On the Hybrid Minimum Principle: The Hamiltonian and Adjoint Boundary Conditions
Ali Pakniyat, Peter E. Caines
Abstract
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.
Topics & Concepts
MathematicsHamiltonian (control theory)Control theory (sociology)Optimal controlState spaceBoundary value problemBoundary (topology)Dimension (graph theory)Hybrid systemApplied mathematicsTopology (electrical circuits)Mathematical analysisMathematical optimizationControl (management)Computer sciencePure mathematicsArtificial intelligenceCombinatoricsStatisticsMachine learningElectric and Hybrid Vehicle TechnologiesControl and Stability of Dynamical SystemsElectric Vehicles and Infrastructure