Time-changed linear quadratic regulators

Many control methods implicitly depend on the assumption that time is accurately known. For example, the finite-horizon linear quadratic regulator is a linear policy with time-varying gains. Such policies may be infeasible for controllers without accurate clocks, such as the motor systems in humans and other animals, since gains would be applied at incorrect times. Little appears to be known, however, about control with imperfect timing. This paper gives a solution to the linear quadratic regulator problem in which the state is perfectly known, but the controller's measure of time is a stochastic process derived from a strictly increasing Lévy process. The optimal controller is linear and can be computed from a generalization of the classical Riccati differential equation.