Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties

Limón, Daniel; Álamo, T.; Camacho, Eduardo F.

doi:10.1109/cdc.2002.1185106

Cited by 199 publications

(156 citation statements)

References 12 publications

Supporting

Mentioning

150

Contrasting

Unclassified

Order By: Relevance

“…Theorem 23 (ISS for RHC) Let W be a polytope and the RHC law µ N (·) be defined as in (23). If A1 and A2 hold, then the origin is ISS for the closed-loop system (24) with region of attraction X sf N .…”

Section: Input-to-state Stability (Iss) For Rhcmentioning

confidence: 99%

See 1 more Smart Citation

Optimization over state feedback policies for robust control with constraints

2006

View full text Add to dashboard Cite

This paper is concerned with the optimal control of linear discrete-time systems subject to unknown but bounded state disturbances and mixed polytopic constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence. This implies that a broad class of constrained finite horizon robust and optimal control problems, where the optimization is over affine state feedback policies, can be solved in a computationally efficient fashion using convex optimization methods. This equivalence result is used to design a robust receding horizon control (RHC) state feedback policy such that the closed-loop system is input-to-state stable (ISS) and the constraints are satisfied for all time and all allowable disturbance sequences. The cost to be minimized in the associated finite horizon optimal control problem is quadratic in the disturbance-free state and input sequences. The value of the receding horizon control law can be calculated at each sample instant using a single, tractable and convex quadratic program (QP) if the disturbance set is polytopic, or a tractable second-order cone program (SOCP) if the disturbance set is given by a 2-norm bound.

show abstract

Section: Input-to-state Stability (Iss) For Rhcmentioning

confidence: 99%

“…As an alternative, we use the notion of input-to-state stability (ISS) [13,15], which has proven to be effective in the study of RHC laws with input constraints only [16] and in the analysis and synthesis of RHC laws with robust constraint satisfaction guarantees [23].…”

Section: Input-to-state Stability (Iss) For Rhcmentioning

confidence: 99%

Optimization over state feedback policies for robust control with constraints

2006

View full text Add to dashboard Cite

show abstract

“…A related analysis is also presented for unconstrained nonlinear MPC problems in [10]. On the other hand, the treatment of constrained MPC systems is more difficult, and in [6,5] a robust analysis is presented based on Pontryagin difference sets, which can lead to conservative controllers.…”

Section: Introductionmentioning

confidence: 99%

“…The results in this paper lead to a criterion that is a sufficient condition for asymptotic stability in the presence of plant/model mismatch. We note, however, that we do not treat the weaker (but very useful) property of input to state stability (ISS), covered in [6,5], although in future work we plan to extend this framework to deal with ISS as well.…”

Section: Introductionmentioning

confidence: 99%

“…A broad review by Mayne et al [7] on constrained MPC points out that while research on stability has reached a relatively mature stage, further research is required to develop implementable robust MPC for nonlinear systems. More recent studies [6,4,5] have analyzed the robust design of nonlinear MPC discrete time controllers. There a robustness margin is derived in conjunction with the Lyapunov stability conditions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A tool to analyze robust stability for constrained nonlinear MPC

Santos¹,

Biegler²,

Castro³

2008

Journal of Process Control

View full text Add to dashboard Cite

A sufficient condition for robust asymptotic stability of nonlinear constrained model predictive control (MPC) is derived with respect to plant/model mismatch. This work is an extension of a previous study on the unconstrained nonlinear MPC problem, and is based on nonlinear programming sensitivity concepts. It addresses the discrete time state feedback problem with all states measured. A strategy to estimate bounds on the plant/model mismatch is proposed that can be used off-line as a tool to assess the extent of model mismatch that can be tolerated to guarantee robust stability.

show abstract

Nonlinear Adaptive Model Predictive Control of Constrained Systems with Offset‐Free Tracking Behavior

Vatankhah

Farrokhi

2017

Asian Journal of Control

View full text Add to dashboard Cite

In this paper, a nonlinear model‐based predictive control strategy for constrained systems based on an adaptive neural network (NN) predictor is proposed. The proposed controller is robust against the model uncertainties and external bounded disturbances. Moreover, it provides offset‐free tracking behavior using the adaptive structure in the model. Based on the uncertainties bounds, the restriction of the system constraints causes robust feasibility and stability of the closed‐loop system. It is shown that the output of the NN predictor converges to the system output. Moreover, offset‐free behavior of the closed‐loop system is investigated using the Lyapunov theorem. Simulation results show the effectiveness of the proposed method as compared to the recently proposed model predictive control methods in the literature.

show abstract

Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties

Cited by 199 publications

References 12 publications

Optimization over state feedback policies for robust control with constraints

Optimization over state feedback policies for robust control with constraints

A tool to analyze robust stability for constrained nonlinear MPC

Nonlinear Adaptive Model Predictive Control of Constrained Systems with Offset‐Free Tracking Behavior

Contact Info

Product

Resources

About