Linear-Like Policy Iteration Based Optimal Control for Continuous-Time Nonlinear Systems

• 成果类型: Article
• 署名作者: Tahirovic, Adnan; Astolfi, Alessandro
• 署名单位: University of Sarajevo; Imperial College London; Sapienza University Rome
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3226671
• 发表日期: 2023
• 页码: 5837-5849
• 关键词: Optimal control; Nonlinear systems; COSTS; mathematical models; trajectory; Linear systems; Jacobian matrices; control design; nonlinear control systems; optimal control

摘要

We propose a novel strategy to construct optimal controllers for continuous-time nonlinear systems by means of linear-like techniques, provided that the optimal value function is differentiable and quadratic-like. This assumption covers a wide range of cases and holds locally around an equilibrium under mild assumptions. The proposed strategy does not require solving the Hamilton-Jacobi-Bellman equation, i.e., a nonlinear partial differential equation, which is known to be hard or impossible to solve. Instead, the Hamilton-Jacobi-Bellman equation is replaced with an easy-solvable state-dependent Lyapunov matrix equation. We exploit a linear-like factorization of the underlying nonlinear system and a policy-iteration algorithm to yield a linear-like policy-iteration for nonlinear systems. The proposed control strategy solves optimal nonlinear control problems in an asymptotically exact, yet still linear-like manner. We prove optimality of the resulting solution and illustrate the results via four examples.