A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Abstract

In this paper, we present a tube-based framework for robust adaptive model predictive control (RAMPC) for nonlinear systems subject to parametric uncertainty and additive disturbances. Set-membership estimation is used to provide accurate bounds on the parametric uncertainty, which are employed for the construction of the tube in a robust MPC scheme. The resulting RAMPC framework ensures robust recursive feasibility and robust constraint satisfaction, while allowing for less conservative operation compared to robust MPC schemes without model/parameter adaptation. Furthermore, by using an additional mean-squared point estimate in the objective function the framework ensures finite-gain L2 stability w.r.t. additive disturbances.As a first contribution we derive suitable monotonicity and non-increasing properties on general parameter estimation algorithms and tube/set based RAMPC schemes that ensure robust recursive feasibility and robust constraint satisfaction under recursive model updates. Then, as the main contribution of this paper, we provide similar conditions for a tube based formulation that is parametrized using an incremental Lyapunov function, a scalar contraction rate and a function bounding the uncertainty. With this result, we can provide simple constructive designs for different RAMPC schemes with varying computational complexity and conservatism. As a corollary, we can demonstrate that state of the art formulations for nonlinear RAMPC are a special case of the proposed framework. We provide a numerical example that demonstrates the flexibility of the proposed framework and showcase improvements compared to state of the art approaches.

Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control

“…In this section, we introduce the RMPC scheme based on [5] (Sec. III-A) and extend it to robust output tracking (Sec.…”

“…In [4], an approach based on min-max differential inequalities is presented to achieve robustness for the nonlinear case. In this work, we build upon the novel nonlinear constraint tightening approach in [5], which provides slightly more conservative results than the approach in [4], but is far more computationally efficient.…”

“…We herein extend [5] to setpoint tracking. Setpoint tracking MPC, as introduced in [6] for nonlinear systems, enables the controller to track piece-wise constant output reference signals.…”

“…Contributions: This letter makes contributions in three main directions: (i) robust setpoint tracking MPC, (ii) approximate MPC via supervised learning with NNs, and (iii) their application to real robotic systems. (i) We present a new RMPC setpoint tracking approach that combines the RMPC [5] with the MPC setpoint tracking in [6] by proposing online optimized terminal ingredients to improve performance subject to safety constraints. The resulting robust approach provides safety guarantees in face of disturbances and uncertainties while yielding fully integrated robot control in one-layer (i.e., robust motion planning and feedback control).…”

“…The proposed AMPC considerably improves performance due to fast NN evaluation, while providing statistical guarantees on safety. (iii) Finally, this work comprises the first experimental implementations of both, the RMPC based on [5] and the AMPC originating from [13]. To the best of our knowledge, this is the first experimental implementation of nonlinear tracking RMPC with safety properties theoretically guaranteed by design.…”