2018/10/31 by Yibei Li, Yu Yao, Li, Yibei +3 · 2 citations
Computer Science · Engineering · #Advanced Control Systems Optimization #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.1811.00129
openalex publication_date 2018/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, the problem of finite horizon inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation of optimal control sequences. We propose the first complete result of the necessary and sufficient condition for the existence of corresponding LQ cost functions. Under feasible cases, the analytic expression of the whole solution space is derived and the equivalence of weighting matrices in LQ problems is discussed. For infeasible problems, an infinite dimensional convex problem is formulated to obtain a best-fit approximate solution with minimal control residual. And the optimality condition is solved under a static quadratic programming framework to facilitate the computation. Finally, numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed methods.