Data-based control of continuous-time linear systems with performance specifications

The design of direct data-based controllers has become a fundamental part of control theory research in the last few years. In this paper, we consider three classes of data-based state feedback control problems for linear systems. These control problems are such that, besides stabilization, some additional performance requirements must be satisfied. First, we formulate and solve a trajectory-reference control problem, on which desired closed-loop trajectories are known and a controller that allows the system to closely follow those trajectories is computed. Then, the solution of the LQR problem for continuous-time systems is presented. Finally, we consider the case in which the precise position of the desired poles of the closed-loop system is known, and introduce a data-based variant of a robust pole-placement procedure. The applicability of the proposed methods is tested using numerical simulations.