Minimax LQG control
Prof Ian Petersen (University of New South Wales)
This talk will consider some recent results on the finite horizon minimax
optimal output feedback control for a class of discrete-time stochastic
uncertain systems. The uncertainty description for the class of stochastic
uncertain systems to be considered involves a constraint on the relative
entropy between a nominal noise distribution and the perturbed noise
distribution. This uncertainty description is a natural extension to the
case of stochastic uncertain systems, of the sum quadratic constraint
uncertainty description which is commonly used in the robust control
literature.
The minimax optimal control problem is solved by converting it into an
equivalent (parameter dependent) risk sensitive control problem. In the
case of linear stochastic uncertain systems, this leads to a linear output
feedback risk sensitive control problem. The solution to this risk
sensitive control problem is well known and given in terms of a pair of
Riccati difference equations which are of the type which occurs in the
finite horizon H infinity control problem. This (parameter dependent)
Riccati equation solution to the minimax optimal control problem reduces to
the standard LQG optimal controller in the case in which the uncertainty is
set to zero in the linear stochastic uncertain system.
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