Abstract
In Chapter 4, linear quadratic (LQ) optimal control problem for a discrete-time LTI system with random input gains is studied. The finite-horizon case can be solved by dynamic programming, while the solvability of the infinite-horizon case is equivalent to the existence of a mean-square stabilizing solution to the associated modified algebraic Riccati equation (MARE). By virtue of the theory of cone-invariant operators, some properties of the associated MARE are obtained and an explicit necessary and sufficient condition ensuring the existence of the mean-square stabilizing solution to the MARE is derived. Such a condition is compatible with the one ensuring the stabilizing solution to the standard algebraic Riccati equation (ARE), and it indicates that the common condition of observability or detectability of certain stochastic systems is unnecessary. With this result, the LQ optimal control problem of networked control systems with random input gains can be well solved under the framework of channel/controller codesign.
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