A Caltech Library Service

Optimal Safe Controller Synthesis: A Density Function Approach

Chen, Yuxiao and Ahmadi, Mohamadreza and Ames, Aaron D. (2020) Optimal Safe Controller Synthesis: A Density Function Approach. In: 2020 American Control Conference (ACC). IEEE , Piscataway, NJ, pp. 5407-5412. ISBN 9781538682661.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


This paper considers the synthesis of optimal safe controllers based on density functions. We present an algorithm for robust constrained optimal control synthesis using the duality relationship between the density function and the value function. The density function follows the Liouville equation and is the dual of the value function, which satisfies Bellman’s optimality principle. Thanks to density functions, constraints over the distribution of states, such as safety constraints, can be posed straightforwardly in an optimal control problem. The constrained optimal control problem is then solved with a primal-dual algorithm. This formulation is extended to the case with external disturbances, and we show that the robust constrained optimal control can be solved with a modified primal-dual algorithm. We apply this formulation to the problem of finding the optimal safe controller that minimizes the cumulative intervention. An adaptive cruise control (ACC) example is used to demonstrate the efficacy of the proposed, wherein we compare the result of the density function approach with the conventional control barrier function (CBF) method.

Item Type:Book Section
Related URLs:
URLURL TypeDescription Paper
Chen, Yuxiao0000-0001-5276-7156
Ahmadi, Mohamadreza0000-0003-1447-3012
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2020 AACC.
Record Number:CaltechAUTHORS:20200730-143942888
Persistent URL:
Official Citation:Y. Chen, M. Ahmadi and A. D. Ames, "Optimal Safe Controller Synthesis: A Density Function Approach," 2020 American Control Conference (ACC), Denver, CO, USA, 2020, pp. 5407-5412, doi: 10.23919/ACC45564.2020.9147721
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104663
Deposited By: George Porter
Deposited On:31 Jul 2020 14:37
Last Modified:16 Nov 2021 18:33

Repository Staff Only: item control page