Least-restrictive robust MPC of periodic affine systems with application to building climate control

Linares, Richard; Oldewurtel, Frauke; Jones, Colin N.

doi:10.1109/cdc.2010.5717371

Cited by 8 publications

(4 citation statements)

References 23 publications

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“…The building models the temperature inside a single room in a larger office building and is adapted from Gondhalekar et al: 44…”

Section: Data Availability Statementmentioning

confidence: 99%

“…The building and battery models are represented in terms of discretized differential equations that are provided in detail in Appendix B.1. The building model is adapted from Gondhalekar et al 44 that describes the dynamic evolution of temperature inside of a single room in a larger office building and is composed of three states

x_{t}^{H C} = {x_{t, 1}^{H C}, x_{t, 2}^{H C}, x_{t, 3}^{H C}}

that represent the indoor building temperature, average interior wall temperature and exterior wall temperature, respectively. The battery model is composed of a single state

x_{t}^{B}

that represents the state‐of‐charge (SOC) of the battery.…”

Section: Case Study: Design Of a Building Heating And Cooling System ...mentioning

confidence: 99%

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Computationally efficient integrated design and predictive control of flexible energy systems using multi‐fidelity simulation‐based Bayesian optimization

Sorourifar

Choksi

Paulson

2021

Optim Control Appl Methods

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We present a multi‐fidelity black‐box optimization approach for integrated design and control (IDC) of constrained nonlinear systems in the presence of uncertainty. The IDC framework is becoming increasingly important for the systematic design of next‐generation (flexible) manufacturing and energy systems. However, identifying optimal solutions to realistic IDC problems is intractable when (i) the dynamics occur on much shorter timescales than the system lifetime, (ii) the uncertainties are described by continuous random variables with high variance, and (iii) operational decisions involve a mixture of discrete and continuous variables. Instead of aggressively simplifying the problem to improve tractability, we develop a simulation‐based optimization procedure using high‐quality decision rules that map information that can be measured online to optimal control actions. In particular, we rely on the Bayesian optimization (BO) framework that has been shown to perform very well on noisy and expensive‐to‐evaluate objective functions. We also discuss how BO can be extended to take advantage of computationally cheaper low‐fidelity approximations to the high‐fidelity IDC cost function. Three major low‐fidelity approximation strategies are described in this work, which are related to the simplification of the system simulator, decision rule solution method, and time grid. Lastly, we demonstrate the advantages of multi‐fidelity BO on the design of a solar‐powered building heating/cooling system (with battery and grid support) under uncertain weather and demand conditions with hourly variation over a year‐long planning horizon.

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“…The building models the temperature inside a single room in a larger office building and is adapted from Gondhalekar et al: 44…”

Section: Data Availability Statementmentioning

confidence: 99%

x_{t}^{H C} = {x_{t, 1}^{H C}, x_{t, 2}^{H C}, x_{t, 3}^{H C}}

that represent the indoor building temperature, average interior wall temperature and exterior wall temperature, respectively. The battery model is composed of a single state

x_{t}^{B}

that represents the state‐of‐charge (SOC) of the battery.…”

Section: Case Study: Design Of a Building Heating And Cooling System ...mentioning

confidence: 99%

Computationally efficient integrated design and predictive control of flexible energy systems using multi‐fidelity simulation‐based Bayesian optimization

Sorourifar

Choksi

Paulson

2021

Optim Control Appl Methods

View full text Add to dashboard Cite

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“…Rule-based control and performance bound methods are also used in Olderwurtel et al 2010, as benchmarks to MPC schemes. Gondhalekar et al (2010) simplified building climate plant proposed by Gwerder et al (2005), is used and periodic MPC control law design is employed. Additionally, Olderwurtel et al (2008) proposed a tractable approximation method for the problem.…”

Section: Model-predictive and Optimal Controlmentioning

confidence: 99%

Small- and Medium-Sized Commercial Building Monitoring and Controls Needs: A Scoping Study

Katipamula¹,

Underhill²,

Goddard³

et al. 2012

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(PNNL) to identify monitoring and control needs for small-and medium-sized commercial buildings, and to recommend possible solutions. The scope of this study is to characterize the monitoring and controls needs for the various end uses (for both efficiency and demand response), determine requirements to develop control packages, and calculate the target cost of doing so. Section 1.0 introduces the study scope and analysis approaches used. Discussions regarding the number of buildings in the U.S that comprise "small-size" and "medium-size" buildings, their lack of building automation systems (BAS) and potential energy improvements, as well as challenges, are detailed in this section. Section 2.0 covers the characterization of both small-and medium-sized buildings. Drawing upon Energy Information Administration's Commercial Building Energy Consumption Survey data from various surveys, detailed discussions of energy end-use and electrical end-use consumption values are provided. This section spring boards into further discussions for the various end-use loads and the present penetration of "intelligent" controls in the existing market. Discussions of existing and possible future control methods, strategies and concepts that are applicable (including heating, ventilation and air conditioning (HVAC); lighting and miscellaneous end-use loads) complete this section. Section 3.0 discusses the different communication architectures that might be found in a small-or medium-sized building BAS, as it relates to the communication networks needed to support them. This discussion covers the different technologies that have been in place (older) or are becoming more prevalent (newer), and how they work. This includes wired solutions, wireless solutions or a combination of both (hybrid wired-wireless) networks and industry standards, open and proprietary protocols. For each solution, the limitations of each technology are detailed (speed, bandwidth, reliability, etc.). Cost factors are also discussed because this relates to how these systems are being pushed to the market, and their acceptance (or lack of). Section 4.0 describes the BAS, as has historically been seen and known in large building applications and the small-or medium-sized building applications. This section describes the history of BASs and how they have evolved and improved over time, and summarizes their core functions. This description proceeds to discuss the major architectural requirements needed by new BASs to allow for greater penetration in the existing building stock in the U.S. This section concludes by providing three different options of what a future BAS configuration might look like for either a small-sized building (two different options) or for a medium-sized building (one option). Section 5.0 presents the requirements and capabilities of various devices used to monitor and control different end-use loads found in small-and medium-sized buildings. This includes a robust presentation of the different requirements for the gateway, master controller, co...

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“…Our approach takes advantage of the notion of controlled invariance, well established in (robust) constrained MPC (see, e.g., [2,6]), bringing stochastic MPC on a sound footing. In fact, we derive results on strong feasibility and least-restrictiveness (see Definitions 1 and 2) analogous to those of [7,9,16] in a stochastic context. This paper is organized as follows.…”

Section: Imentioning

confidence: 99%

Strongly feasible stochastic model predictive control

Korda

Linares

Cigler

et al. 2011

IEEE Conference on Decision and Control and European Control Conference

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Abstract-In this article we develop a systematic approach to enforce strong feasibility of probabilistically constrained stochastic model predictive control problems for linear discretetime systems under affine disturbance feedback policies. Two approaches are presented, both of which capitalize and extend the machinery of invariant sets to a stochastic environment. The first approach employs an invariant set as a terminal constraint, whereas the second one constrains the first predicted state. Consequently, the second approach turns out to be completely independent of the policy in question and moreover it produces the largest feasible set amongst all admissible policies. As a result, a trade-off between computational complexity and performance can be found without compromising feasibility properties. Our results are demonstrated by means of two numerical examples. I. IOver the last two decades, the field of constrained model predictive control (MPC) has matured substantially. There is now a solid and very general theoretical foundation for stability and feasibility of nominal as well as robust MPC problems [14,18]. Nevertheless, the connection to another mature field, stochastic optimal control, is still not fully developed although there has been a considerable research effort in this direction over the last years.The basic ingredient of any receding horizon policy is finite horizon cost minimization, which is the first direction of recent research. This problem lies at the heart of stochastic optimal control theory and is known to be extremely difficult except for a few special cases (e.g., the linear quadratic problem). Thus, one typically seeks a suboptimal solution in a certain finite dimensional subset of admissible control polices. A popular choice is the affine disturbance feedback [10,16], which is also the framework of this article. Here, however, we are not primarily concerned with cost minimization itself, but rather closed-loop constraint satisfaction. A more general approach is that of a nonlinear disturbance feedback where decision variables are the coefficients of a linear combination of nonlinear basis functions of the disturbance [11]. In the presence of unbounded disturbances, the nonlinear functions must be bounded whenever bounded control inputs are required. In this article, however, we are dealing with bounded disturbances only. Closest to the nature of receding horizon control is the question of enforcing recursive feasibility of probabilistic constraints, which is also the topic of this article. The problem was extensively studied in a series of papers [3,4,5,13,17], where various types of constraints and disturbance properties were considered, and a number of techniques to tackle these problems were proposed. The common factor of these papers is the use of a perturbed linear state feedback (or pre-stabilization), which necessarily limits the number of degrees of freedom and as a consequence the resulting performance. In this article, in contrast, the use of affine disturban...

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Least-restrictive robust MPC of periodic affine systems with application to building climate control

Cited by 8 publications

References 23 publications

Computationally efficient integrated design and predictive control of flexible energy systems using multi‐fidelity simulation‐based Bayesian optimization

Computationally efficient integrated design and predictive control of flexible energy systems using multi‐fidelity simulation‐based Bayesian optimization

Small- and Medium-Sized Commercial Building Monitoring and Controls Needs: A Scoping Study

Strongly feasible stochastic model predictive control

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