Intelligent Safe Optimal Control Towards Koopman Operator-Driven Nonlinear Systems with Asymmetric State and Input Constraints

For unknown nonlinear systems subject to asymmetric state and input constraints simultaneously, this article establishes a safe value iteration paradigm to learn an optimal control policy in a data-based manner. Initially, the Koopman operator, instead of the black-box neural network, is applied to extract the inherent dynamics of the controlled systems from the measured data, thereby allowing for explicit analysis of the prediction error. To tackle the issue posed by state and input constraints, a crafted control barrier function is seamlessly incorporated into the canonical utility function, which retains the property of positive definiteness for the asymmetric case. Moreover, the value iteration algorithm with regard to the augmented utility function is adopted to attain a safe optimal controller, where the actor and critic networks are leveraged to approximate the control input and associated value function, respectively. The mono-tonicity, safety, and stability of the raised algorithm are further verified rigorously. Via performing three experiments on the linear system, the nonlinear system, and the manipulator plant, comparative results are obtained to substantiate the superiority and efficacy of the developed approach in achieving optimal performance and safe guarantee.