Hamilton–Jacobi Formulation for Reach–Avoid Differential Games

By Kostas Margellos, John Lygeros. IEEE Transactions on Automatic Control, 2009

301 citations recorded by the source corpus.

A new framework for formulating reachability problems with competing inputs, nonlinear dynamics, and state constraints as optimal control problems is developed. Such reach-avoid problems arise in, among others, the study of safety problems in hybrid systems. Earlier approaches to reach-avoid computations are either restricted to linear systems, or face numerical difficulties due to possible discontinuities in the Hamiltonian of the optimal control problem. The main advantage of the approach proposed in this paper is that it can be applied to a general class of target-hitting continuous dynamic games with nonlinear dynamics, and has very good properties in terms of its numerical solution, since the value function and the Hamiltonian of the system are both continuous. The performance of the proposed method is demonstrated by applying it to a case study, which involves the target-hitting problem of an underactuated underwater vehicle in the presence of obstacles.

Subfields: Aerospace Engineering, Computer Vision and Pattern Recognition, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/7b635f748d953cc79630ba4114240af6fdd3e58d

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Citations in the corpus

Convex Computation of the Region of Attraction of Polynomial Control Systems (2012, methodology): “Most of the existing literature on ROA computation follows Zubov’s approach [31, 47, 18] and uses a dual Lyapunov certiﬁcate; see [43], the survey [16], Section 3.4 in [17], and more recently [40, 8] and [9] and the references therein.”
Optimization-Based Collision Avoidance (2017, methodology): “In this paper, we do not review, or compare, the proposed optimization-based collision avoidance with alternative approaches such as those based on dynamic programming [13], reachability analysis [14, 15, 16], graph search [17, 18, 19], sampling based methods [20, 21, 22, 23] or interpolating curves”
A general Hamilton-Jacobi framework for non-linear state-constrained control problems (2013, unknown): “This kind of penalization has also already been successfully used to study the reachability analysis for some state constrained nonlinear systems, see [15, 34].”