An efficient condensing algorithm for fast closed loop dual-mode nonlinear model predictive control

This paper presents a novel computationally efficient Closed Loop Dual-Mode Nonlinear Model Predictive Control scheme that uses closed loop models for condensing-based multiple-shooting frameworks which result in numerically robust optimisations. The proposed approach uses Time-Varying gains obtained from solving the Time-Varying Discrete Algebraic Ricatti Equation to embed feedback around the multiple-shooting trajectory, and proves the equivalence of the solution with the standard approach, thus resulting in the exact same stability, recursive feasibility and convergence properties. Moreover, the paper proposes an efficient algorithm based on an extension of the well-known 𝑂(𝑁2𝑝) condensing algorithm, which can be used within the so-called Real-Time Iteration Scheme to achieve real-time performance. Simulations of a nonlinear ball-plate system, as well as of an inverted pendulum, and its extension - the triple inverted pendulum, are presented along the paper to demonstrate the advantages along with some disadvantages, focusing on the numerical conditioning, the disturbance rejection properties, and the computational performance.