Search

Extensive research has been dedicated to reinforcement learning (RL) for acquiring proficient optimal controllers through interactions with the environment. However, real-world demands, including enhanced safety performance, introduce considerable challenges to the present design of optimal controllers rooted in RL algorithms. A novel approach is introduced in this article for designing RL-based optimal controllers, employing a control barrier function (CBF) alongside a nonquadratic loss function related to the control signal. The aim is to enable the agent to learn the optimal controller in a secure and efficient manner. To tackle the instability issue in neural network training inherent to traditional RL-based controller design processes, the nonlinear model predictive control (NMPC) technique is employed for initializing the controller network’s weights. A formal demonstration of the method’s optimality is presented. Numerical simulations validate the proposed approach, illustrating its capacity to effectively learn the optimal controller while adhering to the input and state constraints of the system.

The policy gradient adaptive dynamic programming (PGADP) technique has gained recognition as an effective approach for optimizing the performance of nonlinear systems. Nonetheless, existing PGADP algorithms often demand a substantial volume of expensive or potentially risky interaction data with the system. Moreover, the utilization of neural networks in these algorithms can result in suboptimal learning efficiency and unstable training procedures. To address these challenges, a novel algorithm, referred to as OptNet-PGADP, has been introduced. This algorithm integrates an initially tailored control policy based on OptNet to tackle the optimization of control problems in discrete-time nonlinear systems. The OptNet-PGADP algorithm operates through a two-step process. Initially, the input–output trajectory of the system is computed using the nonlinear model predictive control (NMPC) method. Subsequently, an initial admissible control policy is acquired through OptNet. This policy is iteratively enhanced using the PGADP algorithm to attain the optimal controller. The resulting closed-loop control policy can be readily deployed in real-time applications. The implementation of the algorithm employs OptNet for the actor network and integrates an experience replay mechanism to bolster the controller’s learning efficiency. Furthermore, a convergence and optimality analysis of the algorithm is included. Simulation and experimental results conducted on two nonlinear systems conclusively demonstrate that the approach outperforms traditional PGADP and NMPC algorithms. These findings underscore the efficacy of OptNet-PGADP in mitigating the constraints of current methods and achieving superior control performance for nonlinear systems.