Selected Essays on the Conflict of Laws. By Brainerd Currie.

Most subspace identication algorithms are not applicable to closed-loop identication because they require future input to be uncorrelated with pastinnovation. In this paper, we propose a new subspace identication method that remove this requirement by using a parsimonious model formulation with innovation estimation. A simulation example is included to show the effectiveness of the proposed method

Public Law by Private Bargain: Title VII Consent Decrees and the Fairness of Negotiated Institutional Reform

Large-scale Title VII remedies are typical of public law litigation, which differs in kind from the conventional compensatory lawsuit. Title VII remedies are commonly adopted by way of consent decrees. By approving these consent decrees, federal courts take responsibility for extensive institutional reforms while acting independently of the adversary process. Courts have frequently approved consent decrees without fair hearings for those whose interests are at stake. Professor Schwarzschild suggests a systematic procedure for approving Title VII consent decrees. This procedure would not discourage settlements, but would ensure that courts act on the basis of fair hearings, consistently with the quasi-legislative character of public law remedies

Foreword

In this paper, we show that the consistency of closed-loop subspace identification methods (SIMs) can be achieved through innovation estimation. Based on this analysis, a sufficient condition for the consistency of a new proposed closed-loop SIM is given, A consistent estimate of the Kalman gain under closed-loop conditions is also provided based on the algorithm. A multi-input-multi-output simulation shows that itis consistent under closed-loop conditions, when traditional SIMs fail to provide consistent estimates

Probabilistic Reduced-Dimensional Vector Autoregressive Modeling with Oblique Projections

In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model to extract low-dimensional dynamics from high-dimensional noisy data. The model utilizes an oblique projection to partition the measurement space into a subspace that accommodates the reduced-dimensional dynamics and a complementary static subspace. An optimal oblique decomposition is derived for the best predictability regarding prediction error covariance. Building on this, we develop an iterative PredVAR algorithm using maximum likelihood and the expectation-maximization (EM) framework. This algorithm alternately updates the estimates of the latent dynamics and optimal oblique projection, yielding dynamic latent variables with rank-ordered predictability and an explicit latent VAR model that is consistent with the outer projection model. The superior performance and efficiency of the proposed approach are demonstrated using data sets from a synthesized Lorenz system and an industrial process from Eastman Chemical.Comment: 16pages, 5 figure

Probabilistic Reduced-Dimensional Vector Autoregressive Modeling for Dynamics Prediction and Reconstruction with Oblique Projections

In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model with oblique projections. This model partitions the measurement space into a dynamic subspace and a static subspace that do not need to be orthogonal. The partition allows us to apply an oblique projection to extract dynamic latent variables (DLVs) from high-dimensional data with maximized predictability. We develop an alternating iterative PredVAR algorithm that exploits the interaction between updating the latent VAR dynamics and estimating the oblique projection, using expectation maximization (EM) and a statistical constraint. In addition, the noise covariance matrices are estimated as a natural outcome of the EM method. A simulation case study of the nonlinear Lorenz oscillation system illustrates the advantages of the proposed approach over two alternatives

Alternating minimization for simultaneous estimation of a latent variable and identification of a linear continuous-time dynamic system

We propose an optimization formulation for the simultaneous estimation of a latent variable and the identification of a linear continuous-time dynamic system, given a single input-output pair. We justify this approach based on Bayesian maximum a posteriori estimators. Our scheme takes the form of a convex alternating minimization, over the trajectories and the dynamic model respectively. We prove its convergence to a local minimum which verifies a two point-boundary problem for the (latent) state variable and a tensor product expression for the optimal dynamics

Predictive control methods to improve energy efficiency and reduce demand in buildings

Abstract This paper presents an overview of results and future challenges on temperature control and cost optimization in building energy systems. Control and economic optimization issues are discussed and illustrated through sophisticated simulation examples. The paper concludes with effective results from model predictive control solutions and identification of important directions for future work

Real-time experimental implementation of predictive control schemes in a small-scale pasteurization plant

Model predictive control (MPC) is one of the most used optimization-based control strategies for large-scale systems, since this strategy allows to consider a large number of states and multi-objective cost functions in a straightforward way. One of the main issues in the design of multi-objective MPC controllers, which is the tuning of the weights associated to each objective in the cost function, is treated in this work. All the possible combinations of weights within the cost function affect the optimal result in a given Pareto front. Furthermore, when the system has time-varying parameters, e.g., periodic disturbances, the appropriate weight tuning might also vary over time. Moreover, taking into account the computational burden and the selected sampling time in the MPC controller design, the computation time to find a suitable tuning is limited. In this regard, the development of strategies to perform a dynamical tuning in function of the system conditions potentially improves the closed-loop performance. In order to adapt in a dynamical way the weights in the MPC multi-objective cost function, an evolutionary-game approach is proposed. This approach allows to vary the prioritization weights in the proper direction taking as a reference a desired region within the Pareto front. The proper direction for the prioritization is computed by only using the current system values, i.e., the current optimal control action and the measurement of the current states, which establish the system cost function over a certain point in the Pareto front. Finally, some simulations of a multi-objective MPC for a real multi-variable case study show a comparison between the system performance obtained with static and dynamical tuning.Peer ReviewedPostprint (author's final draft

MLPST: MLP is All You Need for Spatio-Temporal Prediction

Traffic prediction is a typical spatio-temporal data mining task and has great significance to the public transportation system. Considering the demand for its grand application, we recognize key factors for an ideal spatio-temporal prediction method: efficient, lightweight, and effective. However, the current deep model-based spatio-temporal prediction solutions generally own intricate architectures with cumbersome optimization, which can hardly meet these expectations. To accomplish the above goals, we propose an intuitive and novel framework, MLPST, a pure multi-layer perceptron architecture for traffic prediction. Specifically, we first capture spatial relationships from both local and global receptive fields. Then, temporal dependencies in different intervals are comprehensively considered. Through compact and swift MLP processing, MLPST can well capture the spatial and temporal dependencies while requiring only linear computational complexity, as well as model parameters that are more than an order of magnitude lower than baselines. Extensive experiments validated the superior effectiveness and efficiency of MLPST against advanced baselines, and among models with optimal accuracy, MLPST achieves the best time and space efficiency