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math.OC2020
Polynomial Approximation of Value Functions and Nonlinear Controller Design with Performance Bounds
Morgan Jones, Matthew M. Peet
For any suitable Optimal Control Problem (OCP) there exists a value function, defined as the unique viscosity solution to the Hamilton-Jacobi-Bellman (HJB) Partial-Differential-Equ…
math.OC2020
A Generalization of Bellman's Equation with Application to Path Planning, Obstacle Avoidance and Invariant Set Estimation
Morgan Jones, Matthew Peet
The standard Dynamic Programming (DP) formulation can be used to solve Multi-Stage Optimization Problems (MSOP's) with additively separable objective functions. In this paper we co…