Model Predictive Regulation on Manifolds in Euclidean Space

One of the crucial problems in control theory is the tracking of exogenous signals by controlled systems. In general, such exogenous signals are generated by exosystems. These tracking problems are formulated as optimal regulation problems for designing optimal tracking control laws. For such a class of optimal regulation problems, we derive a reduced set of novel Francis–Byrnes–Isidori partial differential equations that achieve output regulation asymptotically and are computationally efficient. Moreover, the optimal regulation for systems on Euclidean space is generalized to systems on manifolds. In the proposed technique, the system dynamics on manifolds is stably embedded into Euclidean space, and an optimal feedback control law is designed by employing well studied, output regulation techniques in Euclidean space. The proposed technique is demonstrated with two representative examples: The quadcopter tracking control and the rigid body tracking control. It is concluded from the numerical studies that the proposed technique achieves output regulation asymptotically in contrast to classical approaches.