Model-free reinforcement learning control with zero-min barrier functions for constrained systems

The primary focus of this research is to develop an adaptive output feedback controller designed to minimize a cost-to-go function subject to constraints on input, output, and tracking error for a class of unknown non-affine discrete-time systems. The problem formulation addresses a general class of non-affine dynamics, exemplified by a high-gain DC motor torque control system, in which maintaining safe operation within prescribed input and output limits is critical. These physical limitations necessitate the incorporation of constraints to ensure the plant operates within safe regions. Consequently, a zero-min barrier function is employed in conjunction with a reinforcement learning algorithm to enforce both symmetric and asymmetric constraints. The control law employs actor-critic networks implemented through fuzzy rule-emulated networks, enabling adaptive performance. By deriving online learning laws, the system achieves nearly optimal tracking performance and ensures the forward invariance of the safe operating region, all without requiring inner iterations, thereby enhancing computational efficiency. Experimental validation under extreme disturbances and abrupt changes in the desired trajectory, which present a risk of constraint violations, demonstrates the robustness and effectiveness of the proposed controller. Comparative results further highlight the advantages of the proposed method in achieving a balance between near-optimal performance and strict constraint satisfaction, thereby ensuring stable operation within predefined limits.