Optimization-Based Trajectory Generation and Receding Horizon Control for Systems with Convex Dynamics

In this paper we propose an optimization-based control scheme, which can be used for trajectory generation or receding horizon control for system with nonlinear, but convex dynamics, and both explicit and implicit discrete time models. The scheme uses both the nonlinear model and its linearization to construct a tube containing all possible future system trajectories, and uses this tube to predict performance and ensure constraint satisfaction. The controls sequence and tube cross-sections are optimized online in a sequence of convex programs without the need of pre-computed error bounds. We prove feasibility, stability and non-conservativeness of the approach, with the series of convex programs converging to a point which is a local optimum for the original nonlinear optimal control problem. We further present how a structure- preserving model can be implemented within the approach and used to reduce the number of constraints and guarantee a structure-preserving discrete trajectory solution.