Preview-Enhanced Synchronous Policy Iteration for Zero-Sum Differential Games in a Class of Continuous-Time Lipschitz Nonlinear Systems

This paper presents a preview-enhanced synchronous policy-iteration framework for zero-sum differential games in continuous-time Lipschitz nonlinear systems with differentiable bounded disturbances. By embedding finite-horizon reference preview into an augmented error system, the tracking problem is reformulated as a regulation-oriented zero-sum game. A synchronous actor–critic–disturbance learning scheme is then developed to approximate the value function and the control/disturbance policies without solving the Hamilton–Jacobi–Isaacs equation. The preview signal acts as a known bounded forcing term, enabling anticipative tracking behavior. A Lyapunov-based analysis establishes uniform ultimate boundedness under local approximation, bounded preview forcing, and persistence of excitation. Simulations on a flexible-link robot show earlier tracking response, improved transient performance, bounded augmented dynamics, and stable neural-network weight adaptation compared with the non-preview case.