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This paper presents the design and realization of a linear Model Predictive Controller (MPC) and state estimator for a multi-zone heat pump in the Modelica modeling language, in order to validate closed-loop performance prior to experimental testing. The vapor compression system uses a variable speed compressor and a set of expansion valves for control, and it is required to regulate zone temperatures to set-points without offset. Constraints are imposed on all control inputs and also the values of both measured and unmeasured system outputs. Because experimental testing is both expensive and time-consuming, we have developed a tool chain for software-in-the-loop validation that uses a Modelica model for the plant, integrated with a software representation of the MPC that is realized in a combination of Modelica and C that is suitable for real-time use. We show the results of closed-loop tests of the controller with a nonlinear system model, which provide a partial validation of the controller and tool chain.

Their flexibility to learn general function classes renders nonparametric regression algorithms particularly attractive in system identification and data-based control settings, where little a priori knowledge about a dynamical system is to be presumed. Building on approaches known as NSM- or Lipschitz regression, we propose a new nonparametic machine learning approach. While it inherits theoretical learning guarantees from the methods it is built upon, it is designed to limit the computational effort both for learning and for generating predictions. This renders our method applicable to online system identification and control settings where the desired sample frequency precludes previous nonparametric approaches from being deployed. Apart from deriving a guarantee on the ability of our method to learn any continuous function, we illustrate some of its practical merits on a number of benchmark comparison problems.

Fast Iterative Shrinking-Threshold Algorithm (FISTA) is a popular fast gradient descent method (FGM) in the field of large scale convex optimization problems. However, it can exhibit undesirable periodic oscillatory behaviour in some applications that slows its convergence. Restart schemes seek to improve the convergence of FGM algorithms by suppressing the oscillatory behaviour. Recently, a restart scheme for FGM has been proposed that provides linear convergence for non strongly convex optimization problems that satisfy a quadratic functional growth condition. However, the proposed algorithm requires prior knowledge of the optimal value of the objective function or of the quadratic functional growth parameter. In this paper we present a restart scheme for FISTA algorithm, with global linear convergence, for non strongly convex optimization problems that satisfy the quadratic growth condition without requiring the aforementioned values. We present some numerical simulations that suggest that the proposed approach outperforms other restart FISTA schemes., Comment: This paper constitutes an extended and revised version of "Restart FISTA with Global Linear Convergence" by Teodoro Alamo et. al. presented at the European Control Conference (ECC), 2019. v2: typos corrected and includes the proof of Prop. 1(ii) of "Gradient Based Restart FISTA" by Teodoro Alamo et. al. presented at the Conference on Decision and Control (CDC), 2019. (12 pages, 4 figures)