Time-Varying Optimization for the Control of Differentially Flat Systems With Input Constraints

Adam W. Hall, John W. Simpson-Porco, Angela P. Schoellig

Keywords: control, optimization, robotics

TL;DR: Cascaded time-varying optimization controls flat nonlinear systems with input constraints via differential equation integration, matching predictive control at a fraction of the cost.

Abstract: We present a continuous-time framework for constrained control of differentially flat nonlinear systems using cascaded time-varying optimization (TVO). Flatness-based controllers can exploit exact nonlinear dynamics through convex optimization in flat-output coordinates, but enforcing actuator limits remains challenging because the flat-to-physical input map is nonlinear. To address this, we cascade two TVO layers: an output-level TVO that drives constrained tracking in flat-output space, and an input-level TVO that continuously projects the resulting command onto time-varying actuator limits. Both layers are implemented as coupled ordinary differential equations integrated online, avoiding repeated solution of optimization problems. We detail the problem formulation and controller construction, and validate the approach on a wheeled mobile robot tracking task where the method matches the tracking performance of nonlinear model predictive control while strictly respecting constraints, using only an integrator at deployment rather than an online optimization solver.

Submission Number: 3