Linear output regulation with dynamic optimization for uncertain linear over-actuated systems

This paper considers the linear output regulation problem for uncertain over-actuated plants. The general form of input redundancy considered in this work implies the existence of multiple control inputs and state trajectories compatible with a prescribed reference for the output. On-line selection, according to certain performance criteria, of the most suitable of these inputs-state trajectories leads to a linear output regulation problem with dynamic redundancy allocation. We present a solution that augments the well known internal model control scheme with two additional dynamical systems. The first one, named annihilator, parametrizes the inputs and the corresponding state trajectories that are invisible from the output. The second one, named redundancy allocator, dynamically selects the best solution according to a predefined performance criterion. We derive explicit solutions for the performance criterion equal to relaxed 1, 2, and ∞- norms of the plant input. This set-up is a particular case of the dynamic redundancy allocation problem named dynamic input allocation. The proposed solutions can be implemented in an error feedback form and are especially suitable for optimizing sparsity, power and amplitude of the control input. Finally, structural stability, robustness and existence of a unique steady-state are proven.