The DOI matches its Crossref record; 46 of the 48 references it cites were found in a registry or an index.
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
Citations
Cites
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Varaiya, P. P. (1993) · IEEE Transactions on Automatic Control · doi:10.1109/9.250509 · Cited by 1,393
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2 of the 48 references couldn’t be matched to a known paper.
Research works printed but not linked: 8
- mitter, 1993, 6 291 Special topics Optimal control
- hocking, 1988, Topology
- 10.1109/CDC.1994.411615 · DOI
- bainov, 1989, Systems with Impulse Effect
- hynes, 1993, Vehicle management for the high speed civil transport
- munkres, 1975, Topology
- ge, 1994, Algorithms for chattering approximations to relaxed optimal controls
- brockett, 1983, smooth multimode control systems, Berkeley-Ames Conf Nonlinear Problems Contr Fluid Dynamics, 103
Cited by
Sorted by citations
Control of systems integrating logic, dynamics, and constraints
Bemporad, A., & Morari, M. (1999) · Automatica · doi:10.1016/s0005-1098(98)00178-2 · Cited by 3,048
Goebel, R., Sanfelice, R. G., & Teel, A. R. (2009) · IEEE Control Systems · doi:10.1109/mcs.2008.931718 · Cited by 1,656
Perspectives and results on the stability and stabilizability of hybrid systems
DeCarlo, R. A., Branicky, M. S., Pettersson, S., & Lennartson, B. (2000) · Proceedings of the IEEE · doi:10.1109/5.871309 · Cited by 1,628
Self-citationPredictive Control for Linear and Hybrid Systems
Borrelli, F., Bemporad, A., & Morari, M. (2017) · Cambridge University Press eBooks · doi:10.1017/9781139061759 · Cited by 1,493
Recent Advances in Hierarchical Reinforcement Learning
Barto, A. G., & Mahadevan, S. (2003) · Discrete Event Dynamic Systems · doi:10.1023/a:1022140919877 · Cited by 1,059
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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