Controllers for reachability specifications for hybrid systems

By John Lygeros, Claire Jennifer Tomlin, S. Sastry. 1999

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Citations in the corpus

Aligning AI With Shared Human Values (2020, background): “Similarly, computer scientists who use constraints to ensure safety of their systems (Lygeros et al., 1999) must grapple with the fact that these constraints can be mutually unsatisfiable (Abadi et al.”
Certified Defenses against Adversarial Examples (2018, methodology): “In robotics, certificates of stability are routinely used both for safety verification (Lygeros et al., 1999; Mitchell et al., 2005) and controller synthesis (Başar & Bernhard, 2008; Tedrake et al., 2010).”
Periodic event‐triggered observation and control for nonlinear Lipschitz systems using impulsive observers (2017, background): “In the previous definition, R is usually called reset map [32, 33].”
Digital idle speed control of automotive engines: A safety problem for hybrid systems (2006, methodology): “Once the maximal safe set is computed, following the procedure in [15], it is always possible to derive the maximal controller, i.”
Identification of piecewise affine systems via mixed-integer programming (2004, background): “Most literature on hybrid systems has dealt with modeling [1] [2], stability analysis [3] [4], control [2] [5] [6], verification [7] [8] [9], and fault detection [10] [11].”
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].”
Dynamic programming for constrained optimal control of discrete-time linear hybrid systems (2005, methodology): “A detailed discussion of different modeling frameworks for hybrid systems that appeared in the literature goes beyond the scope of this paper; the main concepts can be found inAntsaklis (2000), Branicky, Borkar, and Mitter (1998), Bemporad and Morari (1999), Lygeros, Tomlin, and Sastry (1999).”
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].”
Hamilton–Jacobi Formulation for Reach–Avoid Differential Games (2009, background): “Numerous problems regarding safety of air traffic management systems [1], [2], flight control [3], [4], [5] ground transportation systems [6], [7], etc.”
A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games (2005, unknown): “We previously explored the idea of using a time-dependent Hamilton–Jacobi–Isaacs (HJI) partial differential equation (PDE) for computing reachable sets in [2] and [3], although the formulation used in those papers was not well suited for numerical implementation.”
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].”
The Information Complexity of Learning Tasks, their Structure and their Distance (2019, methodology): “Numerical methods for reachability computation [12] are restricted to low-dimensional spaces, whereas typical models in use in the practice can have millions of parameters.”