The literature dealing with data-driven analysis and control problems has significantly grown in the recent years. Most of the recent literature deals with linear time-invariant systems in which the uncertainty (if any) is assumed to be deterministic and bounded; relatively little attention has been devoted to stochastic linear time-invariant systems. As a first step in this direction, we propose to equip the recently introduced Data-enabled Predictive Control algorithm with a data-based Extended Kalman Filter to make use of additional available input-output data for reducing the effect of noise, without increasing the computational load of the optimization procedure.
Model Predictive Control (MPC) is the principal control technique used in industrial applications. Although it offers distinguishable qualities that make it ideal for industrial applications, it can be questioned its robustness regarding model uncertainties and external noises. In this paper we propose a robust MPC controller that merges the simplicity in the design of MPC with added robustness. In particular, our control system stems from the idea of adding robustness in the prediction phase of the algorithm through a specific robust Kalman filter recently introduced. Notably, the overall res…
Nonlinear model predictive control has become a popular approach to deal with highly nonlinear and unsteady state systems, the performance of which can however deteriorate due to unaccounted uncertainties. Model predictive control is commonly used with states from a state estimator in place of the exact states without consideration of the error. In this paper an approach is proposed by incorporating the unscented Kalman filter into the NMPC problem, which propagates uncertainty introduced from both the state estimate and additive noise from disturbances forward in time. The feasibility is main…
Model Predictive Control (MPC) represents nowadays one of the main methods employed for process control in industry. Its strong suits comprise a simple algorithm based on a straightforward formulation and the flexibility to deal with constraints. On the other hand it can be questioned its robustness regarding model uncertainties and external noises. Thus, a lot of efforts have been spent in the past years into the search of methods to address these shortcomings. In this paper we propose a robust MPC controller which stems from the idea of adding robustness in the prediction phase of the algori…
We develop an online data-enabled predictive (ODeePC) control method for optimal control of unknown systems, building on the recently proposed DeePC [1]. Our proposed ODeePC method leverages a primal-dual algorithm with real-time measurement feedback to iteratively compute the corresponding real-time optimal control policy as system conditions change. The proposed ODeePC conceptual-wise resembles standard adaptive system identification and model predictive control (MPC), but it provides a new alternative for the standard methods. ODeePC is enabled by computationally efficient methods that expl…
We consider the problem of optimal trajectory tracking for unknown systems. A novel data-enabled predictive control (DeePC) algorithm is presented that computes optimal and safe control policies using real-time feedback driving the unknown system along a desired trajectory while satisfying system constraints. Using a finite number of data samples from the unknown system, our proposed algorithm uses a behavioural systems theory approach to learn a non-parametric system model used to predict future trajectories. The DeePC algorithm is shown to be equivalent to the classical and widely adopted Mo…
In this paper, we study a data-enabled predictive control (DeePC) algorithm applied to unknown stochastic linear time-invariant systems. The algorithm uses noise-corrupted input/output data to predict future trajectories and compute optimal control policies. To robustify against uncertainties in the input/output data, the control policies are computed to minimize a worst-case expectation of a given objective function. Using techniques from distributionally robust stochastic optimization, we prove that for certain objective functions, the worst-case optimization problem coincides with a regular…
We study the problem of finite-time constrained optimal control of unknown stochastic linear time-invariant systems, which is the key ingredient of a predictive control algorithm -- albeit typically having access to a model. We propose a novel distributionally robust data-enabled predictive control (DeePC) algorithm which uses noise-corrupted input/output data to predict future trajectories and compute optimal control inputs while satisfying output chance constraints. The algorithm is based on (i) a non-parametric representation of the subspace spanning the system behaviour, where past traject…
We present a stochastic predictive controller for discrete time linear time invariant systems under incomplete state information. Our approach is based on a suitable choice of control policies, stability constraints, and employment of a Kalman filter to estimate the states of the system from incomplete and corrupt observations. We demonstrate that this approach yields a computationally tractable problem that should be solved online periodically, and that the resulting closed loop system is mean-square bounded for any positive bound on the control actions. Our results allow one to tackle the la…
This paper investigates the use of extended Kalman filtering to train recurrent neural networks with rather general convex loss functions and regularization terms on the network parameters, including $\ell_1$-regularization. We show that the learning method is competitive with respect to stochastic gradient descent in a nonlinear system identification benchmark and in training a linear system with binary outputs. We also explore the use of the algorithm in data-driven nonlinear model predictive control and its relation with disturbance models for offset-free closed-loop tracking.
We propose a provably stabilizing and tractable approach for control of constrained linear systems under intermittent observations and unreliable transmissions of control commands. A smart sensor equipped with a Kalman filter is employed for the estimation of the states from incomplete and corrupt measurements, and an estimator at the controller side optimally feeds the intermittently received sensor data to the controller. The remote controller iteratively solves constrained stochastic optimal control problems and transmits the control commands according to a carefully designed transmission p…
This paper develops a new active fault tolerant control system based on the concept of analytical redundancy. The novel design consists of an observation filter based fault detection and identification system integrated with a nonlinear model predictive controller. A number of observation filters were designed, integrated with the nonlinear controller and tested before reaching the final design which comprises an unscented Kalman filter for fault detection and identification together with a nonlinear model predictive controller to form an active fault tolerant control system design.
In this paper we investigate the design of an active fault tolerant control system applicable to autonomous flight. The system comprises a nonlinear model predictive based controller integrated with an unscented Kalman filter for fault detection and identification. We apply the fault tolerant control system design to a generic aircraft model, and simulate a failed engine scenario. The results show that the system correctly identifies the fault within seconds of occurrence and updates the nonlinear model predictive controller which is then able to reallocate control authority to the healthy act…
The prevalence of COVID-19 has been the most serious health challenge of the 21th century to date, concerning national health systems on a daily basis, since December 2019 when it appeared in Wuhan City. Nevertheless, most of the proposed mathematical methodologies aiming to describe the dynamics of an epidemic, rely on deterministic models that are not able to reflect the true nature of its spread. In this paper, we propose a SEIHCRDV model - an extension/improvement of the classic SIR compartmental model - which also takes into consideration the populations of exposed, hospitalized, admitted…
Model-Free Control for Residential Heating: Deployment and Simulation of Nonlinear Data-Enabled Predictive Control
University of Oslo（奥斯陆大学）；Swiss Federal Laboratories for Materials Science and Technology (Empa)（瑞士联邦材料科技与工程研究院）；University of Pennsylvania（宾夕法尼亚大学）；Eindhoven University of Technology（埃因霍温理工大学）；University of Groningen（格罗宁根大学）
The Kalman filter is an algorithm for the estimation of hidden variables in dynamical systems under linear Gauss-Markov assumptions with widespread applications across different fields. Recently, its Bayesian interpretation has received a growing amount of attention especially in neuroscience, robotics and machine learning. In neuroscience, in particular, models of perception and control under the banners of predictive coding, optimal feedback control, active inference and more generally the so-called Bayesian brain hypothesis, have all heavily relied on ideas behind the Kalman filter. Active …
We present an efficient and practical (polynomial time) algorithm for online prediction in unknown and partially observed linear dynamical systems (LDS) under stochastic noise. When the system parameters are known, the optimal linear predictor is the Kalman filter. However, the performance of existing predictive models is poor in important classes of LDS that are only marginally stable and exhibit long-term forecast memory. We tackle this problem through bounding the generalized Kolmogorov width of the Kalman filter model by spectral methods and conducting tight convex relaxation. We provide a…
The Willems' fundamental lemma, which characterizes linear dynamics with measured trajectories, has found successful applications in controller design and signal processing, which has driven a broad research interest in its extension to nonlinear systems. In this work, we propose to apply the fundamental lemma to a reproducing kernel Hilbert space in order to extend its application to a class of nonlinear systems and we show its application in prediction and in predictive control.
State estimation incorporates the feedback in optimization based advanced process control systems and is very important for the performance of model predictive control. We describe the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and a particle filter for continuous-discrete time nonlinear systems involving stochastic differential equations. Continuous-discrete time nonlinear systems is a natural way to model physical systems controlled by digital controllers. We implement the state estimation methods in Matlab, illustrate and evaluate their performance usin…
