TY - JOUR
T1 - An Efficient Method for Multiobjective Optimal Control and Optimal Control Subject to Integral Constraints
AU - Ajeet Kumar & Alexander Vladimirsky
JO - Journal of Computational Mathematics
VL - 4
SP - 517
EP - 551
PY - 2010
DA - 2010/08
SN - 28
DO - http://doi.org/10.4208/jcm.1003-m0015
UR - https://global-sci.org/intro/article_detail/jcm/8535.html
KW - Optimal control, Multiobjective optimization, Pareto front, Vector dynamic
programming, Hamilton-Jacobi equation, Discontinuous viscosity solution, Semi-Lagrangian discretization.
AB - <p style="text-align: justify;">We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a &quot;budget&quot; remaining to satisfy each constraint; the augmented Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our approach hinges on the causality in that PDE, i.e., the monotonicity of characteristic curves in one of the newly added dimensions. A semi-Lagrangian &quot;marching&quot; method is used to approximate the discontinuous viscosity solution efficiently. We compare this to a recently introduced &quot;weighted sum&quot; based algorithm for the same problem [25]. We illustrate our method using examples from flight path planning and robotic navigation in the presence of friendly and adversarial observers.</p>