Probabilistic Constrained MPC for Multiplicative and Additive Stochastic Uncertainty

Cannon, Mark; Kouvaritakis, B.; Wu, Xingjian

doi:10.1109/tac.2009.2017970

Cited by 155 publications

(116 citation statements)

References 12 publications

Supporting

Mentioning

113

Contrasting

Order By: Relevance

“…This notion is a commonly used in SMPC, where control policies involve a fixed prestabilizing feedback in conjunction with online optimization of control actions (see e.g., [5,26]). However, such control policies would introduce additional suboptimality in the control law as they do not take feedback into account during prediction in the SMPC problem.…”

Section: Joint Chance Constraintsmentioning

confidence: 99%

“…The first class consists of stochastic tube approaches [5,6,7] that use stochastic tubes with fixed or variable cross sections to replace chance constraints with linear constraints on the nominal state predictions and to construct terminal sets for guaranteeing recursive feasibility. These approaches use a prestabilizing feedback controller to ensure closed-loop stability.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic model predictive control with joint chance constraints

Paulson

Buehler

Braatz

et al. 2017

International Journal of Control

View full text Add to dashboard Cite

This article considers the stochastic optimal control of discrete-time linear systems subject to (possibly) unbounded stochastic disturbances, hard constraints on the manipulated variables, and joint chance constraints on the states.A tractable convex second-order cone program (SOCP) is derived for calculating the receding-horizon control law at each time step. Feedback is incorporated during prediction by parametrizing the control law as an affine function of the disturbances. Hard input constraints are guaranteed by saturating the disturbances that appear in the control law parametrization. The joint state chance constraints are conservatively approximated as a collection of individual chance constraints that are subsequently relaxed via the Cantelli-Chebyshev inequality. Feasibility of the SOCP is guaranteed by softening the approximated chance constraints using the exact penalty function method. Closed-loop stability in a stochastic sense is established by establishing that the states satisfy a geometric drift condition outside of a compact set such that their variance is bounded at all times. The SMPC approach is demonstrated using a continuous acetone-butanol-ethanol fermentation process, which is used for production of high-value-added drop-in biofuels.

show abstract

Section: Joint Chance Constraintsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic model predictive control with joint chance constraints

Paulson

Buehler

Braatz

et al. 2017

International Journal of Control

View full text Add to dashboard Cite

show abstract

“…While some MPC approaches in the literature indeed solve stochastic optimal control problems (see, e.g., Couchman et al (2006) or Cannon et al (2009) and the references therein), in this paper we follow the simpler certainty equivalence approach similar to (Bertsekas;2005, Section 6.1) which does in general not compute the true stochastic optimum but in the case of stochastic perturbations with low intensities may still yield reasonably good approximately optimal results. To this end, we replace the stochastic dynamics by its expected counterpart…”

Section: Outlook On Nmpc For Stochastic Problemsmentioning

confidence: 99%

Using Nonlinear Model Predictive Control for Dynamic Decision Problems In Economics

2013

View full text Add to dashboard Cite

This paper presents a new approach to solve dynamic decision models in economics. The proposed procedure, called Nonlinear Model Predictive Control (NMPC), relies on the iterative solution of optimal control problems on finite time horizons and is well established in engineering applications for stabilization and tracking problems. Only quite recently, extensions to more general optimal control problems including those appearing in economic applications have been investigated. Like Dynamic Programming (DP), NMPC does not rely on linearization techniques but uses the full nonlinear model and in this sense provides a global solution to the problem. However, unlike DP, NMPC only computes one optimal trajectory at a time, thus avoids to grid the state space and for this reason the computational demand grows much more moderately with the space dimension than for DP. In this paper we explain the basic idea of NMPC, give a proof concerning the accuracy of NMPC for discounted optimal control problems, present implementational details, and demonstrate the ability of NMPC to solve dynamic decision problems in economics by solving low and high dimensional examples, including models with multiple equilibria, tracking and stochastic problems.

show abstract

“…Previous approaches [6,7,8,9,18,20] considered constraints on the marginal distribution of the state, typically point-wise in time probabilistic constraints. In those works the constraints were enforced by controlling the conditional probability of constraint violations between two consecutive time instances without taking into account the past behavior of the state process.…”

Section: Introductionmentioning

confidence: 99%

“…Other examples include energy-efficient datacenter cooling subject to the constraints on the number of delayed queries per unit of time (see, e.g., [17]), or performance (e.g., power output) maximization of a machine subject to fatigue constraints (see [9] for a concrete example of wind-turbine control).…”

Section: Introductionmentioning

confidence: 99%

Stochastic MPC Framework for Controlling the Average Constraint Violation

Korda

Linares

Oldewurtel

et al. 2014

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

This paper considers linear discrete-time systems with additive, bounded, disturbances subject to hard control input bounds and a stochastic constraint on the amount of state-constraint violation averaged over time. The amount of violations is quantified by a loss function and the averaging can be weighted, corresponding to exponential forgetting of past violations. The freedom in the choice of the loss function makes this formulation highly flexible -for instance, probabilistic constraints or integrated chance constraints can be enforced by an appropriate choice of the loss function. For the type of constraint considered, we develop a recursively feasible receding horizon control scheme exploiting the averaged-over-time nature by explicitly taking into account the amount of past constraint violations when determining the current control input. This leads to a significant reduction in conservatism. As a simple extension of the proposed approach we show how time-varying state-constraints can be handled within our framework. The computational complexity (online as well as offline) is comparable to existing model predictive control schemes. The effectiveness of the proposed methodology is demonstrated by means of a numerical example.

show abstract

Probabilistic Constrained MPC for Multiplicative and Additive Stochastic Uncertainty

Cited by 155 publications

References 12 publications

Stochastic model predictive control with joint chance constraints

Stochastic model predictive control with joint chance constraints

Using Nonlinear Model Predictive Control for Dynamic Decision Problems In Economics

Stochastic MPC Framework for Controlling the Average Constraint Violation

Contact Info

Product

Resources

About