Decentralized Control of Switched Systems With Receding Horizon Modal Information and Path-Dependent Performance Specifications: Theory and an Application

In this article, we develop synthesis methods for decentralized control of switched systems with mode-dependent (more generally, path-dependent) performance specifications and apply them to an experimental vehicular testbed. This specification flexibility is important when achievable system performance varies greatly between modes, as a mode-independent specification will lead to designs that do not extract all the system performance available in each mode. More specifically, under these specifications, we derive exact conditions for the existence of block lower triangular path-dependent controllers with $\ell _{2}$ -induced-norm performance. The synthesis conditions are given in the form of a semidefinite program (SDP) for both uniform and path-dependent performance bounds. Building on previous results, we also introduce a basis-based approach that allows computational complexity to be more carefully controlled. We apply the resulting design methods to a group of miniature quadcopters, illustrating different features of the presented methods, along with some practical engineering considerations.