Sensor and Actuator Scheduling in Bilinear Dynamical Networks

In this paper, we investigate the problem of finding a sparse sensor and actuator (S/A) schedule that minimizes the approximation error between the input-output behavior of the fully sensed/actuated bilinear system and the system with the scheduling. The quality of this approximation is measured by an ℋ
2
-like metric, which is defined for a bilinear (time-varying) system with S/A scheduling based on the discrete Laplace transform of its Volterra kernels. First, we discuss the difficulties of designing S/A schedules for bilinear systems, which prevented us from finding a polynomial time algorithm for solving the problem. We then propose a polynomial-time S/A scheduling heuristic that selects a fraction of sensors and node actuators at each time step while maintaining a small approximation error between the input-output behavior of the fully sensed/actuated system and the one with S/A scheduling in this ℋ
2
-based sense. Numerical experiments illustrate the good approximation quality of our proposed methods.