A Computationally Efficient Hamilton-Jacobi-based Formula for State-Constrained Optimal Control Problems

Understand

This paper investigates a Hamilton-Jacobi (HJ) analysis to solve finite-horizon optimal control problems for high-dimensional systems.

• Although grid-based methods, such as the level-set method [1], numerically solve a general class of HJ partial differential equations, the computational complexity is exponential in the dimension of the continuous state.
• To manage this computational complexity, methods based on Lax-Hopf theory have been developed for the state-unconstrained optimal control problem under certain assumptions, such as affine dynamics and state-independent stage cost.
• Based on the Lax formula [2], this paper proposes an HJ formula for the state-constrained optimal control problem for nonlinear systems.