(485a) Integrated Design and Model Predictive Control of Multiscale Systems Using a Multi-Fidelity Bayesian Optimization Approach

Design and control are interconnected activities that need to be performed simultaneously so that designs with a large degree of operational flexibility can be readily identified [1]. In practice, however, design is typically tackled first (with little-to-no considerations of the dynamics), which can lead to heavily constrained processes with few degrees of freedom available for control. While there is a vast body of literature available on the topic [2]–[4], a tractable and unified framework for optimal integrated design and control (IDC) has remained elusive. This type of framework is needed to enable the systematic design of next-generation (so-called “flexible”) manufacturing and energy systems including smart grid technology [5], multiproduct or personalized chemical plants [6], and combined heat and power systems [7]. Although optimal IDC problems can be formulated as multistage stochastic programs (MSPs), they quickly become intractable when the following features are present [8]: (i) relevant dynamics and uncertainties occur on much shorter timescales than the lifetime of the system; (ii) uncertainties are present that are best described by continuous random variables with large variance; and/or (iii) important operational decisions are discrete (e.g., adaptive scheduling and unit commitment). The first two features relate to the multiscale nature of realistic IDC problems, which pose a major challenge for MSPs that suffer from the curse-of-dimensionality (i.e., exponential growth in number of decision variables as the control decisions can differ for each realization of the uncertainty) [9]. The third feature implies the system model is nonlinear with mixed-integer decisions such that a scenario approximation to the MSP is a very large-scale mixed-integer nonlinear program (MINLP) that is far beyond the capabilities of existing solvers, even when an equation-oriented system model is available.

Most previous work on optimal IDC focused on making tractable approximations to the MSP by relaxing features (i)-(iii) (see, e.g., [10]–[13] for several examples including substantially reducing the number of operational stages and uncertainty scenarios). Although these simplifications make the MSP more tractable, they degrade the accuracy of the IDC solution in exactly the ways that need to be captured in order to model the flexibility of the process. To address these challenges, in [14], we proposed a simulation-based optimization (SO) strategy that can tackle a general class of IDC problems consisting of an outer optimization over the relevant design variables and an inner stochastic simulation that evaluates the expected operating costs and constraints that appear in the outer problem. To reduce dimensionality of the outer problem, we rely on so-called decision rule (DR) approximations [8] to parametrize the recourse/control decisions in a way that scales much more favorably with respect to (i) and (ii) above. In particular, we presented a mixed-integer model predictive control (MIMPC) approach that is able to simultaneously handle scheduling and control decisions mentioned in (iii); this is a significantly more advanced DR than available alternatives that mostly consider PID controllers [15]–[17], with some exploring linear MPC [18], [19]. Due to the multiscale nature of the IDC problems of interest, we utilized Bayesian optimization (BO) that has become a popular tool for solving black-box optimization problems with objective and/or constraint functions that are prohibitively expensive to compute repeatedly and, therefore, must be evaluated as few times as possible.

In [14], we focused on conventional BO, which assumes only a single (computationally intensive) high-fidelity simulator is available. In IDC problems, however, we have access to several cheap approximations to this simulator such as the previously mentioned simplification methods in, e.g., [10]–[13]. As long as the lower fidelity approximations are reasonably correlated to the high-fidelity simulator, they can be used to cheaply eliminate “bad” designs and thus reserve the most expensive simulations for the most promising designs. To take advantage of these approximations here, we extend [14] by replacing traditional BO with a multi-fidelity BO (MFBO) algorithm [20]. To demonstrate its advantages, we apply MFBO to the design of a solar-powered building heating ventilation and air-conditioning (HVAC) system, with grid and battery support, under uncertain weather and demand conditions that vary at the hour scale for a year-long horizon. We show that MFBO repeatedly identifies more profitable designs than single fidelity BO under a fixed computational budget. In addition, we highlight that the choice and sequence of the lower-fidelity models has a strong impact on the rate of convergence of MFBO.

References

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