The hybrid minimum principle is presented for the optimal control of deterministic hybrid systems with both autonomous and controlled switchings and jumps where state jumps at the switching instants are permitted to be accompanied by changes in the dimension of the state space. A feature of particul...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2021-03, Vol.66 (3), p.1246-1253
Main Authors: Pakniyat, Ali, Caines, Peter E.
Format: Article
Language:English
Subjects:
Algorithms
Automata
Boundary conditions
Electric vehicles
Hybrid systems
Manifolds
Minimization
minimum principle (MP)
nonlinear control systems
Optimal control
Pontryagin maximum principle
Powertrain
Switches
Vehicle dynamics
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Summary:The hybrid minimum principle is presented for the optimal control of deterministic hybrid systems with both autonomous and controlled switchings and jumps where state jumps at the switching instants are permitted to be accompanied by changes in the dimension of the state space. A feature of particular importance is the explicit presentation of the boundary conditions on the Hamiltonians and the adjoint processes before and after switchings and jumps. The numerical benefit of these expressions are demonstrated on a modified version of the multiple autonomous switchings algorithm. The results are illustrated for the hybrid model of an electric vehicle powertrain with a two-speed transmission.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2020.2992450