Motivated by the design question of additional fuel
needed to complete a task in an uncertain environment, this
paper introduces metrics to quantify the maximal additional
energy used by a control system in the presence of bounded
disturbances, compared to a nominal, disturbance-free system.
In particular, we consider the task of finite-time stabilization for
a linear, time-invariant system. We compare the nominal energy
required to achieve this task in the disturbance-free system to
the worst-case energy over all feasible disturbances. Solving
for the worst-case energy over all disturbances first leads to an
optimal control problem with a least-squares solution, and then
an infinite-dimensional optimization problem where we derive
an upper bound on the solution. The comparison of energies
is accomplished using additive and multiplicative metrics, for
which we derive bounds. Simulation examples on an ADMIRE
fighter jet model demonstrate the practicability of these metrics,
and their variation with the distance of the initial condition
from the origin and the task completion time.
Published: May 15, 2025
Citation
Padmanabhan R., C. Bakker, S.A. Dinkar, and M. Ornik. 2024.How Much Reserve Fuel: Quantifying the Maximal Energy Cost of System Disturbances. In IEEE 63rd Conference on Decision and Control (CDC 2024), December 16-19, 2024, Milan, Italy, 5326-5331. Piscataway, New Jersey:IEEE.PNNL-SA-196356.doi:10.1109/CDC56724.2024.10886030