Performance bounds for linear stochastic control

Yang, Wang; Boyd, Stephen

doi:10.1016/j.sysconle.2008.10.004

Cited by 59 publications

(72 citation statements)

References 19 publications

(25 reference statements)

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“…Here, is the (planning) horizon, the function is the terminal cost function, which we assume is quadratic with , and is the terminal state constraint. There are many methods for choosing the MPC parameters , and ; see, e.g., [44]- [48]. The problem (4) is a convex QP with problem data Let be optimal for the QP (4).…”

Section: E Model Predictive Controlmentioning

confidence: 99%

“…For example, let us consider the case with box constraints. We can work out the linear control obtained using the associated LQR problem, ignoring the constraints, or using the techniques described in [44], and then project this trajectory a small distance into the feasible set (which is a box). This warm start initialization has the (possible) advantage of depending only on , and not on the previous states or any controller state.…”

Section: Warm Startmentioning

confidence: 99%

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Fast Model Predictive Control Using Online Optimization

Wang

Boyd

2008

IFAC Proceedings Volumes

Self Cite

484

764

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Abstract-A widely recognized shortcoming of model predictive control (MPC) is that it can usually only be used in applications with slow dynamics, where the sample time is measured in seconds or minutes. A well-known technique for implementing fast MPC is to compute the entire control law offline, in which case the online controller can be implemented as a lookup table. This method works well for systems with small state and input dimensions (say, no more than five), few constraints, and short time horizons. In this paper, we describe a collection of methods for improving the speed of MPC, using online optimization. These custom methods, which exploit the particular structure of the MPC problem, can compute the control action on the order of 100 times faster than a method that uses a generic optimizer. As an example, our method computes the control actions for a problem with 12 states, 3 controls, and horizon of 30 time steps (which entails solving a quadratic program with 450 variables and 1284 constraints) in around 5 ms, allowing MPC to be carried out at 200 Hz.Index Terms-Model predictive control (MPC), real-time convex optimization.

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Section: E Model Predictive Controlmentioning

confidence: 99%

Section: Warm Startmentioning

confidence: 99%

Fast Model Predictive Control Using Online Optimization

Wang

Boyd

2008

IFAC Proceedings Volumes

Self Cite

484

764

View full text Add to dashboard Cite

show abstract

“…The standard approach in stochastic programming is to consider discrete distributions and then to look at different scenarios, which can be computationally very demanding. Various approaches have been proposed for stochastic MPC, see [26]- [28] and the references therein.…”

Section: B Formulation Of Chance Constraintsmentioning

confidence: 99%

Stochastic Model Predictive Control for Building Climate Control

Oldewurtel

Jones

Parisio

et al. 2014

IEEE Trans. Contr. Syst. Technol.

117

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Abstract-In this brief paper, a Stochastic Model PredictiveControl formulation tractable for large-scale systems is developed. The proposed formulation combines the use of Affine Disturbance Feedback, a formulation successfully applied in robust control, with a deterministic reformulation of chance constraints. A novel approximation of the resulting stochastic finite horizon optimal control problem targeted at building climate control is introduced to ensure computational tractability. This work provides a systematic approach toward finding a control formulation which is shown to be useful for the application domain of building climate control. The analysis follows two steps: 1) a small-scale example reflecting the basic behavior of a building, but being simple enough for providing insight into the behavior of the considered approaches, is used to choose a suitable formulation; and 2) the chosen formulation is then further analyzed on a large-scale example from the project OptiControl, where people from industry and other research institutions worked together to create building models for realistic controller comparison. The proposed Stochastic Model Predictive Control formulation is compared with a theoretical benchmark and shown to outperform current control practice for buildings.

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“…The controller only requires predictions of future quantities, which can be based on historical data, stochastic models, weather forecasts, or analyst predictions. In many problems, even when the predictions are poor, the controller often performs exceptionally well (Wang and Boyd [2009]). …”

Section: Introductionmentioning

confidence: 99%

Operation and Configuration of a Storage Portfolio via Convex Optimization

Kraning¹,

Wang²,

Akuiyibo³

et al. 2011

IFAC Proceedings Volumes

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We consider a portfolio of storage devices which is used to modify a commodity flow so as to minimize an average cost function. The individual storage devices have different parameters that characterize attributes such as capacity, maximum charging rates, and losses in charging and storage. We address two problems related to such a system. The first is the problem of operating a portfolio of storage devices in real-time, i.e., making real-time decisions as to how to charge or discharge each of the storage devices in response to the fluctuating commodity flow and cost function. The second is the problem of configuring the portfolio of storage devices, i.e., choosing a single portfolio from a set of candidate portfolios. Here we are given the cost of each candidate portfolio as a function of its parameters, and seek to minimize a combination of initial configuration cost and average operating cost. In this paper, we show how both problems can be approximately solved using convex optimization.

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Performance bounds for linear stochastic control

Cited by 59 publications

References 19 publications

Fast Model Predictive Control Using Online Optimization

Fast Model Predictive Control Using Online Optimization

Stochastic Model Predictive Control for Building Climate Control

Operation and Configuration of a Storage Portfolio via Convex Optimization

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