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.

Back to Control Seminars Page.