Design of smooth hybrid controllers for a class of non‐linear systems

Abstract

Symbolic planning techniques rely on abstract information about a continuous system to design a discrete planner to satisfy desired high-level objectives. However, applying the generated discrete commands of the discrete planner to the original system may face several challenges, including real-time implementation, preserving the properties of high-level objectives in the continuous domain, and issues such as discontinuity in control signals that may physically harm the system. To address these issues and challenges, the authors proposed a novel hybrid control structure for systems with non-linear multi-affine dynamics over rectangular partitions. In the proposed framework, a discrete planner can be separately designed to achieve high-level specifications. Then, the proposed hybrid controller generates jumpless continuous control signals to drive the system over the partitioned space executing the discrete commands of the planner. The hybrid controller generates continuous signals in realtime while respecting the dynamics of the system and preserving the desired objectives of the high-level plan. The design process is described in detail and the existence and uniqueness of the proposed solution are investigated. Finally, several case studies are provided to verify the effectiveness of the developed technique.

Decentralized modular hybrid supervisory control for the formation of unmanned helicopters

“…In our earlier study [37], a hybrid supervisory control framework was introduced for the formation control of UAVs. The basic idea was to use polar abstraction of the motion space and utilize the properties of multi-affine functions [38][39][40] over the partitioned space. The abstraction techniques [41,42] can convert the original continuous system with infinite states into a finite state machine for which one can use the well-developed theory of supervisory control of Discrete Event Systems (DES) [43][44][45].…”