Robust Optimal Control of Nonlinear Communication Systems under Parametric Uncertainty

Abstract

Parametric uncertainty and external disturbances, nonlinear dynamics, interference, and changes in system parameters all greatly influence the performance of nonlinear communication systems and classical robust control techniques with a fixed level of disturbance rejection may be conservative. The present paper proposes a new disturbance attenuation function, ????(????)which is (globally) bounded by a positive scalar to establish a new and more powerful optimal-control framework for nonlinear communication systems with parametric uncertainties. The proposed formulation introduces a mechanism for state-dependent robustness instead of using a fixed robustness parameter, which is commonly used in existing formulations. The notion of generalized state dependent ℒ2-gain condition is given in terms of a dissipation inequality, and a nonlinear minimax differential game is formulated. Based on the Hamilton–Jacobi–Isaacs (HJI) framework, the corresponding optimal control and worst-case disturbance are computed, leading to a modified HJI equation which includes the state dependent term 1/????2(????) in the robustness. Parametric uncertainty is treated by a normalized bounded uncertainty representation and an augmented disturbance vector, which can be used to treat external disturbances and parametric uncertainty in a unified manner. In addition, a Lyapunov-based robust stability theorem is developed that ensures nominal asymptotic stability and state-dependent disturbance-attenuation performance. Analytical comparison and evaluation with the conventional one with fixed-???? show that the proposed framework is a generalization of the conventional one, provides more robust adaptability and has the potential to reduce the conservatism.