In the last few years, the application of Model Predictive Control (MPC) for energy management in buildings has received significant attention from the research community. MPC is becoming more and more viable because of the increase in computational power of building automation systems and the availability of a significant amount of monitored building data. MPC has found successful implementation in building thermal regulation, fully exploiting the potential of building thermal mass. Moreover, MPC has been positively applied to active energy storage systems, as well as to the optimal management of on-site renewable energy sources. MPC also opens up several opportunities for enhancing energy efficiency in the operation of Heating Ventilation and Air Conditioning (HVAC) systems because of its ability to consider constraints, prediction of disturbances and multiple conflicting objectives, such as indoor thermal comfort and building energy demand. Despite the application of MPC algorithms in building control has been thoroughly investigated in various works, a unified framework that fully describes and formulates the implementation is still lacking. Firstly, this work introduces a common dictionary and taxonomy that gives a common ground to all the engineering disciplines involved in building design and control. Secondly the main scope of this paper is to define the MPC formulation framework and critically discuss the outcomes of different existing MPC algorithms for building and HVAC system management. The potential benefits of the application of MPC in improving energy efficiency in buildings were highlighted.

Model Predictive Control (MPC) is an enabling technology in applications requiring controlling physical processes in an optimized way under constraints on inputs and outputs. However, in MPC closed-loop performance is pushed to the limits only if the plant under control is accurately modeled; otherwise, robust architectures need to be employed, at the price of reduced performance due to worst-case conservative assumptions. In this paper, instead of adapting the controller to handle uncertainty, we adapt the learning procedure so that the prediction model is selected to provide the best closed-loop performance. More specifically, we apply for the first time the above “identification for control” rationale to hierarchical MPC using data-driven methods and Bayesian optimization.

The control based on online optimization, popularly known as model predictive control (MPC), has long been recognized as the winning alternative for constrained systems. The main limitation of MPC is, however, its online computational complexity. For discrete-time linear time-invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly the state feedback control law associated with MPC, and show that it is piecewise linear and continuous. The controller inherits all the stability and performance properties of MPC, but the online computation is reduced to a simple linear function evaluation instead of the expensive quadratic program. The new technique is expected to enlarge the scope of applicability of MPC to small-size/fast-sampling applications which cannot be covered satisfactorily with anti-windup schemes.

Active-set methods are recognized to often outperform other methods in terms of speed and solution accuracy when solving small-size Quadratic Programming (QP) problems, making them very attractive in embedded linear Model Predictive Control (MPC) applications. A drawback of active-set methods is the lack of tight bounds on the worst-case number of iterations, a fundamental requirement for their implementation in a real-time system. Extensive simulation campaigns provide an indication of the expected worst-case computation load, but not a complete guarantee. This paper solves such a certification problem by proposing an algorithm to compute the exact bound on the maximum number of iterations and floating point operations required by a state-of-the-art dual active-set QP solver. The algorithm is applicable to a given QP problem whose linear term of the cost function and right hand side of the constraints depend linearly on a vector of parameters, as in the case of linear MPC. In addition, a new solver is presented that combines explicit and implicit MPC ideas, guaranteeing improvements of the worst-case computation time. The ability of the approach to exactly quantify memory and worst-case computation requirements is tested on a few MPC examples, also highlighting when on-line optimization should be preferred to explicit MPC.

This technical note proposes an active set method based on nonnegative least squares (NNLS) to solve strictly convex quadratic programming (QP) problems, such as those that arise in Model Predictive Control (MPC). The main idea is to rephrase the QP problem as a Least Distance Problem (LDP) that is solved via a NNLS reformulation. While the method is rather general for solving strictly convex QP's subject to linear inequality constraints, it is particularly useful for embedded MPC because (i) is very fast, compared to other existing state-of-the-art QP algorithms, (ii) is very simple to code, requiring only basic arithmetic operations for computing LDL^T decompositions recursively to solve linear systems of equations, (iii) contrary to iterative methods, provides the solution or recognizes infeasibility in a finite number of steps.