Data-driven Control Research Articles

On the Design of Persistently Exciting Inputs for Data-Driven Control of Linear and Nonlinear Systems

In the context of data-driven control, persistence of excitation (PE) of an input sequence is defined in terms of a rank condition on the Hankel matrix of the input data. For nonlinear systems, recent results employed rank conditions involving collected input and state/output data, for which no guidelines are available on how to satisfy them a priori. In this paper, we first show that a set of discrete impulses is guaranteed to be persistently exciting for any controllable LTI system. Based on this result, for certain classes of nonlinear systems, we guarantee persistence of excitation of sequences of basis functions a priori, by design of the physical input only.

Deep Learning based Uncertainty Decomposition for Real-time Control

Data-driven control in unknown environments requires a clear understanding of the involved uncertainties for ensuring safety and efficient exploration. While aleatoric uncertainty that arises from measurement noise can often be explicitly modeled given a parametric description, it can be harder to model epistemic uncertainty, which describes the presence or absence of training data. The latter can be particularly useful for implementing exploratory control strategies when system dynamics are unknown. We propose a novel method for detecting the absence of training data using deep learning, which gives a continuous valued scalar output between 0 (indicating low uncertainty) and 1 (indicating high uncertainty). We utilize this detector as a proxy for epistemic uncertainty and show its advantages over existing approaches on synthetic and real-world datasets. Our approach can be directly combined with aleatoric uncertainty estimates and allows for uncertainty estimation in real-time as the inference is sample-free unlike existing approaches for uncertainty modeling. We further demonstrate the practicality of this uncertainty estimate in deploying online data-efficient control on a simulated quadcopter acted upon by an unknown disturbance model.

Closed-form and robust expressions for data-driven LQ control

This article provides an overview of certain direct data-driven control results, where control sequences are computed from (noisy) data collected during offline control experiments without an explicit identification of the system dynamics. For the case of noiseless datasets, we derive several closed-form data-driven expressions that solve a variety of optimal control problems for linear systems with quadratic cost functions of the state and input (including the linear quadratic regulator problem, the minimum energy control problem, and the linear quadratic control problem with terminal constraints), discuss their advantages and drawbacks with respect to alternative data-driven and model-based approaches, and showcase their effectiveness through a number of numerical studies. Interestingly, these results provide an alternative and explicit way of solving classic control problems that, for instance, does not require the solution of an implicit and recursive Riccati equation as in the model-based setting. For the case of noisy datasets, we show how the closed-form expressions derived in the noiseless setting can be modified to compensate for the bias induced by noise, and perform a sensitivity analysis to reveal favorable asymptotic robustness properties of the derived data-driven controls. We conclude the paper with some considerations and a discussion of outstanding questions and directions of future investigation.

Gaussian inference for data-driven state-feedback design of nonlinear systems

Data-driven control of nonlinear systems with rigorous guarantees is a challenging problem as it usually calls for nonconvex optimization and often requires the knowledge of the true basis functions of the unknown system dynamics. To tackle these drawbacks, this work is based on a data-driven polynomial representation of general nonlinear systems exploiting Taylor polynomials. Thereby, we design state-feedback laws that render a known equilibrium globally asymptotically stable while operating with respect to a desired quadratic performance criterion. The calculation of the polynomial state feedback boils down to a sum-of-squares optimization problem, and hence to computationally tractable linear matrix inequalities. Moreover, we examine state-input data in presence of Gaussian noise by Bayesian inference to overcome the conservatism of deterministic noise characterizations from recent data-driven control approaches for Gaussian noise.

Behavioral theory for stochastic systems? A data-driven journey from Willems to Wiener and back again

The fundamental lemma by Jan C. Willems and co-workers is deeply rooted in behavioral systems theory and it has become one of the supporting pillars of the recent progress on data-driven control and system analysis. This tutorial-style paper combines recent insights into stochastic and descriptor-system formulations of the lemma to further extend and broaden the formal basis for behavioral theory of stochastic linear systems. We show that series expansions – in particular Polynomial Chaos Expansions (PCE) of L2-random variables, which date back to Norbert Wiener’s seminal work – enable equivalent behavioral characterizations of linear stochastic systems. Specifically, we prove that under mild assumptions the behavior of the dynamics of the L2-random variables is equivalent to the behavior of the dynamics of the series expansion coefficients and that it entails the behavior composed of sampled realization trajectories. We also illustrate the short-comings of the behavior associated to the time-evolution of the statistical moments. The paper culminates in the formulation of the stochastic fundamental lemma for linear time-invariant systems, which in turn enables numerically tractable formulations of data-driven stochastic optimal control combining Hankel matrices in realization data (i.e. in measurements) with PCE concepts.

Intelligent Edge Sensing and Control Co-Design for Industrial Cyber-Physical System

In the new generation of industrial cyber-physical system (ICPS), data-driven control is one of the emerging intelligent control methods to realize efficient production adjustment. In most existing works, the perfect sensing process is regarded as the fundamental assumption. However the experienced sensing strategies deployed in advance are increasingly difficult to adapt to the expanding network scale and diversified production demands in the Industry 4.0 era. To tackle the challenges, we propose the novel intelligent edge sensing and control co-design (IESCC) framework under ICPS. The cooperation of five constructed graph convolutional neural networks respectively related to system model, sensing model, estimator, actor and critic is adopted to approximate the coupled optimality conditions of sensing and control strategies. The structure of learning networks is designed in advance for online strategy solving tailored for the real-time industrial requirements and edge computing power. In particular, the representation capabilities of learning networks under different scales are quantitatively analyzed from the perspectives of observability and controllability. Besides, the feasible region of learning rates is explicitly depicted to ensure convergence. Finally, the proposed algorithm is applied into the laminar cooling process in the semi-physical simulation. Compared with the state-of-the-art approaches, our method can always guarantee observability and controllability. And up to 27.9 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> overall performance of sensing and control is improved, and 38 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> execution time reduction is achieved on average.

Data-Driven Control Design With LMIs and Dynamic Programming

The goal of this paper is to study model-free data-driven control evaluation and design strategies for discrete-time linear time-invariant systems, where the system model is unknown. In particular, our main contribution is twofold: 1) new state-input exploration and data collection schemes from experiences; 2) new data-driven linear matrix inequalities and dynamic programming methods for stabilization and optimal control problems. The proposed exploration and data collection schemes theoretically guarantee to acquire sufficient information from the system’s state-input trajectories that can solve the underlying control design problems. We prove that under mild assumptions, as more and more data is accumulated, the collected data can solve the problems with higher probability along with the proposed algorithms.

Direct data-driven LPV control of nonlinear systems: An experimental result

We demonstrate that direct data-driven control of nonlinear systems can be successfully accomplished via a behavioral approach that builds on a Linear Parameter-Varying (LPV) system concept. An LPV data-driven representation is used as a surrogate LPV form of the data-driven representation of the original nonlinear system. The LPV data-driven control design that builds on this representation form uses only measurement data from the nonlinear system and a priori information on a scheduling map that can lead to an LPV embedding of the nonlinear system behavior. Efficiency of the proposed approach is demonstrated experimentally on a nonlinear unbalanced disc system showing for the first time in the literature that behavioral data-driven methods are capable to stabilize arbitrary forced equilibria of a real-world nonlinear system by the use of only 7 data points.

A practitioner's guide to noise handling strategies in data-driven predictive control

Today's increasing availability of data is having a remarkable impact on control design. However, for data-driven control approaches to become widespread in practical applications, it is necessary to devise strategies that can effectively handle the presence of noise in the data used to design the controller. In this work, we analyse the existing approaches to deal with noisy measurements in data-driven predictive control (DDPC) and we highlight the advantages and downsides of each technique from a practitioner's perspective. Our qualitative conclusions are supported by the results obtained from two benchmark examples.

Maximum Likelihood and Neural Network Estimators for Distributed Production Control

Cyber-physical systems have become increasingly common in recent years, providing a multitude of information regarding production processes. At the same time, increasing volatilities, uncertainties, complexity and ambiguity (VUCA) are challenging existing production control approaches for manufacturing networks. Data-driven control approaches are an avenue to address VUCA, but require further study in research and practice. We utilize a multi-agent based discrete-event simulation to compare the aptitudes of a maximum likelihood and neural network based estimator for distributed production control, and provide insights into application of machine learning to address ever increasing information and VUCA.

Data-driven control of input-affine systems via approximate nonlinearity cancellation

We consider data-driven control of input-affine systems via approximate nonlinearity cancellation. Data-dependent semi-definite program is developed to characterize the stabilizer such that the linear dynamics of the closed-loop systems is stabilized and the influence of the nonlinear dynamics is decreased. Because of the additional nonlinearity brought by the state-dependent input vector field, nonlinearity cancellation is more difficult to achieve. We show that under some assumptions on the nonlinearity, the nonlinearity cancellation control approach can render the equilibrium locally asymptotically stable even if the additional nonlinearity is neglected. Data-based estimation of the region of the attraction is also presented.

A Reliable Data-Driven Control Method for Planting Temperature in Smart Agricultural Systems

With the rapid development of intelligent computing technologies, the smart agricultural systems has gradually received more research attention. Precisely controlling planting conditions via intelligent means, it is expected to technically improve reliability of smart agricultural systems. For this purpose, this paper introduces the idea of big data fusion, and proposes a reliable data-driven control method for planting temperature in smart agricultural systems. Firstly, a variety of sensors are used to collect the values of environmental factors such as air temperature and light intensity during the experiment, and the “Digi” wireless communication technology is used to transmit the data. Then, the collected data is sent to the server through the 5G module, and the important data of the growth process is stored in the MySQL database. Taking the cultivation of yams as the investigation object, experiments on the real-world data are utilized to evaluate the proposal. And it is shown that the propose framework can work well to control temperature for yam planting from the perspective of data fusion.

Data-Driven Controller Synthesis via Finite Abstractions With Formal Guarantees

Data-Driven Controller Synthesis via Finite Abstractions With Formal Guarantees

A Non-Iterative Approach to Direct Data-Driven Control Design of MIMO LTI Systems

A Non-Iterative Approach to Direct Data-Driven Control Design of MIMO LTI Systems

Youlaパラメータをもつ制御器に対するVirtual Internal Model Tuning

In this paper, we propose tuning methods of free parameters for control systems with stabilizing compensators. Here, we study a generalized internal model control system (GIMC). This control systems are generally designed based on a nominal models. However, it is difficult to redesign them in case of a nominal model have modeling errors between the original one. Therefore, we consider tuning the free parameters in this control systems using Virtual Internal Model Tuning (VIMT) which is one of the data-driven control. At the end of this paper, we verify the usefulness of the proposed method using numerical examples.

A Quantitative Notion of Persistency of Excitation and the Robust Fundamental Lemma

The fundamental lemma by Willems and coauthors enables a parameterization of all trajectories of a linear time-invariant system in terms of a single, measured one. This result plays a key role in data-driven simulation and control. The fundamental lemma relies on a persistently exciting input to the system to ensure that the Hankel matrix of resulting input/output data has the “right” rank, meaning that its columns span the entire subspace of trajectories. However, such binary rank conditions are known to be fragile in the sense that a small additive noise could already cause the Hankel matrix to have full rank. In this letter we present a robust version of the fundamental lemma. The idea behind the approach is to guarantee certain lower bounds on the singular values of the data Hankel matrix, rather than qualitative rank conditions. This is achieved by designing the inputs of the experiment such that the minimum singular value of an input Hankel matrix is sufficiently large, inspiring a quantitative notion of persistency of excitation. We highlight the relevance of the result in a data-driven control case study by comparing the predictive control performance for varying degrees of persistently exciting data.

Compensation-Based Distributed Model-Free Adaptive Control for Cyber-Attacks

In this work, three different types of cyber-attacks are considered together to develop a unified data-driven control method for a nonlinear networked multi-agent system bypassing any modeling processes. To this end, a distributed output is defined for every agent to show its relationship with the adjacent agents. Then, the nonlinear dynamics of the distributed output is transformed into a linear data model by using a dynamic linearization method, which is further used to predict the distributed output of the agent if the unconfined cyber-attack occurs. By introducing a stochastic variable, the compensated distributed output is reformulated to build a relationship between the actually measured one and the virtually predicted one. In the sequence, a compensation-based distribute model-free adaptive control (cDMFAC) is proposed to resist the unconfined cyberattacks. The convergence is proved rigorously in the sense of mathematical expectation. The simulation study further confirms the effectiveness of the proposed cDMFAC method.

Noise Reduction for Data-driven Control by Correlation Analysis and High-order ARX Identification

Noise Reduction for Data-driven Control by Correlation Analysis and High-order ARX Identification

A Modeling and Data-driven Control Framework for Rigid-soft Hybrid Robot with Visual Servoing

A Modeling and Data-driven Control Framework for Rigid-soft Hybrid Robot with Visual Servoing

Robust Data-Driven Control Barrier Functions for Unknown Continuous Control Affine Systems

In this letter, we introduce robust data-driven control barrier functions (CBF-DDs) to guarantee robust safety of unknown continuous control affine systems despite worst-case realizations of generalization errors from prior data under various continuity assumptions. To achieve this, we leverage non-parametric data-driven approaches for learning guaranteed upper and lower bounds of an unknown function from the data set to formulate/obtain a safe input set for a given state. By incorporating the safe input set into an optimization-based controller, the safety of the system can be ensured. Moreover, we present several complexity reduction approaches including providing subproblems that can be solved in parallel and downsampling strategies to improve computational performance.