Tracking Control for Affine Nonlinear Systems: A Non-Zero-Sum Game Approach With Incomplete Discount Factors

Abstract

In optimal tracking control problems for affine nonlinear systems, the nonzero steady-state control input often leads to an unbounded infinite-horizon cost function, which makes it difficult to achieve asymptotic convergence of tracking errors. This paper reformulates the non-zero-sum game framework of the tracking control problem and proposes a control method utilizing incomplete discount factors, achieving asymptotic convergence of the tracking error for affine nonlinear systems with respect to any bounded reference trajectory. The cost functions corresponding to the steady-state and transient components are constructed to meet the control objectives while simultaneously seeking a Nash equilibrium solution. The actor-critic structure approximates each participant and their respective cost function independently. Coupled Hamilton-Jacobi (HJ) equations are addressed using input-output data without explicit system models, and the least squares method updates neural networks (NNs) weights concurrently. Simulation results demonstrate that this approach achieves reduced tracking errors compared to traditional methods that use a discount factor.