HYPERBOLIC-TANGENT-BASED DOUBLE-SMOOTHING METHOD AND ITS APPLICATION IN OPTIMAL CONTROL

2018 Univelt Inc. All rights reserved. In a large number of dynamical systems and depending on the form of performance index, their Hamiltonian may turn out to be affine in control. Extremal control of such systems may switch between the bounds of the admissible set or take on values interior to its admissible set, i.e., singular arcs. On the other hand, the existence of singular arcs is not evident until certain existence and solvability conditions are satisfied and this logic complicates the detection and consequent inclusion of singular sub-arcs in the extremal trajectory. Moreover, the presence of abrupt changes in the control inputs jeopardizes the numerical solution of optimal control problems unless care is taken to isolate precise time transition points where sharp switches occur. This investigation illustrates a double-smoothing method capable for problem in which the extremal control has a composite structure. Application of the method is demonstrated by solving the maximum-altitude Goddard rocket problem with a known bang-singular-bang control structure. Additional physical insights on singular control are also offered by the use of associated singular surface and first principles.

HYPERBOLIC-TANGENT-BASED DOUBLE-SMOOTHING METHOD AND ITS APPLICATION IN OPTIMAL CONTROL Conference Paper