A game theoretic approach to controller design for hybrid systems

By Claire Jennifer Tomlin, John Lygeros, S. Sastry. Proceedings of the IEEE, 2000

613 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Hardware and Architecture

View Paper: https://www.semanticscholar.org/paper/43e4c234996d4d287e83d73ef2d1134d381a8909

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Citations in the corpus

Discrete abstractions of hybrid systems (2000, background): “attention in the hybrid systems community, and the reader is referred to [3], [11], [23], [25], [33], [42], [55], and [73] for expositions to much of the research in the field.”
Computational techniques for the verification of hybrid systems (2003, methodology): “In our work, we have developed a reachability computation method based on level set techniques [5], [45], [46] and viscosity solutions to Hamilton–Jacobi equations [47], [48] using the ideas presented in [7] and [49].”
A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games (2005, neutral): “Our previous publications [3]–[5] have called this problem the three dimensional aircraft collision avoidance example .”
A Toolbox of Level Set Methods (2005, positive): “The discrete iteration proposed in [34] and repeated with minor modi cations in [17,35] can be coded manually into an m- le, as is done in section 2.”
Predictive Control for Linear and Hybrid Systems (2017, background): “For continuous-time hybrid systems, most authors either studied necessary conditions for a trajectory to be optimal [235, 271], or focused on the computation of optimal/suboptimal solutions by means of dynamic programming or the maximum principle [128, 245, 143, 144, 80, 292, 192, 261, 264, 266, 273”
Multiplayer reach-avoid games via low dimensional solutions and maximum matching (2014, background): “The optimal control input for the attacking team is given by [25], [26], [5]:”
Hamilton–Jacobi Formulation for Reach–Avoid Differential Games (2009, background): “The authors of [1] and [22] developed a reach–avoid computation, whose value function was characterized as a solution to a pair of coupled partial differential equations.”
On reachability and minimum cost optimal control (2004, methodology): “Following [6], we consider a simplified rectangular envelope; improvements that can be introduced to make the envelope more realistic are discussed in [4].”
Impulse differential inclusions: a viability approach to hybrid systems (2002, background): “Definitions 2 and 3 suggest that impulse differential inclusions are intimately related to other modeling languages found in the literature, such as different variants of hybrid automata (HA) [9], [13], [36], [38] and hybrid input/output automata (HIOA) [7].”
Constrained Optimal Control of Linear and Hybrid Systems (2003, methodology): “Different methods for the analysis and design of controllers for hybrid systems have emerged over the last few years [136, 146, 43, 81, 106, 23].”