arXiv subjects

Roy S. Smith

Publications and source records attributed to Roy S. Smith.

At least 55 records · Page 3Linked to original sources

arXiv2022

Scalable Power System Line Upgrade Planning With Policy Constraints: A "Branch and Benders" Approach

The integration of more renewable energy sources into the power system is presenting system operators with various challenges. At the distribution system level, voltage magnitudes that violate operating limits near large photovoltaic installations have been observed. While these issues can be partially mitigated with more advanced control, hardware upgrades are required at some point. This work presents a scalable, optimization-based approach for deciding which lines in a network to upgrade. Compared to existing approaches, it explicitly takes the operating policy of the system into account and provides both reasonable solutions in short computation times as well as globally optimal solutions when run to completion. Compared to earlier work on the same topic, an extended computational approach is taken that can simultaneously optimize for many load scenarios across arbitrary configurations of machines and CPU cores per machine in a scalable manner by using the Benders decomposition. In addition to the theory, numerical experiments are presented along with a discussion of the scaling properties of the Benders-based approach, giving potential users a better basis to decide whether their problem is big enough for the approach to make sense.

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arXiv2021

Maximum Likelihood Estimation in Data-Driven Modeling and Control

Recently, various algorithms for data-driven simulation and control have been proposed based on the Willems' fundamental lemma. However, when collected data are noisy, these methods lead to ill-conditioned data-driven model structures. In this work, we present a maximum likelihood framework to obtain an optimal data-driven model, the signal matrix model, in the presence of output noise. Data compression and noise level estimation schemes are also proposed to apply the algorithm efficiently to large datasets and unknown noise level scenarios. Two approaches in system identification and receding horizon control are developed based on the derived optimal estimator. The first one identifies a finite impulse response model. This approach improves the least-squares estimator with less restrictive assumptions. The second one applies the signal matrix model as the predictor in predictive control. The control performance is shown to be better than existing data-driven predictive control algorithms, especially under high noise levels. Both approaches demonstrate that the derived estimator provides a promising framework to apply data-driven algorithms to noisy data.

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arXiv2021

Maximum Likelihood Signal Matrix Model for Data-Driven Predictive Control

The paper presents a data-driven predictive control framework based on an implicit input-output mapping derived directly from the signal matrix of collected data. This signal matrix model is derived by maximum likelihood estimation with noise-corrupted data. By linearizing online, the implicit model can be used as a linear constraint to characterize possible trajectories of the system in receding horizon control. The signal matrix can also be updated online with new measurements. This algorithm can be applied to large datasets and slowly time-varying systems, possibly with high noise levels. An additional regularization term on the prediction error can be introduced to enhance the predictability and thus the control performance. Numerical results demonstrate that the proposed signal matrix model predictive control algorithm is effective in multiple applications and performs better than existing data-driven predictive control algorithm.

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arXiv2021

Data-Driven Prediction with Stochastic Data: Confidence Regions and Minimum Mean-Squared Error Estimates

Recently, direct data-driven prediction has found important applications for controlling unknown systems, particularly in predictive control. Such an approach provides exact prediction using behavioral system theory when noise-free data are available. For stochastic data, although approximate predictors exist based on different statistical criteria, they fail to provide statistical guarantees of prediction accuracy. In this paper, confidence regions are provided for these stochastic predictors based on the prediction error distribution. Leveraging this, an optimal predictor which achieves minimum mean-squared prediction error is also proposed to enhance prediction accuracy. These results depend on some true model parameters, but they can also be replaced with an approximate data-driven formulation in practice. Numerical results show that the derived confidence region is valid and smaller prediction errors are observed for the proposed minimum mean-squared error estimate, even with the approximate data-driven formulation.

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arXiv2021

Regularized Identification with Internal Positivity Side-Information

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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arXiv2021

Distributed Model Predictive Control of Buildings and Energy Hubs

Model predictive control (MPC) strategies can be applied to the coordination of energy hubs to reduce their energy consumption. Despite the effectiveness of these techniques, their potential for energy savings are potentially underutilized due to the fact that energy demands are often assumed to be fixed quantities rather than controlled dynamic variables. The joint optimization of energy hubs and buildings' energy management systems can result in higher energy savings. This paper investigates how different MPC strategies perform on energy management systems in buildings and energy hubs. We first discuss two MPC approaches; centralized and decentralized. While the centralized control strategy offers optimal performance, its implementation is computationally prohibitive and raises privacy concerns. On the other hand, the decentralized control approach, which offers ease of implementation, displays significantly lower performance. We propose a third strategy, distributed control based on dual decomposition, which has the advantages of both approaches. Numerical case studies and comparisons demonstrate that the performance of distributed control is close to the performance of the centralized case, while maintaining a significantly lower computational burden, especially in large-scale scenarios with many agents. Finally, we validate and verify the reliability of the proposed method through an experiment on a full-scale energy hub system in the NEST demonstrator in Dübendorf, Switzerland.

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arXiv2021

Design of input for data-driven simulation with Hankel and Page matrices

The paper deals with the problem of designing informative input trajectories for data-driven simulation. First, the excitation requirements in the case of noise-free data are discussed and new weaker conditions, which assume the simulated input to be known in advance, are provided. Then, the case of noisy data trajectories is considered and an input design problem based on a recently proposed maximum likelihood estimator is formulated. A Bayesian interpretation is provided, and the implications of using Hankel and Page matrix representations are demonstrated. Numerical examples show the impact of the designed input on the predictive accuracy.

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arXiv2021

Discrete-Time Linear-Quadratic Regulation via Optimal Transport

In this paper, we consider a discrete-time stochastic control problem with uncertain initial and target states. We first discuss the connection between optimal transport and stochastic control problems of this form. Next, we formulate a linear-quadratic regulator problem where the initial and terminal states are distributed according to specified probability densities. A closed-form solution for the optimal transport map in the case of linear-time varying systems is derived, along with an algorithm for computing the optimal map. Two numerical examples pertaining to swarm deployment demonstrate the practical applicability of the model, and performance of the numerical method.

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arXiv2021

Robust Adaptive Model Predictive Control of Quadrotors

Robust adaptive model predictive control (RAMPC) is a novel control method that combines robustness guarantees with respect to unknown parameters and bounded disturbances into a model predictive control scheme. However, RAMPC has so far only been developed in theory. The goal of this paper is to apply RAMPC to a physical quadrotor experiment. To the best of our knowledge this is the first time that RAMPC has been applied in practice using a state space formulation. In doing so, we highlight important practical challenges such as computation of $λ$-contractive polytopes and dealing with measurement noise, and propose modifications to RAMPC so that it can be applied on a quadrotor. We first simulate quadrotor flight with a direct and a decoupled control architecture in different scenarios. The scenarios include: (i) an unknown mass of the quadrotor as a package delivery scenario with wind as a bounded disturbance; and (ii) all rotor efficiencies drop as a power delivery problem. We then implement these scenarios on a physical quadrotor and present the experimental results.

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arXiv2021

Safety-Aware Cascade Controller Tuning Using Constrained Bayesian Optimization

This paper presents an automated, model-free, data-driven method for the safe tuning of PID cascade controller gains based on Bayesian optimization. The optimization objective is composed of data-driven performance metrics and modeled using Gaussian processes. We further introduce a data-driven constraint that captures the stability requirements from system data. Numerical evaluation shows that the proposed approach outperforms relay feedback autotuning and quickly converges to the global optimum, thanks to a tailored stopping criterion. We demonstrate the performance of the method in simulations and experiments. For experimental implementation, in addition to the introduced safety constraint, we integrate a method for automatic detection of the critical gains and extend the optimization objective with a penalty depending on the proximity of the current candidate points to the critical gains. The resulting automated tuning method optimizes system performance while ensuring stability and standardization

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arXiv2021

The Balanced Mode Decomposition Algorithm for Data-Driven LPV Low-Order Models of Aeroservoelastic Systems

A novel approach to reduced-order modeling of high-dimensional time varying systems is proposed. It leverages the formalism of the Dynamic Mode Decomposition technique together with the concept of balanced realization. It is assumed that the only information available on the system comes from input, state, and output trajectories generated by numerical simulations or recorded and estimated during experiments, thus the approach is fully data-driven. The goal is to obtain an input-output low dimensional linear model which approximates the system across its operating range. Since the dynamics of aeroservoelastic systems markedly changes in operation (e.g. due to change in flight speed or altitude), time-varying features are retained in the constructed models. This is achieved by generating a Linear Parameter-Varying representation made of a collection of state-consistent linear time-invariant reduced-order models. The algorithm formulation hinges on the idea of replacing the orthogonal projection onto the Proper Orthogonal Decomposition modes, used in Dynamic Mode Decomposition-based approaches, with a balancing oblique projection constructed entirely from data. As a consequence, the input-output information captured in the lower-dimensional representation is increased compared to other projections onto subspaces of same or lower size. Moreover, a parameter-varying projection is possible while also achieving state-consistency. The validity of the proposed approach is demonstrated on a morphing wing for airborne wind energy applications by comparing the performance against two algorithms recently proposed in the literature. Comparisons cover both prediction accuracy and performance in model predictive control applications.

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arXiv2021

On Robustness of Kernel-Based Regularized System Identification

This paper presents a novel feature of the kernel-based system identification method. We prove that the regularized kernel-based approach for the estimation of a finite impulse response is equivalent to a robust least-squares problem with a particular uncertainty set defined in terms of the kernel matrix, and thus, it is called kernel-based uncertainty set. We provide a theoretical foundation for the robustness of the kernel-based approach to input disturbances. Based on robust and regularized least-squares methods, different formulations of system identification are considered, where the kernel-based uncertainty set is employed in some of them. We apply these methods to a case where the input measurements are subject to disturbances. Subsequently, we perform extensive numerical experiments and compare the results to examine the impact of utilizing kernel-based uncertainty sets in the identification procedure. The numerical experiments confirm that the robust least square identification approach with the kernel-based uncertainty set improves the robustness of the estimation to the input disturbances.

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arXiv2021

Experiment design for impulse response identification with signal matrix models

This paper formulates an input design approach for truncated infinite impulse response identification in the context of implicit model representations recently used as basis for data-driven simulation and control approaches. Precisely, the considered model consists of a linear combination of the columns of a data (or signal) matrix. An optimal combination for the case of noisy data was recently proposed using a maximum likelihood approach, and the objective here is to optimize the input entries of the data matrix such that the mean-square error matrix of the estimate is minimized. A least-norm problem is derived in terms of the optimality criteria typically considered in the experiment design literature. Numerical results showcase the improved estimation fit achieved with the optimized input.

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arXiv2021

Structured exploration in the finite horizon linear quadratic dual control problem

This paper presents a novel approach to synthesize dual controllers for unknown linear time-invariant systems with the tasks of optimizing a quadratic cost while reducing the uncertainty. To this end, a synthesis problem is defined where the feedback law has to simultaneously gain knowledge of the system and robustly optimize the cost. By framing the problem in a finite horizon setting, the trade-offs arising when the tasks include both identification and control are formally captured in the optimization problem. Results show that efficient exploration strategies are achieved when the structure of the problem is exploited.

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arXiv2021

Active exploration in adaptive model predictive control

A dual adaptive model predictive control (MPC) algorithm is presented for linear, time-invariant systems subject to bounded disturbances and parametric uncertainty in the state-space matrices. Online set-membership identification is performed to reduce the uncertainty and thus control affects both the informativity of identification and the system's performance. The main contribution of the paper is to include this dual effect in the MPC optimization problem using a predicted worst-case cost in the objective function. This allows the controller to perform active exploration, that is, the control input reduces the uncertainty in the regions of the parameter space that have most influence on the performance. Additionally, the MPC algorithm ensures robust constraint satisfaction of state and input constraints. Advantages of the proposed algorithm are shown by comparing it to a passive adaptive MPC algorithm from the literature.

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arXiv2020

Parameter Identification for Digital Fabrication: A Gaussian Process Learning Approach

Tensioned cable nets can be used as supporting structures for the efficient construction of lightweight building elements, such as thin concrete shell structures. To guarantee important mechanical properties of the latter, the tolerances on deviations of the tensioned cable net geometry from the desired target form are very tight. Therefore, the form needs to be readjusted on the construction site. In order to employ model-based optimization techniques, the precise identification of important uncertain model parameters of the cable net system is required. This paper proposes the use of Gaussian process regression to learn the function that maps the cable net geometry to the uncertain parameters. In contrast to previously proposed methods, this approach requires only a single form measurement for the identification of the cable net model parameters. This is beneficial since measurements of the cable net form on the construction site are very expensive. For the training of the Gaussian processes, simulated data is efficiently computed via convex programming. The effectiveness of the proposed method and the impact of the precise identification of the parameters on the form of the cable net are demonstrated in numerical experiments on a quarter-scale prototype of a roof structure.

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arXiv2020

On Low-Rank Hankel Matrix Denoising

The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank matrix. However, standard low-rank approximation approaches are not guaranteed to perform well in estimating the noise-free matrix. In this paper, recent results in matrix denoising by singular value shrinkage are reviewed. A novel approach is proposed to solve the low-rank Hankel matrix denoising problem by using an iterative algorithm in structured low-rank approximation modified with data-driven singular value shrinkage. It is shown numerically in both the input-output trajectory denoising and the impulse response denoising problems, that the proposed method performs the best in terms of estimating the noise-free matrix among existing algorithms of low-rank matrix approximation and denoising.

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arXiv2020

Extended Full Block S-Procedure for Distributed Control of Interconnected Systems

This paper proposes a novel method for distributed controller synthesis of homogeneous interconnected systems consisting of identical subsystems. The objective of the designed controller is to minimize the L2-gain of the performance channel. The proposed method is an extended formulation of the Full Block S-Procedure (FBSP) where we introduce an additional set of variables. This allows relaxing the block-diagonal structural assumptions on the Lyapunov and multiplier matrices required for distributed control design, which reduces conservatism w.r.t most existing approaches. We show how to decompose the proposed extended FBSP into small synthesis conditions, of the size of one individual subsystem.

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