Numerical evaluation of stochastic control systems under randomly varying distributed delays

This paper provides numerical evaluation and verifies spacial properties of the Linear Quadratic Coupled Delay Compensator (LQCDC) which was designed to circumvent the effects of the randomly varying distributed delays, both from sensor to controller and from controller to actuator, in addition to the time skew caused by mis- synchronization of sensor and controller sampling instants. With ensured numerical convergence, an oblique projection matrix is established such that its column and row spaces, respectively, constitute the control and estimation subspaces of the coupled delay compensator. Factorization of the projection matrix and a calculation method to find the steady state control gains are suggested. Two illustrative examples are demonstrated. One is used as a counter example to explore the potential instability of the linear quadratic Guassian controller that is valid only if the certainty equivalence principle holds. The other demonstrates the simulation experiment results of an aircraft flight control in longitudinal motion to verify the superiority and stability with respect to delay traffic uncertainty of the proposed LQCDC.