Static Output-Feedback ${H}_{∞}$ Control Design Procedures for Continuous-Time Systems With Different Levels of Model Knowledge

This article suggests a collection of model-based and model-free output-feedback optimal solutions to a general ${H_{infinity}}$ control design criterion of a continuous-time linear system. The goal is to obtain a static output-feedback controller while the design criterion is formulated with an exponential term, divergent or convergent, depending on the designer's choice. Two offline policy-iteration algorithms are presented first, which form the foundations for a family of online off-policy designs. These algorithms cover all different cases of partial or complete model knowledge and provide the designer with a collection of design alternatives. It is shown that such a design for partial model knowledge can reduce the number of unknown matrices to be solved online. In particular, if the disturbance input matrix of the model is given, off-policy learning can be done with no disturbance excitation. This alternative is useful in situations where a measurable disturbance is not available in the learning phase. The utility of these design procedures is demonstrated for the case of an optimal lane tracking controller of an automated car.