In this paper, we study the system identification problem for linear time-invariant dynamics with bilinear observation models. Accordingly, we consider a suitable parametric description for the system model and formulate the identification problem as estimating the parameters characterizing the mathematical representation of the system through input-output measurement data. To this end, we employ a probabilistic framework aiming to obtain the maximum likelihood estimates of the parameters. Accordingly, we propose utilizing the expectation-maximization approach to improve the tractability of the identification procedure. Through the numerical experiments, we verify the efficacy of the proposed scheme and demonstrate its performance.@en

In this paper, we use dual dynamic programming to address the myopic nature of MPC for scheduling of district heating networks by designing value functions that can approximate the effects of time-varying elements on the objective function beyond the initial prediction horizon. To this end, we formulate the control problem as a two-level MPC. More precisely, in the first-level, we consider a short-horizon nonlinear MPC equipped with a terminal cost approximating the value function. Subsequently, a long-horizon linear MPC is solved in the second-level to establish a lower bound on the terminal cost function from the first-level, thereby improving the value function approximation. Specifically, we consider scheduling of thermal and hydraulic components within district heating networks. Our numerical example demonstrates that our method can anticipate demand variations beyond the prediction horizon while maintaining computational efficiency.@en

Research into the impact of innovative sustainable energy experiments and demonstrations is crucial to diversifying, scaling up, and accelerating the sustainable energy transition. Although there is vast research into sustainable energy experiments and demonstrations, research literature offers a fragmented collection of findings. A coherent overview of themes and insights regarding the transformative impact of innovative sustainable energy experiments and demonstrations on sustainable energy systems from the past, present, and near future is lacking and necessary to increase experiments and demonstrations' impact on the sustainable energy transition. The research in this study fills this knowledge gap by providing such an overview and yields novel insights into the organized function and impact of experiments and demonstrations. It spans a broad spectrum of sustainable energy technologies, the empirical domains where these are invented, developed and applied, and the stakeholders involved. The overview is the outcome of a Delphi study in which the insights of 47 international scientific research experts in sustainable energy experiments and demonstrations are bundled and explained. This study presents a thematic overview of the significant insights regarding past and current sustainable energy experiments and demonstrations and outlines a research agenda for the future. Policymakers, practitioners, and scientists can leverage this to inform their sustainable energy policies, business strategies, and research programs.@en

This article presents the guided Bayesian optimization (BO) algorithm as an efficient data-driven method for iteratively tuning closed-loop controller parameters using a digital twin of the system. The digital twin is built using closed-loop data acquired during standard BO iterations, and activated when the uncertainty in the Gaussian Process model of the optimization objective on the real system is high. We define a controller tuning framework independent of the controller or the plant structure. Our proposed methodology is model-free, making it suitable for nonlinear and unmodelled plants with measurement noise. The objective function consists of performance metrics modeled by Gaussian processes. We utilize the available information in the closed-loop system to progressively maintain a digital twin that guides the optimizer, improving the data efficiency of our method. Switching the digital twin on and off is triggered by our data-driven criteria related to the digital twin’s uncertainty estimations in the BO tuning framework. Effectively, it replaces much of the exploration of the real system with exploration performed on the digital twin. We analyze the properties of our method in simulation and demonstrate its performance on two real closed-loop systems with different plant and controller structures. The experimental results show that our method requires fewer experiments on the physical plant than Bayesian optimization to find the optimal controller parameters.

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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.

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Dynamic Programming suffers from the curse of dimensionality due to large state and action spaces, a challenge further compounded by uncertainties in the environment. To mitigate these issue, we explore an off-policy based Temporal Difference Approximate Dynamic Programming approach that preserves contraction mapping when projecting the problem into a subspace of selected features, accounting for the probability distribution of the perturbed transition probability matrix. We further demonstrate how this Approximate Dynamic Programming approach can be implemented as a particular variant of the Temporal Difference learning algorithm, adapted for handling perturbations. To validate our theoretical findings, we provide a numerical example using a Markov Decision Process corresponding to a resource allocation problem.

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This article introduces output prediction methods for two types of systems containing sinusoidal-input uniformly convergent (SIUC) elements. The first method considers these elements in combination with single-input single-output linear time-invariant (LTI) systems before, after, and in parallel to them. The second method considers a multiple-input multiple-output LTI system where each input is controlled by an SIUC element. The output prediction only requires frequency-response functions of the LTI elements and is fully accurate for sinusoidal inputs.

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In this paper, we discuss the learning and discovery problem for the dynamical systems described through stable evolutionary Partial Differential Equations (PDEs). The main idea is to employ a suitable learning approach for creating a map from boundary conditions to the corresponding output. More precisely, in order to accurately uncover the evolutionary PDE dynamics, we propose a scheme that employs large-scale system identification to construct such a map using sufficiently informative measurements. Accordingly, we first develop a scalable implementation for the subspace identification method, enforcing stability on the identified system. To this end, numerical optimization techniques such as coordinate descent, randomized singular value decomposition, and large-scale semidefinite programming are employed. The performance and complexity of the resulting scheme are discussed and demonstrated through numerical experiments on generic identification examples. Following this, we validate the effectiveness of the proposed approach on an example of a stable evolutionary partial differential equation. The numerical results confirm the efficacy of the proposed learning scheme.

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We study the problem of identifying a linear time-varying output map from measurements and linear time-varying system states, which are perturbed with Gaussian observation noise and process uncertainty, respectively. Employing a stochastic model as prior knowledge for the parameters of the unknown output map, we reconstruct their estimates from input/output pairs via a Bayesian approach to optimize the posterior probability density of the output map parameters. The resulting problem is a non-convex optimization, for which we propose a tractable linear matrix inequalities approximation to warm-start a first-order subsequent method. The efficacy of our algorithm is shown experimentally against classical Expectation Maximization and Dual Kalman Smoother approaches.

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The inherently nonlinear, large-scale, and time-varying nature of district heating systems pose significant challenges from a control perspective. In this paper, we address these challenges by applying an economic MPC. Economic MPC is a dynamic real-time optimization method, enabling both optimal planning and stability of the closed-loop system. Our strategy constitutes several steps. First, we introduce a discrete-time modular framework for the district heating system, establishing its strict dissipativity with respect to a desired, potentially time-varying, equilibrium. We identify a set of meaningful objective functions for the district heating systems, preserving this property. Second, we show how strict dissipativity implies the turnpike property, which, in turn, guarantees approximate optimality, practical stability, and recursive feasibility for the EMPC closed-loop. Finally, we provide numerical simulations to demonstrate the effectiveness of our work.

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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.

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The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In the resulting framework, the impulse response estimation problem is formulated as a regularized optimization defined on an infinite-dimensional RKHS consisting of stable impulse responses. The consequent estimation problem is well-defined under the central assumption that the convolution operators restricted to the RKHS are continuous linear functionals. Moreover, according to this assumption, the representer theorem hold, and therefore, the impulse response can be estimated by solving a finite-dimensional program. Thus, the continuity feature plays a significant role in kernel-based system identification. We show that this central assumption is guaranteed to be satisfied in considerably general situations, namely when the input signal is bounded, the kernel is an integrable function, and in the case of continuous-time dynamics, continuous. Furthermore, the strong convexity of the optimization problem and the continuity property of the convolution operators imply that the kernel-based system identification admits a unique solution. Consequently, it follows that kernel-based system identification is a well-defined approach.

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This paper discusses the problem of system identification when frequency domain side-information is available. We mainly consider the case where the side-information is provided as the H_∞-norm of the system being bounded by a given scalar. This framework allows considering different forms of frequency domain side-information, such as the dissipativity of the system. We propose a nonparametric identification approach for estimating the impulse response of the system under the given side-information. The estimation problem is formulated as a constrained optimization in a stable reproducing kernel Hilbert space, where suitable constraints are considered for incorporating the desired frequency domain features. The resulting optimization has an infinite-dimensional feasible set with an infinite number of constraints. We show that this problem is a well-defined convex program with a unique solution. We propose a heuristic that tightly approximates this unique solution. The proposed approach is equivalent to solving a finite-dimensional convex quadratically constrained quadratic program. The efficiency of the discussed method is verified by several numerical examples.

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In this work, we consider the problem of learning the Koopman operator for discrete-time autonomous systems. The learning problem is formulated as a generic constrained regularized empirical loss minimization in the infinite-dimensional space of linear operators. We show that a representer theorem holds for the introduced learning problem under certain but general conditions, which allows convex reformulation of the problem in a specific finite-dimensional space without any approximation and loss of precision. We discuss the inclusion of various forms of regularization and constraints in the learning problem, such as the operator norm, the Frobenius norm, the operator rank, the nuclear norm, and the stability. Subsequently, we derive the corresponding equivalent finite-dimensional problem. Furthermore, we demonstrate the connection between the proposed formulation and the extended dynamic mode decomposition. We present several numerical examples to illustrate the theoretical results and verify the performance of regularized learning of the Koopman operators.

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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.

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