Low-authority controller design via convex optimization

The premise in low-authority control (LAG) is that the actuators have limited authority, and hence cannot significantly shift the eigenvalues of the system. We introduce a near method for low authority controller design, based on convex programming. We formulate the LAC design problem as a nonlinear convex optimization problem, which can then be solved efficiently by interior-point methods. We show that by optimizing the l₁ norm of the gains, we can arrive at sparse designs, i.e., designs in which only a small number of the control gains are non-zero. Thus, we can also solve actuator/sensor placement or controller architecture design problems. Moreover, it is possible to address the robustness of the LAG, i.e., a closed-loop performance subject to uncertainties or variations in the plant model. Therefore, by combining all these, for example, we can solve the problem of robust actuator/sensor placement and LAC design in one step