Feedback Control Approach Based on Classes of Zonal Control Actions

Abstract

This paper presents a feedback control synthesis approach for nonlinear dynamic systems with lumped parameters under partial observability and time delays. We propose a zonal feedback control framework, where the state space of observable components is partitioned into finitely many zones, each associated with constant or linear feedback gains. Unlike traditional feedback laws that continuously depend on the instantaneous state, the control input here changes only when the system transitions between predefined zones. This reduces the infinite-dimensional feedback synthesis problem to a finite-dimensional parametric optimization problem, enabling efficient computation of control parameters. The control design problem is formulated as the minimization of an objective functional that accounts for both the system’s dynamic response and control energy, averaged over uncertain initial conditions and parameter variations. To solve this problem, we derive analytical formulas for the gradient of the objective functional with respect to the zonal feedback parameters by employing perturbation techniques and adjoint systems. These gradient formulas allow the implementation of first-order optimization methods, such as the projected gradient algorithm, to determine optimal zonal gains while satisfying control constraints. The presented approach has potential applications in robotics, autonomous systems, and other domains where real-time computation and robustness to uncertainties are critical.