Stochastic receding horizon control with output feedback and bounded controls

Hokayem, Peter; Cinquemani, Eugenio; Chatterjee, Debasish; Ramponi, Federico; Lygeros, John

doi:10.1016/j.automatica.2011.09.048

Cited by 106 publications

(119 citation statements)

References 38 publications

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“…However, these approaches would not provide a rigorous guarantee for fulfillment of (2) with respect to all disturbance realizations. 4 In this work, the disturbance terms in the control policy (14) are saturated to enable dealing with unbounded disturbances [12,21]. The control policy (14) in the admissible set Π N (x) is replaced with…”

Section: Saturation Of Stochastic Disturbances For Handling Hard Inpumentioning

confidence: 99%

“…In addition, the SMPC approach in [9] results in a nonconvex program, which can become impractical for large-scale systems. On the other hand, the main contribution of this paper with respect to [12] is the ability to handle joint chance constraints while retaining the hard input constraints.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, unlike [12], the presented SMPC approach guarantees stability by design without using a stability constraint that can possibly limit the domain of attraction of the controller. In this work, the SMPC approach is demonstrated using an experimentally validated continuous acetone-butanol-ethanol (ABE) fermentation case study [17], which consists of 12 state variables.…”

Section: Introductionmentioning

confidence: 99%

“…The problem setup considered in this paper is similar to that in [12,9]. Hard input constraints are relaxed to chance constraints in [9] to cope with the unbounded nature of disturbances, whereas the SMPC program presented in this work allows for directly handling the hard input constraints in an unbounded disturbance setting.…”

Section: Introductionmentioning

confidence: 99%

“…The second class of SMPC approaches use affine parameterizations of feedback control laws to obtain a tractable convex SMPC formulation [10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

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Stochastic model predictive control with joint chance constraints

Paulson

Buehler

Braatz

et al. 2017

International Journal of Control

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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.

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Section: Saturation Of Stochastic Disturbances For Handling Hard Inpumentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The second class of SMPC approaches use affine parameterizations of feedback control laws to obtain a tractable convex SMPC formulation [10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

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Stochastic model predictive control with joint chance constraints

Paulson

Buehler

Braatz

et al. 2017

International Journal of Control

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Dynamic Output Feedback Robust MPC Using General Polyhedral State Bounds for the Polytopic Uncertain System With Bounded Disturbance

Ding¹,

Gao²,

Ping³

2015

Asian Journal of Control

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This paper considers the dynamic output feedback robust model predictive control (MPC) for a system with both polytopic model parametric uncertainty and bounded disturbance. For this topic, the techniques for handling the unknown true state are crucial, and the strict guarantee of the input/output/state constraints favors replacing the true state by its bound in the optimization problems. The previous utilized polyhedral bounds, constructed by virtue of the error signals which are some linear combinations of the true state, the estimated state and the output, are generalized, where a bias item is utilized. Based on this unified bounding approach, new techniques for handling the unknown true state are given for both the main and the auxiliary optimization problems. As before, the main optimization problem calculates the control law parameters conditionally, and the auxiliary optimization problem determines the time to refresh these parameters. By applying the proposed method, the augmented state of the closed‐loop system is guaranteed to converge to the neighborhood of the equilibrium point. A numerical example is given to illustrate the effectiveness of the new method.

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Output‐feedback model predictive control for stochastic systems with multiplicative and additive uncertainty

Yang

et al. 2017

Intl J Robust & Nonlinear

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SummaryThis paper studies the output-feedback model predictive control (MPC) design problem for linear systems with multiplicative and additive random uncertainty.We first present an off-line optimization algorithm to optimize feedback gains of the observer and the dual-mode control policy. After that, by defining a cuboid tube whose center and boundary are both time-varying variables, we develop a set sequence with increased freedom to contain stochastic system trajectories. A quadratic performance function with analytic upper and lower bounds is minimized such that it decreases exponentially to a finite range under the expectation. The resulting MPC algorithms are proved to guarantee practically stochastic input-to-state stability. A numerical example of the wind turbine model illustrates the properties of the MPC algorithms.

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Stochastic receding horizon control with output feedback and bounded controls

Cited by 106 publications

References 38 publications

Stochastic model predictive control with joint chance constraints

Stochastic model predictive control with joint chance constraints

Dynamic Output Feedback Robust MPC Using General Polyhedral State Bounds for the Polytopic Uncertain System With Bounded Disturbance

Output‐feedback model predictive control for stochastic systems with multiplicative and additive uncertainty

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