An SQP Method for the Optimal Control of Large-Scale Dynamical Systems
We propose a sequential quadratic programming (SQP) method for the
optimal control of large-scale dynamical systems. The method uses
modified multiple shooting to discretize the dynamical constraints.
When these systems have relatively few parameters, the computational
complexity of the modified method is much less than that of standard
multiple shooting. Moreover, the proposed method is demonstrably more
robust than single shooting. In the context of the SQP method, the use
of modified multiple shooting involves a transformation of the
constraint Jacobian. The affected rows are those associated with the
continuity constraints and any path constraints applied within the
shooting intervals. Path constraints enforced at the shooting points
(and other constraints involving only discretized states) are not
transformed. The transformation is cast almost entirely at the user
level and requires minimal changes to the optimization software. We
show that the modified quadratic subproblem yields a descent direction
for the L-1 penalty function. Numerical experiments verify the
efficiency of the modified method.
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