Model Predictive Control

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.

show abstract

“…The inclusion (6c) can then be implemented using linear inequality constraints, compare e.g. [6], [7], [8] and [35,Chap. 5].…”

Section: Setup and General Theorymentioning

confidence: 99%

“…Again, the complexity of computing (35) is similar to the computation of a Lipschitz constant (2 p times).…”

Section: Algorithm 1 Moving Window Set Membership Updatesmentioning

confidence: 99%

See 1 more Smart Citation

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

Köhler

Soloperto

Müller

et al. 2021

IEEE Trans. Automat. Contr.

134

133

View full text Add to dashboard Cite

show abstract

“…Furthermore, the on-line problem (45)-(46) is recursive feasible if it is solved at time k ≥ 0. The augmented closed-loop system is robust stable such that the controlled system (1) converges to a neighborhood of the origin. The input and state constraints in (2) are satisfied for all time k ≥ 0.…”

Section: Recursive Feasibility and Robust Stability Theorem 2 For Thmentioning

confidence: 99%

“…Robust model predictive control (MPC) is an effective technology for controlling complex plants characterized by uncertainties, nonlinearities, and constraints. [1][2][3] In the field of robust control, linear parameter varying (LPV) systems can approximate real nonlinear systems or represent uncertain systems by a polytopic family of linear systems, whose dynamics depend on time-varying scheduling parameters. 4,5 Over the last two decades, research activities in robust MPC for LPV systems have become an important branch, eg, state feedback robust MPC with measurable system states [6][7][8][9][10] and output feedback robust MPC with unknown system states.…”

Section: Introductionmentioning

confidence: 99%

An observer‐based output feedback robust MPC approach for constrained LPV systems with bounded disturbance and noise

Ping

Yang

Wang

et al. 2019

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Summary The present paper addresses an observer‐based output feedback robust model predictive control for the linear parameter varying system with bounded disturbance and noise subject to input and state constraints. The main contribution is that the on‐line convex optimization problem not only simultaneously optimizes the observer and controller gains to stabilize the augmented closed‐loop system but also incorporates the refreshment of bounds of the estimation error set. The optimization problem steers the nominal augmented closed‐loop system to converge to the origin, and the real augmented closed‐loop system bounded within robust positive invariant set converges to a neighborhood of the origin such that recursive feasibility of the optimization and robust stability of the controlled system are ensured. Two numerical examples are given to illustrate the effectiveness of the method.

show abstract

Theoretical Base of MPC

2017

Multivariable Predictive Control

View full text Add to dashboard Cite

Model Predictive Control

Cited by 326 publications

References 0 publications

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

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

An observer‐based output feedback robust MPC approach for constrained LPV systems with bounded disturbance and noise

Theoretical Base of MPC

Contact Info

Product

Resources

About