Simulation-based Integrated Design and Control with Embedded Mixed-Integer MPC using Constrained Bayesian Optimization

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

“…This assumption was made for simplicity, but our framework can easily accommodate such decision as shown in our previous work. 16…”

“…Nonlinear MPC Paulson & co-workers (2021), 16 Li & co-workers (2017) 92 Review articles Sharifzadeh(2013), 93 Gani and co-workers(2012), 94 Vega and co-workers(2014), 95,96 Ricardez Sandoval and co-workers(2009), 97 Pistikopolous and co-workers (2004, 2016, 2019) 5,98,99 nonlinear process dynamics, Mohideen et al 51 introduced a mixed-integer dynamic optimization (MIDO) formulation of the IDC problem assuming a proportional-integral-derivative (PID) controller structure to counteract a nominal disturbance profile. Since MIDOs take advantage of derivative-based optimization methods, it is not trivial to extend these approaches to more advanced control strategies, such as model predictive control (MPC), in which the input values are represented implicitly as the solution to an underlying optimization problem.…”

“…Lastly, the dynamics may involve a mixture of continuous and discrete decisions, which implies () is a hybrid system that is not continuously differentiable and thus not amenable to derivative‐based solvers. In our recent work, 16 we demonstrated how Bayesian optimization can help overcome these limitations by simultaneously sampling values of (co‐optimizing design and MPC tuning) in an intelligent fashion to search for the global solution to () as quickly as possible. After summarizing this idea in the next section, we extend the concept to account for multiple cheaper approximate models to better guide the search in Sections 4 and 5.…”

“…In practice, several smaller HC units may be required to satisfy the load—if each unit has a fixed duty cycle, then we would need to include discrete/integer decisions in the model that represent, for example, turning on or off certain units in certain time periods. This assumption was made for simplicity, but our framework can easily accommodate such decision as shown in our previous work 16 …”

“…There has been a significant amount of work on the development of specialized MPC methods in the context of energy systems, [9][10][11][12] including recent contributions that directly incorporate nonlinear effects 13,14 and online adaptation of the internal model. 15 In our previous work, 16 we showed how a mixed-integer extension of MPC could be used as a much higher-quality DR than simplified PID or linear MPC structures. Regardless of the specific controller structure that is selected, there remain some "tuning parameters" that can have a strong influence on performance and must be adequately chosen to ensure good closed-loop performance.…”