Optimal finite wordlength linear quadratic regulation

The authors consider the design of an LQG regulator, implemented in fixed-point arithmetic, which is optimized with respect to its state wordlength and structure. The approach extends previous design methods so that arithmetic errors are directly included. The optimal finite controller gains are computed as a function of the arithmetic wordlength subject to an l₂-scaling constant on the controller states. The design method used permits the cost for the (near) optimal structure to be developed so that this can then be used as a basis for comparison to other less complex structures