Optimal quadratic control of jump linear systems with Gaussian noise in discrete-time

An optimal discrete-time jump linear quadratic Gaussian (JLQG) control problem is investigated. The system to be controlled is linear, except for randomly jumping parameters which obey a discrete-time finite-state Markov process. A quadratic expected cost is minimized, for systems subject to additive Gaussian input and measurement noise. It is assumed that the system structure (i.e. jumping parameters) is known at each time. A separation property enables the authors to design the optimal JLQ controller and optimal x-state estimator separately. Based on the appropriate controllability and observability properties for discrete-time jump linear systems, the infinite-time-horizon JLQG problem is solved. The optimal infinite-time-horizon JLQG compensator has a steady-state control law but does not have a steady-state filter. A suboptimal JLQG compensator, using a filter which converges to a steady-state filter, is then constructed