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A gradient flow approach for computing jump linear quadratic optimal feedback gains
A class of linear systems subject to sudden jumps
values is considered. To solve this class of stochastic
control problem, we try
to find the best feedback control law depending both
on the measurable output
as well as the mode of the system.
A gradient flow based algorithm is derived
for this problem. It is shown that an optimal solution
can be successfully
computed by finding the limiting solution of an ordinary differential equation
which is given in terms of the gradient flow associated
with the cost function.
Several important properties are obtained.
A numerical example is solved.