Decomposition of Reachable Sets and Tubes for a Class of Nonlinear Systems

Reachability analysis provides formal guarantees for performance and safety properties of nonlinear control systems. Here, one aims to compute the backward reachable set (BRS) or tube (BRT)-the set of states from which the system can be driven into a target set at a particular time or within a time...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2018-11, Vol.63 (11), p.3675-3688
Main Authors: Chen, Mo, Herbert, Sylvia L., Vashishtha, Mahesh S., Bansal, Somil, Tomlin, Claire J.
Format: Article
Language:English
Subjects:
Autonomous systems
Computation
computational efficiency
Control systems
control theory
Decomposition
Disturbances
Dynamical systems
Electron tubes
Nonlinear analysis
Nonlinear control
Nonlinear control systems
Nonlinear systems
Polytopes
reachability analysis
Safety
scalability
System dynamics
system verification
Trajectory
Tubes
Vehicle dynamics
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Summary:Reachability analysis provides formal guarantees for performance and safety properties of nonlinear control systems. Here, one aims to compute the backward reachable set (BRS) or tube (BRT)-the set of states from which the system can be driven into a target set at a particular time or within a time interval, respectively. The computational complexity of current approaches scales poorly, making application to high-dimensional systems intractable. We propose a technique that decomposes the dynamics of a general class of nonlinear systems into subsystems which may be coupled through common states, controls, and disturbances. Despite this coupling, BRSs and BRTs can be computed efficiently using our technique without incurring additional approximation errors and without the need for linearizing dynamics or approximating sets as polytopes. Computations of BRSs and BRTs now become orders of magnitude faster, and for the first time BRSs and BRTs for many high-dimensional nonlinear control systems can be computed using the Hamilton-Jacobi formulation. In situations involving bounded adversarial disturbances, our proposed method can obtain slightly conservative results. We demonstrate our theory by numerically computing BRSs and BRTs for several systems, including the six-dimensional Acrobatic Quadrotor using the HJ formulation.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2018.2797194