The difference and unity of irregular LQ control and standard LQ control and its solution

Irregular linear quadratic control (LQ, was called Singular LQ) has been a long-standing problem since 1970s. This paper will show that an irregular LQ (deterministic) is solvable (for arbitrary initial value) if and only the cost functional can be rewritten as regular one by changing terminal x ? ( T ) Hx to )[ H + P 1 )] ), while optimal controller achieve = 0 at same time. In other words, (if exists) needs do two things time, thing minimize constraint 0, which clarifies essential difference of from standard where only. With this breakthrough, we further study for stochastic systems with multiplicative noise. A sufficient solving condition presented based on Riccati equations.