Structured feedback control of discrete linear stochastic systems with quadratic costs

The problem of selecting a state feedback controller with a specified structure so as to minimize the expected value of quadratic cost for a discrete linear system disturbed by a zero-mean white noise disturbance is posed. The cost is expressed as a quadratic form in the gains associated with a given time. It is then suggested that an optimal control policy of specified structure might be computed by repeatedly replacing the gains associated with each time instant with an optimal choice given that the gains associated with all other time instants are held fixed. The properties of the solution and of the solution procedure are discussed. An example is given illustrating that simplified controllers can often have near optimal performance. It is then shown that problems involving dynamic controllers of specified structure can be transformed into structured state feedback problems.