A novel unified framework for solving reachability and invariance problems

Abstract

The level set method is a widely used tool for solving reachability and invariance problems. However, some shortcomings, such as large amount of storage space consumption and the difficulty of constructing terminal conditions for solving the Hamilton–Jacobi partial differential equation, limit the application of the level set method in some problems, especially those with irregular target sets. This paper proposes a method that can effectively avoid the above tricky issues and thus has better generality. In the proposed method, the reachable or invariant sets with different time horizons are characterised by some non-zero sublevel sets of a value function. This value function is not obtained by solving a viscosity solution of the partial differential equation but by recursion and interpolation approximation. At the end of this paper, some examples are taken to illustrate the accuracy and generality of the proposed method.

Keywords:

• Reachability
• invariance
• optimal control
• non-affine nonlinear system

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Defense Outstanding Youth Science Foundation [2018-JCJQ-ZQ-053] and Central University Basic Scientific Research Operating Expenses Special Fund Project Support [NF2018001].