Cited by 1,313Advanced Control Systems OptimizationFormal Methods in VerificationStability and Control of Uncertain Systems

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A unified framework for hybrid control: model and optimal control theory

Branicky, M.S., Borkar, V.S., Mitter, S.K.·1998·IEEE Transactions on Automatic Control

DOI 10.1109/9.654885

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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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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Guckenheimer, J., & Holmes, P. (1983) · Applied Mathematical Sciences · doi:10.1007/978-1-4612-1140-2 · Cited by 16,144
Convergence of Probability Measures
Billingsley, P. (1999) · Wiley series in probability and statistics · doi:10.1002/9780470316962 · Cited by 14,153
Ordinary Differential Equations
Stewart, J. M. (2017) · Cambridge University Press eBooks · doi:10.1017/9781108120241.010 · Cited by 7,299
Convergence of Probability Measures
Kingmán, J. F. C., & Billingsley, P. (1969) · Revue de l Institut International de Statistique / Review of the International Statistical Institute · doi:10.2307/1402124 · Cited by 7,196
Statecharts: a visual formalism for complex systems
Harel, D. (1987) · Science of Computer Programming · doi:10.1016/0167-6423(87)90035-9 · Cited by 6,771
User’s guide to viscosity solutions of second order partial differential equations
Crandall, M. G., Ishii, H., & Lions, P. (1992) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-1992-00266-5 · Cited by 4,998
Differential Equations, Dynamical Systems, and Linear Algebra
Hirsch, M. W., & Smale, S. (1974) · Pure and applied mathematics · doi:10.1016/s0079-8169(08)x6044-1 · Cited by 3,119
Smart cars on smart roads: problems of control
Varaiya, P. P. (1993) · IEEE Transactions on Automatic Control · doi:10.1109/9.250509 · Cited by 1,393
Mathematical Control Theory
Sontag, E. D. (1998) · Texts in applied mathematics · doi:10.1007/978-1-4612-0577-7 · Cited by 1,339
On a theory of computation and complexity over the real numbers: 𝑁𝑃- completeness, recursive functions and universal machines
Blum, L., Shub, M., & Smale, S. (1989) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-1989-15750-9 · Cited by 1,090

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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

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On the Hybrid Minimum Principle: The Hamiltonian and Adjoint Boundary Conditions
Pakniyat, A., & Caines, P. E. (2020) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2020.2992450 · Cited by 24

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)
ORCID: Branicky, M.S.
Borkar, V.S.
Mitter, S.K.
Venue: IEEE Transactions on Automatic Control
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Published: 1998
Volume: 43
Issue: 1
Pages: 31-45
ISSN: 0018-9286 (ISSN-L)
DOI: 10.1109/9.654885
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
Licence: ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html (vor)
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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A unified framework for hybrid control: model and optimal control theory

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