Risk-Aware Maximum Hands-Off Control Using Worst-Case Conditional Value-at-Risk

With the view of risks, this article deals with the problems of maximum hands-off control that aims at minimizing the length of nonzero control input. More specifically, we consider stochastic systems and seek sparse control inputs that bring the system state to a ball centered at the origin, such that the expected value of the states that are further than a given threshold from the origin is small, thus minimizing the risk that the system state is outside of the ball. To deal with this problem, we employ the worst-case conditional value-at-risk under the assumption that the first two moments of the disturbance distribution are known. In particular, we consider two kinds of risk-aware maximum hands-off control problems: one enhances the sparsity within a given risk threshold, and the other minimizes the risk subject to a sparsity constraint. We also derive a risk-constrained sparse model predictive control and provide a numerical example that shows the effectiveness of the proposed approach in networked control systems.