arXiv subjects

Taotao Liang

Publications and source records attributed to Taotao Liang.

3 recordsLinked to original sources

arXiv2022

An Improved Level Set Method for Reachability Problems in Differential Games

This study focuses on reachability problems in differential games. An improved level set method for computing reachable tubes is proposed in this paper. The reachable tube is described as a sublevel set of a value function, which is the viscosity solution of a Hamilton-Jacobi equation with running cost. We generalize the concept of reachable tubes and propose a new class of reachable tubes, which are referred to as cost-limited one. In particular, a performance index can be specified for the system, and a cost-limited reachable tube is a set of initial states of the system's trajectories that can reach the target set before the performance index increases to a given admissible cost. Such a reachable tube can be obtained by specifying the corresponding running cost function for the Hamilton-Jacobi equation. Different non-zero sublevel sets of the viscosity solution of the Hamilton-Jacobi equation at a certain time point can be used to characterize the cost-limited reachable tubes with different admissible costs (or the reachable tubes with different time horizons), thus reducing the storage space consumption. Several examples are provided to illustrate the validity and accuracy of the proposed method.

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arXiv2021

A Novel Unified Framework for Solving Reachability, Viability and Invariance Problems

The level set method is a widely used tool for solving reachability and invariance problems. However, some shortcomings, such as the difficulties of handling dissipation function and constructing terminal conditions for solving the Hamilton-Jacobi partial differential equation, limit the application of the level set method in some problems with non-affine nonlinear systems and 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 characterized 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.

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arXiv2021

Probabilistic Reach-Avoid Reachability in Nondeterministic Systems with Time-VaryingTargets and Obstacles

The probabilistic reachability problems of nondeterministic systems are studied. Based on the existing studies, the definition of probabilistic reachable sets is generalized by taking into account time-varying target set and obstacle. A numerical method is proposed to compute probabilistic reachable sets. First, a scalar function in the state space is constructed by backward recursion and grid interpolation, and then the probability reachable set is represented as a nonzero level set of this scalar function. In addition, based on the constructed scalar function, the optimal control policy can be designed. At the end of this paper, some examples are taken to illustrate the validity and accuracy of the proposed method.

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