arXiv subjects

Jizhou Lai

Publications and source records attributed to Jizhou Lai.

3 recordsLinked to original sources

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.

eess.SY↗

arXiv2021

Smooth Q-learning: Accelerate Convergence of Q-learning Using Similarity

An improvement of Q-learning is proposed in this paper. It is different from classic Q-learning in that the similarity between different states and actions is considered in the proposed method. During the training, a new updating mechanism is used, in which the Q value of the similar state-action pairs are updated synchronously. The proposed method can be used in combination with both tabular Q-learning function and deep Q-learning. And the results of numerical examples illustrate that compared to the classic Q-learning, the proposed method has a significantly better performance.

cs.AI↗

arXiv2020

Recursive Regret Matching: A General Method for Solving Time-invariant Nonlinear Zero-sum Differential Games

In this paper, a new method is proposed to compute the rolling Nash equilibrium of the time-invariant nonlinear two-person zero-sum differential games. The idea is to discretize the time to transform a differential game into a sequential game with several steps, and by introducing state-value function, transform the sequential game into a recursion consisting of several normal-form games, finally, each normal-form game is solved with action abstraction and regret matching. To improve the real-time property of the proposed method, the state-value function can be kept in memory. This method can deal with the situations that the saddle point exists or does not exist, and the analysises of the existence of the saddle point can be avoided. If the saddle point does not exist, the mixed optimal control pair can be obtained. At the end of this paper, some examples are taken to illustrate the validity of the proposed method.

eess.SY↗