arXiv subjects

Roy S. Smith

Publications and source records attributed to Roy S. Smith.

At least 37 records · Page 2Linked to original sources

arXiv2023

Closed-Loop Identification of Stabilized Models Using Dual Input-Output Parameterization

This paper introduces a dual input-output parameterization (dual IOP) for the identification of linear time-invariant systems from closed-loop data. It draws inspiration from the recent input-output parameterization developed to synthesize a stabilizing controller. The controller is parameterized in terms of closed-loop transfer functions, from the external disturbances to the input and output of the system, constrained to lie in a given subspace. Analogously, the dual IOP method parameterizes the unknown plant with analogous closed-loop transfer functions, also referred to as dual parameters. In this case, these closed-loop transfer functions are constrained to lie in an affine subspace guaranteeing that the identified plant is \emph{stabilized} by the known controller. Compared with existing closed-loop identification techniques guaranteeing closed-loop stability, such as the dual Youla parameterization, the dual IOP neither requires a doubly-coprime factorization of the controller nor a nominal plant that is stabilized by the controller. The dual IOP does not depend on the order and the state-space realization of the controller either, as in the dual system-level parameterization. Simulation shows that the dual IOP outperforms the existing benchmark methods.

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arXiv2023

Distributed Multi-Horizon Model Predictive Control for Network of Energy Hubs

The increasing penetration of renewable energy resources has transformed the energy system from traditional hierarchical energy delivery paradigm to a distributed structure. Such development is accompanied with continuous liberalization in the energy sector, giving rise to possible energy trading among networked local energy hub. Joint operation of such hubs can improve energy efficiency and support the integration of renewable energy resource. Acknowledging peer-to-peer trading between hubs, their optimal operation within the network can maximize consumption of locally produced energy. However, for such complex systems involving multiple stakeholders, both computational tractability and privacy concerns need to be accounted for. We investigate both decentralized and centralized model predictive control (MPC) approaches for a network of energy hubs. While the centralized control strategy offers superior performance to the decentralized method, its implementation is computationally prohibitive and raises privacy concerns, as the information of each hub has to be shared extensively. On the other hand, a classical decentralized control approach can ease the implementation at the expense of sub-optimal performance of the overall system. In this work, a distributed scheme based on a consensus alternating direction method of multipliers (ADMM) algorithm is proposed. It combines the performance of the centralized approach with the privacy preservation of decentralized approach. A novel multi-horizon MPC framework is also introduced to increase the prediction horizon without compromising the time discretization or making the problem computationally intractable. A benchmark three-hub network is used to compare the performance of the mentioned methods. The results show superior performance in terms of total cost, computational time, robustness to demand and prices variations.

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arXiv2023

A Dual System-Level Parameterization for Identification from Closed-Loop Data

This work presents a dual system-level parameterization (D-SLP) method for closed-loop system identification. The recent system-level synthesis framework parameterizes all stabilizing controllers via linear constraints on closed-loop response functions, known as system-level parameters. It was demonstrated that several structural, locality, and communication constraints on the controller can be posed as convex constraints on these system-level parameters. In the current work, the identification problem is treated as a {\em dual} of the system-level synthesis problem. The plant model is identified from the dual system-level parameters associated to the plant. In comparison to existing closed-loop identification approaches (such as the dual-Youla parameterization), the D-SLP framework neither requires the knowledge of a nominal plant that is stabilized by the known controller, nor depends upon the choice of factorization of the nominal plant and the stabilizing controller. Numerical simulations demonstrate the efficacy of the proposed D-SLP method in terms of identification errors, compared to existing closed-loop identification techniques.

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arXiv2023

Once upon a time step: A closed-loop approach to robust MPC design

A novel perspective on the design of robust model predictive control (MPC) methods is presented, whereby closed-loop constraint satisfaction is ensured using recursive feasibility of the MPC optimization. Necessary and sufficient conditions are derived for recursive feasibility, based on the effects of model perturbations and disturbances occurring at one time step. Using these conditions and Farkas' lemma, sufficient conditions suitable for design are formulated. The proposed method is called a closed-loop design, as only the existence of feasible inputs at the next time step is enforced by design. This is in contrast to most existing formulations, which compute control policies that are feasible under the worst-case realizations of all model perturbations and exogenous disturbances in the MPC prediction horizon. The proposed method has an online computational complexity similar to nominal MPC methods while preserving guarantees of constraint satisfaction, recursive feasibility and stability. Numerical simulations demonstrate the efficacy of our proposed approach.

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arXiv2023

Error Bounds for Kernel-Based Linear System Identification with Unknown Hyperparameters

The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the posterior covariance, which are useful in robust and stochastic control. However, the error bounds require knowledge of the true hyperparameters in the kernel design and are demonstrated to be inaccurate with estimated hyperparameters for lightly damped systems or in the presence of high noise. In this work, we provide reliable quantification of the estimation error when the hyperparameters are unknown. The bounds are obtained by first constructing a high-probability set for the true hyperparameters from the marginal likelihood function and then finding the worst-case posterior covariance within the set. The proposed bound is proven to contain the true model with a high probability and its validity is verified in numerical simulation.

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arXiv2023

Diagonally Square Root Integrable Kernels in System Identification

In recent years, the reproducing kernel Hilbert space (RKHS) theory has played a crucial role in linear system identification. The core of a RKHS is the associated kernel characterizing its properties. Accordingly, this work studies the class of diagonally square root integrable (DSRI) kernels. We demonstrate that various well-known stable kernels introduced in system identification belong to this category. Moreover, it is shown that any DSRI kernel is also stable and integrable. We look into certain topological features of the RKHSs associated with DSRI kernels, particularly the continuity of linear operators defined on the respective RKHSs. For the stability of a Gaussian process centered at a stable impulse response, we show that the necessary and sufficient condition is the diagonally square root integrability of the corresponding kernel. Furthermore, we elaborate on this result by providing proper interpretations.

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arXiv2022

Dual adaptive MPC using an exact set-membership reformulation

Adaptive model predictive control (MPC) methods using set-membership identification to reduce parameter uncertainty are considered in this work. Strong duality is used to reformulate the set-membership equations exactly within the MPC optimization. A predicted worst-case cost is then used to enable performance-oriented exploration. The proposed approach guarantees robust constraint satisfaction and recursive feasibility. It is shown that method can be implemented using homothetic tube and flexible tube parameterizations of state tubes, and a simulation study demonstrates performance improvement over state-of-the-art controllers.

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arXiv2022

Computationally efficient robust MPC using optimized constraint tightening

A robust model predictive control (MPC) method is presented for linear, time-invariant systems affected by bounded additive disturbances. The main contribution is the offline design of a disturbance-affine feedback gain whereby the resulting constraint tightening is minimized. This is achieved by formulating the constraint tightening problem as a convex optimization problem with the feedback term as a variable. The resulting MPC controller has the computational complexity of nominal MPC, and guarantees recursive feasibility, stability and constraint satisfaction. The advantages of the proposed approach compared to existing robust MPC methods are demonstrated using numerical examples.

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arXiv2022

Kernel-based Impulse Response Identification with Side-Information on Steady-State Gain

In this paper, we consider the problem of system identification when side-information is available on the steady-state (or DC) gain 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 steady-state gain 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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arXiv2022

Kernel-Based Identification with Frequency Domain Side-Information

In this paper, we discuss the problem of system identification when frequency domain side information is available on the system. Initially, we consider the case where the prior knowledge is provided as being the $\Hcal_{\infty}$-norm of the system bounded by a given scalar. This framework provides the opportunity of considering various forms of side information such as the dissipativity of the system as well as other forms of frequency domain prior knowledge. We propose a nonparametric identification method for estimating the impulse response of the system under the given side information. The estimation problem is formulated as an optimization in a reproducing kernel Hilbert space (RKHS) endowed with a stable kernel. The corresponding objective function consists of a term for minimizing the fitting error, and a regularization term defined based on the norm of the impulse response in the employed RKHS. To guarantee the desired frequency domain features defined based on the prior knowledge, suitable constraints are imposed on the estimation problem. 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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arXiv2022

Infinite-Dimensional Sparse Learning in Linear System Identification

Regularized methods have been widely applied to system identification problems without known model structures. This paper proposes an infinite-dimensional sparse learning algorithm based on atomic norm regularization. Atomic norm regularization decomposes the transfer function into first-order atomic models and solves a group lasso problem that selects a sparse set of poles and identifies the corresponding coefficients. The difficulty in solving the problem lies in the fact that there are an infinite number of possible atomic models. This work proposes a greedy algorithm that generates new candidate atomic models maximizing the violation of the optimality condition of the existing problem. This algorithm is able to solve the infinite-dimensional group lasso problem with high precision. The algorithm is further extended to reduce the bias and reject false positives in pole location estimation by iteratively reweighted adaptive group lasso and complementary pairs stability selection respectively. Numerical results demonstrate that the proposed algorithm performs better than benchmark parameterized and regularized methods in terms of both impulse response fitting and pole location estimation.

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arXiv2022

Kernel-Based Identification of Local Limit Cycle Dynamics with Linear Periodically Parameter-Varying Models

Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be modelled as systems experiencing limit cycle behavior. The goal of this work is to identify from data, the local dynamics around the limit cycle using linear periodically parameter-varying models. Using a coordinate transformation onto transversal surfaces, the dynamics are decomposed into two parts: one along the limit cycle, and one on the transversal surfaces. Then, the model is identified from trajectory data using kernel-based methods with a periodic kernel design. The kernel-based model is extended to also account for variations in system parameters associated with different operating conditions. The performance of the proposed identification method is demonstrated on a benchmark nonlinear system and on a simplified airborne wind energy model. The method provides accurate model parameter estimation, compared to the analytical linearization, and good prediction capability.

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arXiv2022

Scalable tube model predictive control of uncertain linear systems using ellipsoidal sets

This work proposes a novel robust model predictive control (MPC) algorithm for linear systems affected by dynamic model uncertainty and exogenous disturbances. The uncertainty is modeled using a linear fractional perturbation structure with a time-varying perturbation matrix, enabling the algorithm to be applied to a large model class. The MPC controller constructs a state tube as a sequence of parameterized ellipsoidal sets to bound the state trajectories of the system. The proposed approach results in a semidefinite program to be solved online, whose size scales linearly with the order of the system. The design of the state tube is formulated as an offline optimization problem, which offers flexibility to impose desirable features such as robust invariance on the terminal set. This contrasts with most existing tube MPC strategies using polytopic sets in the state tube, which are difficult to design and whose complexity grows combinatorially with the system order. The algorithm guarantees constraint satisfaction, recursive feasibility, and stability of the closed loop. The advantages of the algorithm are demonstrated using two simulation studies.

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arXiv2022

The Existence and Uniqueness of Solutions for Kernel-Based System Identification

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. This paper shows that this central assumption is guaranteed to be satisfied in considerably general situations, namely when the kernel is an integrable function and the input signal is bounded. 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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arXiv2022

Regret Analysis of Online Gradient Descent-based Iterative Learning Control with Model Mismatch

In Iterative Learning Control (ILC), a sequence of feedforward control actions is generated at each iteration on the basis of partial model knowledge and past measurements with the goal of steering the system toward a desired reference trajectory. This is framed here as an online learning task, where the decision-maker takes sequential decisions by solving a sequence of optimization problems having only partial knowledge of the cost functions. Having established this connection, the performance of an online gradient-descent based scheme using inexact gradient information is analyzed in the setting of dynamic and static regret, standard measures in online learning. Fundamental limitations of the scheme and its integration with adaptation mechanisms are further investigated, followed by numerical simulations on a benchmark ILC problem.

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arXiv2022

Robust MPC with data-driven demand forecasting for frequency regulation with heat pumps

With the increased amount of volatile renewable energy sources connected to the electricity grid, and the phase-out of fossil fuel based power plants, there is an increased need for frequency regulation. On the demand side, frequency regulation services can be offered by buildings or districts that are equipped with electric heating or cooling systems, by exploiting their thermal inertia. Existing approaches for tapping into this potential typically rely on dynamic building models, which in practice can be challenging to obtain and maintain. As a result, practical implementations of such systems are scarce. Moreover, actively controlling buildings requires extensive control infrastructure and may cause privacy concerns in district energy systems. Motivated by this, we exploit the thermal inertia of buffer storage for reserves, reducing the building models to demand forecasts here. By combining a control scheme based on Robust Model Predictive Control, with affine policies, and heating demand forecasting based on Artificial Neural Networks with online correction methods, we offer frequency regulation reserves and maintain user comfort with a system comprising a heat pump and buffer storage. While the robust approach ensures occupant comfort, the use of affine policies reduces the effect of disturbance uncertainty on the system state. In a first-of-its-kind experiment with a real district-like building energy system, we demonstrate that the scheme is able to offer reserves in a variety of conditions and track a regulation signal while meeting the heating demand of the connected buildings. 13.4% of the consumed electricity is flexible. In additional numerical studies, we demonstrate that using affine policies significantly decreases the cost function and increases the amount of offered reserves and we investigate the suboptimality in comparison to an omniscient control system.

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arXiv2022

An explicit dual control approach for constrained reference tracking of uncertain linear systems

A finite horizon optimal tracking problem is considered for linear dynamical systems subject to parametric uncertainties in the state-space matrices and exogenous disturbances. A suboptimal solution is proposed using a model predictive control (MPC) based explicit dual control approach which enables active uncertainty learning. A novel algorithm for the design of robustly invariant online terminal sets and terminal controllers is presented. Set membership identification is used to update the parameter uncertainty online. A predicted worst-case cost is used in the MPC optimization problem to model the dual effect of the control input. The cost-to-go is estimated using contractivity of the proposed terminal set and the remaining time horizon, so that the optimizer can estimate future benefits of exploration. The proposed dual control algorithm ensures robust constraint satisfaction and recursive feasibility, and navigates the exploration-exploitation trade-off using a robust performance metric.

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arXiv2022

Physics-informed linear regression is competitive with two Machine Learning methods in residential building MPC

Because physics-based building models are difficult to obtain as each building is individual, there is an increasing interest in generating models suitable for building MPC directly from measurement data. Machine learning methods have been widely applied to this problem and validated mostly in simulation; there are, however, few studies on a direct comparison of different models or validation in real buildings to be found in the literature. Methods that are indeed validated in application often lead to computationally complex non-convex optimization problems. Here we compare physics-informed Autoregressive-Moving-Average with Exogenous Inputs (ARMAX) models to Machine Learning models based on Random Forests and Input Convex Neural Networks and the resulting convex MPC schemes in experiments on a practical building application with the goal of minimizing energy consumption while maintaining occupant comfort, and in a numerical case study. We demonstrate that Predictive Control in general leads to savings between 26% and 49% of heating and cooling energy, compared to the building's baseline hysteresis controller. Moreover, we show that all model types lead to satisfactory control performance in terms of constraint satisfaction and energy reduction. However, we also see that the physics-informed ARMAX models have a lower computational burden, and a superior sample efficiency compared to the Machine Learning based models. Moreover, even if abundant training data is available, the ARMAX models have a significantly lower prediction error than the Machine Learning models, which indicates that the encoded physics-based prior of the former cannot independently be found by the latter.

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