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Level set method is a widely used tool for solving reachability, viability and invariance problems. However, some shortcomings, such as the difficulties of handling dissipation function and constructing terminal condition for solving the Hamilton-Jacobi partial differential equation, limit the application of level set method in some problems with non-affine nonlinear systems and irregular target sets. In this paper, we propose a method which can effectively avoid the above difficult issues thus has better generality. In the proposed method, the reachable, viable and invariant sets are characterized by some non-zero level sets of different value functions. Instead of solving partial differential equations, the value functions are approximated by recursion and interpolation. At the end of this paper, some examples are taken to illustrate the accuracy and generality of the proposed method.

Directional stability during the roll-out phase is crucial to the safety and reusability of the aircraft. Because of the mechanical properties, the wheel-skid aircraft is more prone to produce course instability. To address this issue, the taxiing safe set of the wheel-skid aircraft is discussed based on the reachability theory. A dynamic model of the on-ground aircraft is established firstly, considering the complex condition of the ground loads. Then, the particular Hamilton–Jacobi partial differential equation is used to obtain the safe set. According to the safe set results, the optimal control of the rudder is built in the state space. Its effectiveness is verified by the comparison with other robust methods. In addition, three structural parameters are selected to analyze the influences on the safe set. Results indicate that the maximum safe yaw angle increases from [Formula: see text] to [Formula: see text] at 70 m/s under the optimal control of the rudder when the steering of nose wheel is locked. The safe boundary in the middle–high-speed region expands by 43.5% under the rudder control. Because of the mechanical properties, uncontrollable deflection will appear due to the asymmetric disturbances when the longitudinal velocity is lower than 42 m/s.

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