The advanced-step NMPC controller: Optimality, stability and robustness

Zavala, Ví­ctor M.; Biegler, Lorenz T.

doi:10.1016/j.automatica.2008.06.011

Cited by 357 publications

(203 citation statements)

References 18 publications

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“…Then, for I t in the neighborhood ofĪ t , ∃ k x , k J , t ≥ 0, such that Proof: We note thatx o t−N (I t ) = z o 0 (I t ). Bound (16a) follows from Taylor's theorem [6,22], while (16b) follows from (16a) and the Lipschitz continuity of the cost, as stated in Theorem 2. The error t is always nonnegative because, ifx o t−N (I t ) satisfies SSOC, then…”

Section: Assumption 1 (System Properties)mentioning

confidence: 99%

Stability analysis of an approximate scheme for moving horizon estimation

Zavala

2010

Computers & Chemical Engineering

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We analyze the stability properties of an approximate algorithm for moving horizon estimation (MHE). The strategy provides instantaneous state estimates and is thus suitable for large-scale feedback control. In particular, we study the interplay between numerical approximation errors and the convergence of the estimator error. In addition, we establish connections between the numerical properties of the Hessian of the MHE problem and traditional observability definitions. We demonstrate the developments through a simulation case study.

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Section: Assumption 1 (System Properties)mentioning

confidence: 99%

Stability analysis of an approximate scheme for moving horizon estimation

Zavala

2010

Computers & Chemical Engineering

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“…for all ω and the continuous measurement setting of (5). Based on our assumptions and considerations, we define the OED problem with fixed u as min…”

Section: Optimal Experimental Design Problemsmentioning

confidence: 99%

“…As a fast feedback of the controller is important in many applications, clever approaches doing most of the necessary calculations before a new measurement arrives have been proposed in the literature. The most important numerical concepts comprise real-time iterations [4,5], multi-level iterations [6], parallel multi-level iterations [7], an exploitation of the KKT structures [8,9], adaptive control [10], automatic code export [11,12], and usage of parametric QPs [13,14]. For a benchmark problem, the continuously stirred tank reactor of [15], a speedup of approximately 150,000 has been achieved comparing the 60 seconds per iteration reported in 1997 [16] and the 400 microseconds per iteration reported in 2011 by [17].…”

Section: Introductionmentioning

confidence: 99%

A Feedback Optimal Control Algorithm with Optimal Measurement Time Points

Jost

Säger

2017

Processes

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Nonlinear model predictive control has been established as a powerful methodology to provide feedback for dynamic processes over the last decades. In practice it is usually combined with parameter and state estimation techniques, which allows to cope with uncertainty on many levels. To reduce the uncertainty it has also been suggested to include optimal experimental design into the sequential process of estimation and control calculation. Most of the focus so far was on dual control approaches, i.e., on using the controls to simultaneously excite the system dynamics (learning) as well as minimizing a given objective (performing). We propose a new algorithm, which sequentially solves robust optimal control, optimal experimental design, state and parameter estimation problems. Thus, we decouple the control and the experimental design problems. This has the advantages that we can analyze the impact of measurement timing (sampling) independently, and is practically relevant for applications with either an ethical limitation on system excitation (e.g., chemotherapy treatment) or the need for fast feedback. The algorithm shows promising results with a 36% reduction of parameter uncertainties for the Lotka-Volterra fishing benchmark example.

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“…A survey of the numerical methods for on-line solution of NMPC problems is given in [4]. Most recently, an advanced-step NMPC controller with reduced on-line computational delay has been proposed in [5]. Several approaches to explicit solution of NMPC problems have been suggested in the literature.…”

Section: Introductionmentioning

confidence: 99%

A computational approach to explicit feedback stochastic Nonlinear Model Predictive Control

Grancharova

Johansen

2010

49th IEEE Conference on Decision and Control (CDC)

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Abstract-Nonlinear Model Predictive Control (NMPC)involves the solution at each sampling instant of a finite horizon optimal control problem subject to nonlinear system dynamics, and state and input constraints. Mathematical models of engineering systems usually contain some amount of uncertainty. In the robust NMPC problem formulation, the model uncertainty is taken into account. This paper presents an approximate multi-parametric Nonlinear Programming approach to explicit solution of feedback stochastic MPC problems for constrained nonlinear systems in the presence of stochastic uncertainty. It is assumed that the discrete probability distribution of the uncertainty is known. The mathematical expectation of the cost function is minimized subject to state and input constraints. The approximate explicit approach constructs a piecewise nonlinear approximation to the optimal sequence of feedback control policies. It is demonstrated by explicit feedback stochastic NMPC for a cart moving on a plane and attached to the wall via a spring.

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The advanced-step NMPC controller: Optimality, stability and robustness

Cited by 357 publications

References 18 publications

Stability analysis of an approximate scheme for moving horizon estimation

Stability analysis of an approximate scheme for moving horizon estimation

A Feedback Optimal Control Algorithm with Optimal Measurement Time Points

A computational approach to explicit feedback stochastic Nonlinear Model Predictive Control

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