Abstract
Optimization of hybrid dynamic systems typically involves characterizing
switching times and mode sequences. Operating autonomous hybrid systems
with varying event timings presents multiple challenges. Complexity
often arises from optimal mode sequence determination, making
optimization of the corresponding hybrid automaton more difficult. An
experimental autonomous hybrid dynamic system experiencing switching due
to choked flow conditions is presented. Implementing gradient-based
optimization algorithms may be difficult due to complex switching
patterns of the hybrid dynamic systems. To mitigate this, an
approximation of the Heaviside step function is applied to transform the
hybrid switching functions to a continuous and smooth forms. Using the
Control Vector Parameterization (CVP) approach and evaluating gradients
using the variational method, an open-loop time-optimal control problem
is presented. Modeling and control methods are demonstrated using an
experimental two-tank air system. The optimal control formulation can
include constraints to avoid specific undesirable modes of operation.