In this paper, we present an impulse response identification scheme that incorporates the internal positivity side-information of the system. The realization theory of positive systems establishes specific criteria for the existence of a positive realization for a given transfer function. These transfer function criteria are translated to a set of suitable conditions on the shape and structure of the impulse responses of positive systems. Utilizing these conditions, the impulse response estimation problem is formulated as a constrained optimization in a reproducing kernel Hilbert space equipped with a stable kernel, and suitable constraints are imposed to encode the internal positivity side-information. The optimization problem is infinite-dimensional with an infinite number of constraints. An equivalent finite-dimensional convex optimization in the form of a convex quadratic program is derived. The resulting equivalent reformulation makes the proposed approach suitable for numerical simulation and practical implementation. A Monte Carlo numerical experiment evaluates the impact of incorporating the internal positivity side-information in the proposed identification scheme. The effectiveness of the proposed method is demonstrated using data from a heating system experiment.

Model Predictive Control can cope with conflicting control objectives in building energy managements. In terms of user satisfaction, visual comfort has been proven in several studies to be a crucial factor, however thermal comfort is typically considered the only important aspect. Besides human well-being, visual comfort strongly impacts the productivity of the occupants in offices. Therefore, from an economic point of view, it is essential to include visual comfort in Model Predictive Control for buildings. In this paper semi-linear support vector machine is applied to learn suitable models for visual comfort measured by Daylight Glare Probability. The resulting model is incorporated into a Model Predictive Control framework, together with an autoregressive exogenous model accounting for the thermal dynamics of the building. The approach is validated through an extensive numerical case study, and the benefits of including visual comfort and blind control in the Model Predictive Control problem are evaluated. We observe that the proposed Model Predictive Control scheme ensures both the thermal and visual comfort constraints at the expense of 2.2% to 7.2% higher energy consumption compared to the benchmark Model Predictive Control configuration, which considers only the thermal comfort constraints.

In this article, we consider the problem of system identification when side-information is available on the steady-state gain (SSG) of the system. We formulate a general nonparametric identification method as an infinite-dimensional constrained convex program over the reproducing kernel Hilbert space (RKHS) of stable impulse responses. The objective function of this optimization problem is the empirical loss regularized with the norm of RKHS, and the constraint is considered for enforcing the integration of the SSG side-information. The proposed formulation addresses both the discrete-time and continuous-time cases. We show that this program has a unique solution obtained by solving an equivalent finite-dimensional convex optimization. This solution has a closed-form when the empirical loss and regularization functions are quadratic and exact side-information is considered. We perform extensive numerical comparisons to verify the efficiency of the proposed identification methodology.