Optimal Control of Nonlinear Systems with Input and State Constraints Using Koopman Operator

To address the challenges of infinite-time horizon optimal control in nonlinear systems with constraints, this work presents a constrained optimization framework. Specifically, the Koopman operator theory is employed first to transform the nonlinear system into a linear system. The optimal control problem for a nonlinear system with constraints on control inputs and states is then reformulated as the optimal control problem for a linear system with constraints. Subsequently, by using an iterative algorithm and the concept of X-contractivity, the constrained optimal control for the linear system is solved. Finally, two examples are used to demonstrate the effectiveness and advantages of the proposed strategy.