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The problem of optimal stochastic (LQG) regulation based on output feedback and disturbance measurement feedforward is solved via polynomial techniques. Two independent couples of polynomial equations are derived which yield the feedback and the feedforward parts of the regulator. Two different approaches are described which result in the same equations. The optimum feedforward is shown to improve the cost.

Thc problem of LQ optilmisation for the “standard” control structure is studied. We obtain a solution for the scalar case of this problem using the polynomial equation approach

The problem of optimal stochastic regulation based on output feedback and disturbance measurement feedforward for multivariable systems is solved using the polynomial equation approach. Two independent couples of polynomial matrix equations are derived which yield the feedback and the feedforward parts of the regulator.

The general solution of the optimal LQG problem using the polynomial equation approach involves the solution of a couple of two-sided matrix polynomial equations. The conditions under which a single one-sided equation which is related to the original two (the 'implied' diophantine equation) yields the unique optimal controller are derived in this paper. The result has considerable relevance to aspects such as computation and self-tuning control applications.