On the linear regulator with cross terms in the performance index

Abstract

The linear regulator theory which is perhaps the most used result of modern control theory is known to apply even when the performance index contains cross terms in control and state. Bryson and Ho (1960) present this result in terms of an equivalent problem. Conditions which guarantee the existence of a solution to the optimal gain equation for the finite and infinite time eases are well known for the equivalent problem. This note presents these conditions in terms of the original problem.