Document detail
ID
oai:arXiv.org:2403.16979
Topic
Mathematics - Optimization and Con... Electrical Engineering and Systems...Author
Mohamed, Mohamed Naveed Gul Sharma, Aayushman Goyal, Raman Chakravorty, SumanCategory
Computer Science
Year
2024
listing date
3/27/2024
Keywords
set nonlinear systems terminal controlAbstract
This paper considers the infinite horizon optimal control problem for nonlinear systems.
Under the condition of nonlinear controllability of the system to any terminal set containing the origin and forward invariance of the terminal set, we establish a regularized solution approach consisting of a ``finite free final time" optimal transfer problem to the terminal set which renders the set globally asymptotically stable.
Further, we show that the approximations converge to the optimal infinite horizon cost as the size of the terminal set decreases to zero.
We also perform the analysis for the discounted problem and show that the terminal set is asymptotically stable only for a subset of the state space and not globally.
The theory is empirically evaluated on various nonholonomic robotic systems to show that the cost of our approximate problem converges and the transfer time into the terminal set is dependent on the initial state of the system, necessitating the free final time formulation.
Mohamed, Mohamed Naveed Gul,Sharma, Aayushman,Goyal, Raman,Chakravorty, Suman, 2024, An Optimal Solution to Infinite Horizon Nonlinear Control Problems: Part II
