Stochastic optimal control under randomly varying distributed delays.

摘要

A methodology for synthesis of stochastic optimal control and estimation law, referred to as Linear Quadratic Random Delay Compensation (LQRDC), has been developed in this dissertation. The objective is to circumvent the detrimental effects, both in stability and dynamic performance, of the randomly varying delays, from sensor to controller and from controller to actuator, in network-based control systems that are also subjected to plant disturbance and measurement noise. The LQRDC gain matrices and two pairs of discrete-time modified matrix Riccati and Lyapunov equations are simultaneously synthesized in the proposed methodology. In contrast to the conventional LQG problem, the pairs of modified matrix Riccati and Lyapunov equations under LQRDC are coupled by a projection matrix whose column and row spaces are shown to represent the control and estimation subspaces, respectively. The coupling between optimal control and estimation is the cause of breakdown of the certainty equivalence principle. It is shown that a set of conditions of mean square compensatability, for the closed-loop system, and mean square detectability, for the models of cost evaluation and noise covariance, are sufficient, and necessary in general, for the existence of a unique optimal LQRDC law. Furthermore, under these conditions, the stability of the closed-loop system is ensured in mean square sense.;Stability and performance of LQRDC are tested by two simulation experiments. One of these experiments is used to demonstrate that the closed-loop system may become unstable if, like LQG, the control and estimation laws are separately synthesized and then integrated whereas the LQRDC system remains inherently stable. The second simulation experiment exhibits the performance of LQRDC with ensured stability of a linearized Multiple-Input and Multiple-Output (MIMO) model of the longitudinal motion of an advanced aircraft.