Optimal Control of Networked Systems with Limited Communication: a Combined Heuristic Search and Convex Optimization Approach

This paper discusses the optimal H2 and H∞ control problems for networked systems with limited communication constraint. The limited communication constraint in control networks is taken into consideration in controller design by employing the notion of communication sequence. Our objective is to find an optimal communication sequence and the corresponding optimal controller for the given plant and communication resource under the H∞ or H2 performance index. For a given communication sequence, the problem is formulated into a periodic control problem for which a direct LMI design method is developed. We also propose a heuristic search method for seeking a sub-optimal communication sequence, which in conjunction with the convex optimization gives a solution to the optimal limited communication control problem. As compared with the exhaustive search of communication sequence, our approach greatly reduces the computational cost. Several examples are used to illustrate the design method. They clearly indicate that the solution of the heuristic search converges to the optimal communication sequence.