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A unified framework for hybrid control: model and optimal control theory
Abstract
We propose a very general framework that systematizes the notion of a hybrid system, combining differential equations and automata, governed by a hybrid controller that issues continuous-variable commands and makes logical decisions. We first identify the phenomena that arise in real-world hybrid systems. Then, we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems, evolving on continuous-variable state spaces and subject to continuous controls and discrete transitions. The model captures the identified phenomena, subsumes previous models, yet retains enough structure to pose and solve meaningful control problems. We develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework. In particular, we demonstrate the existence of optimal (relaxed) and near-optimal (precise) controls and derive "generalized quasi-variational inequalities" that the associated value function satisfies. We summarize algorithms for solving these inequalities based on a generalized Bellman equation, impulse control, and linear programming.
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“Hybrid control refers to hierarchically organized systems that choose among discrete control modes at higher levels, and for each of these modes, different continuous controllers operate at lower levels (Branicky et al., 1998; Goebel et al., 2009).”
From Lessons for Robotics From the Control Architecture of the Octopus (2022) · cites this paper as Branicky et al., 1998
In the citing paper
“These agents then select from a subset of actions (local motor control) over a continuous domain as defined by the action decided by the brain, similar to hybrid control strategies (Branicky et al., 1998).”
From Lessons for Robotics From the Control Architecture of the Octopus (2022) · cites this paper as Branicky et al., 1998
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Metadata
- Authors
- Branicky, M. S., Borkar, V. S., & Mitter, S. K.
- Affiliations
- Case Western Reserve University (US)
- Indian Institute of Science Bangalore (IN)
- Massachusetts Institute of Technology (US)
- Venue
- IEEE Transactions on Automatic Control
- Published
- 1998
- Volume
- 43
- Issue
- 1
- Pages
- 31-45
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W2152185829
- Cited by
- 1,313
- References
- 48
- Citations by year
- 2026: 6 · 2025: 14 · 2024: 27 · 2023: 10 · 2022: 19 · 2021: 39 · 2020: 22 · 2019: 36 · 2018: 34 · 2017: 42 · 2016: 50 · 2015: 53 · 2014: 66 · 2013: 49 · 2012: 56
- FWCI
- 73.47
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Automatic Control (publishedVersion)
- NOT FOUND REPOSITORY (Indian Institute of Science Bangalore) (acceptedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Optimization
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Formal Methods in Verification
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Keywords
- hybrid systems, hybrid control, optimal control, relaxed controls, quasi-variational inequalities, value function, Bellman equation, impulse control, linear programming, automata, discrete transitions, continuous control
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