Towards Spline-based Dynamic Input Allocation

In this paper, a novel design for dynamic input allocation is proposed. Given a closed-loop system including an input redundant plant (i.e. having more inputs than outputs), the allocator modifies the plant's input by injecting an allocation signal in such a way that the plant's output is unmodified but the steady-state evolution of the control input is optimized with respect to a suitable Lagrange cost. The proposed solution extends previous work by replacing simple harmonic allocation signals by periodic piecewise polynomial ones, thus providing the basic tool to realize spline-based allocation with enhanced potential for applications in more challenging or nonlinear contexts such as flexible robotics or drone swarms, where simple harmonic allocation signals might be inadequate.