We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms. We model such algorithms as a network of interacting dynamical systems and derive tests for convergence based on incremental dissipativity and contraction theory. This approach yields a step-by-step analysis pipeline independent of the network structure, with conditions expressed as linear matrix inequalities. In addition, a numerical comparison with traditional analysis methods is presented, in the context of distributed gradient descent.

We consider data-based predictive control based on behavioral systems theory. In the linear setting this means that a system is described as a subspace of trajectories, and predictive control can be formulated using a projection onto the intersection of this behavior and a constraint set. Instead of learning the model, or subspace, we focus on determining this projection from data. Motivated by the use of regularization in data-enabled predictive control (DeePC), we introduce the use of soft projections, which approximate the true projector onto the behavior from noisy data. In the simplest case, these are equivalent to known regularized DeePC schemes, but they exhibit a number of benefits. First, we provide a bound on the approximation error consisting of a bias and a variance term that can be traded-off by the regularization weight. The derived bound is independent of the true system order, highlighting the benefit of soft projections compared to low-dimensional subspace estimates. Moreover, soft projections allow for intuitive generalizations, one of which we show has superior performance on a case study. Finally, we provide update formulas for soft projectors enabling the efficient adaptation of the proposed data-driven control methods in the case of streaming data.

We consider the policy gradient adaptive control (PGAC) framework, which adaptively updates a control policy in real time, by performing data-based gradient descent steps on the linear quadratic regulator cost. This method has empirically shown to react to changing circumstances, such as model parameters, efficiently. To formalize this observation, we design a PGAC method which stabilizes linear switched systems, where both model parameters and switching time are unknown. We use sliding window data for the policy gradient estimate and show that under a dwell time condition and small dynamics variation, the policy can track the switching dynamics and ensure closed-loop stability. We perform simulations to validate our theoretical results.

Static structured control refers to the task of designing a state-feedback controller such that the control gain satisfies a subspace constraint. Structured control has applications in control of communication-inhibited dynamical systems, such as systems in networked environments. This work performs H_2-suboptimal regulation under a common structured state-feedback controller for a class of data-consistent plants. The certification of H_2-performance is attained through a combination of standard H_2 LMIs, convex sufficient conditions for structured control, and a matrix S-lemma for set-membership. The resulting convex optimization problems are linear matrix inequalities whose size scales independently of the number of data samples collected. Data-driven structured H_2-regulation control is demonstrated on example systems.

This paper proposes Select-Data-driven Predictive Control (Select-DPC), a new method for controlling nonlinear systems using output-feedback for which data are available but an explicit model is not. At each timestep, Select-DPC employs only the most relevant data to implicitly linearize the dynamics in "trajectory space". Then, taking user-defined output constraints into account, it makes control decisions using a convex optimization. This optimal control is applied in a receding-horizon manner. As the online data-selection is the core of Select-DPC, we propose and verify both norm-based and manifold-embedding-based selection methods. We evaluate Select-DPC on three benchmark nonlinear system simulators – rocket-landing, a robotic arm and cart-pole inverted pendulum swing-up – comparing them with standard Data-enabled Predictive Control (DeePC) and Time-Windowed DeePC methods, and find that Select-DPC outperforms both methods.

This paper deals with the problem of accurately determining guaranteed suboptimal values of an unknown cost function on the basis of noisy measurements. We consider a set-valued variant to regression where, instead of finding a best estimate of the cost function, we reason over all functions compatible with the measurements and apply robust methods explicitly in terms of the data. Our treatment provides data-based conditions under which closed-form expressions of upper bounds of the unknown function can be obtained, and regularity properties like convexity and Lipschitzness can be established. These results allow us to perform point- and set-wise verification of suboptimality, and tackle the cautious optimization of the unknown function in both one-shot and online scenarios. We showcase the versatility of the proposed methods in two control-relevant problems: data-driven contraction analysis of unknown nonlinear systems and suboptimal regulation with unknown dynamics and cost. Simulations illustrate our results.

This paper considers the stabilization of unknown switched linear systems using data. Instead of a full system model, we have access to a finite number of trajectories of each of the different modes prior to the online operation of the system. On the basis of informative enough measurements, formally characterized in terms of linear matrix inequalities, we design an online switched controller that alternates between a mode detection phase and a stabilization phase. Since the specific currently-active mode is unknown, the controller employs the most recent online measurements to determine it by implementing computationally efficient tests that check compatibility with the set of systems consistent with the pre-collected measurements. The stabilization phase applies the stabilizing feedback gain corresponding to the identified active mode and monitors the evolution of the associated Lyapunov function to detect switches. When a switch is detected, the controller returns to the mode-detection phase. Under average dwell- and activation-time assumptions on the switching signal, we show that the proposed controller guarantees an input-to-state-like stability property of the closed-loop switched system. Various simulations illustrate our results.

We propose data-driven decentralized control algorithms for stabilizing interconnected systems. We first derive a data-driven condition to synthesize a local controller that ensures the dissipativity of the local subsystems. Then, we propose data-driven decentralized stability conditions for the global system based on the dissipativity of each local system. Since both conditions take the form of linear matrix inequalities and are based on dissipativity theory, this yields a unified pipeline, resulting in a data-driven decentralized control algorithm. As a special case, we also consider stabilizing systems interconnected through diffusive coupling and propose a control algorithm. We validate the effectiveness and the scalability of the proposed control algorithms in numerical examples in the context of microgrids.

This paper introduces a notion of data informativity for stabilization tailored to continuous-time signals and systems. We establish results comparable to those known for discrete-time systems with sampled data. We justify that additional assumptions on the properties of the noise signals are needed to understand when sampled versions of continuous-time signals are informative for stabilization, thereby introducing the notions of square Lipschitzness and total bounded variation. This allows us to connect the continuous and discrete domains, yielding sufficient conditions to synthesize a stabilizing controller for the true continuous-time system on the basis of sampled data. Simulations illustrate our results.

We consider the problem of learning time-varying functions in a distributed fashion, where agents collect local information to collaboratively achieve a shared estimate. This task is particularly relevant in control applications, whenever real-time and robust estimation of dynamic cost/reward functions in safety critical settings has to be performed. In this paper, we,adopt a finite-dimensional approximation of a Gaussian Process, corresponding to a Bayesian linear regression in an appropriate feature space, and propose a new algorithm, DistKP, to track the time-varying coefficients via a distributed Kalman filter. The proposed method works for arbitrary kernels and under weaker assumptions on the time-evolution of the function to learn compared to the literature. We validate our results using a simulation example in which a fleet of Unmanned Aerial Vehicles (UAVs) learns a dynamically changing wind field.

Affine systems are ubiquitous in modeling and emerge naturally from the linearization of nonlinear dynamics. Despite their relevance in applications, their identification remains largely ad hoc, relying on centering the data before applying linear identification methods. This heuristic approach assumes constant offset and can introduce bias. We develop a dedicated framework for affine system identification, deriving identifiability conditions and identification methods based on difference equation representations. Unlike the classical two-step approach, our method identifies the data-generating system under conditions verifiable from data and system complexity. For noisy data in the errors-in-variables setting, we recast the problem as a structured low-rank approximation, leveraging existing optimization techniques for efficient computation.

How would you pitch your Ph.D. dissertation in one paragraph?

A promising step from linear towards nonlinear data-driven control is via the design of controllers for linear parameter-varying (LPV) systems, which are linear systems whose parameters are varying along a measurable scheduling signal. However, the interplay between uncertainty arising from corrupted data and the parameter-varying nature of these systems impacts the stability analysis and limits the generalization of well-understood data-driven methods available for linear time-invariant systems. In this work, we decouple this interplay using a recently developed variant of the Fundamental Lemma for LPV systems and the concept of data-informativity, in combination with biquadratic Lyapunov forms. Together, these allow us to develop novel linear matrix inequality conditions for the existence of scheduling-dependent Lyapunov functions, incorporating the intrinsic nonlinearity. Appealingly, these results are stated purely in terms of the collected data and bounds on the noise, and they are computationally favorable to check.

This paper deals with data-driven stability analysis and feedback stabillization of linear input-output systems in autoregressive (AR) form. We assume that noisy input-output data on a finite time-interval have been obtained from some unknown AR system. Data-based tests are then developed to analyse whether the unknown system is stable, or to verify whether a stabilizing dynamic feedback controller exists. If so, stabilizing controllers are computed using the data. In order to do this, we employ the behavioral approach to systems and control, meaning a departure from existing methods in data driven control. Our results heavily rely on a characterization of asymptotic stability of systems in AR form using the notion of quadratic difference form (QDF) as a natural framework for Lyapunov functions of autonomous AR systems. We introduce the concepts of informative data for quadratic stability and quadratic stabilization in the context of input-output AR systems and establish necessary and sufficient conditions for these properties to hold. In addition, this paper will build on results on quadratic matrix inequalties (QMIs) and a matrix version of Yakubovich's S-lemma.

We consider optimization algorithms that are open systems, that is, with external inputs and outputs. Such algorithms arise for instance, when analyzing the effect of noise or disturbance on an algorithm, or when an algorithm is part of control loop without timescale separation. Bridging between monotone operator theory and energy-based modeling, we consider analysis results in the form of incremental dissipativity certificates, yielding tests in the form of linear matrix inequalities. To be precise, we consider robustness in terms of incremental small gain, and composition results for optimization algorithms operating in closed loop.

This paper deals with the problem of finding suboptimal values of an unknown function on the basis of measured data corrupted by bounded noise. As a prior, we assume that the unknown function is parameterized in terms of a number of basis functions. Inspired by the informativity approach, we view the problem as the suboptimization of the worst-case estimate of the function. The paper provides closed form solutions and convexity results for this function, which enables us to solve the problem. After this, an online implementation is investigated, where we iteratively measure the function and perform a suboptimization. This nets a procedure that is safe at each step, and which, under mild assumptions, converges to the true optimizer.

This paper studies several problems related to quadratic matrix inequalities (QMI's), i.e., inequalities in the Loewner order involving quadratic functions of matrix variables. In particular, we provide conditions under which the solution set of a QMI is nonempty, convex, bounded, or has nonempty interior. We also provide a parameterization of the solution set of a given QMI. In addition, we state results regarding the image of such sets under linear maps, which characterize a subset of “structured" solutions to a QMI. Thereafter, we derive matrix versions of the classical S-lemma and Finsler's lemma, that provide conditions under which all solutions to one QMI also satisfy another QMI. The results will be compared to related work in the robust control literature, such as the full block S-procedure and Petersen's lemma, and it is demonstrated how existing results can be obtained from the results of this paper as special cases. Finally, we show how the various results for QMI's can be applied to the problem of data-driven stabilization. This problem involves finding a stabilizing feedback controller for an unknown dynamical system influenced by noise on the basis of a finite set of data. We provide general necessary and sufficient conditions for data-based quadratic stabilization. In addition, we demonstrate how to reduce the computational complexity of data-based stabilization by leveraging the aforementioned results. This involves separating the computation of the Lyapunov function and the controller, and also leads to explicit formulas for data-guided feedback gains.

Roughly speaking, systems and control theory deals with the problem of making a concrete physical system behave according to certain desired specifications. To achieve this desired behavior, the system can be interconnected with a physical device, called a controller. The problem of finding a mathematical description of such a controller is called the control design problem .

This paper proposes a novel online data-driven adaptive control for discrete-time unknown linear time-varying systems. Initialized with an empirical feedback gain, the algorithm periodically updates this gain based on the data collected over a short time window before each update. Meanwhile, the stability of the closed-loop system is analyzed in detail, which shows that under some mild assumptions, the proposed online data-driven adaptive control scheme can guarantee practical global exponential stability. Finally, the proposed algorithm is demonstrated by numerical simulations and its performance is compared with other control algorithms for unknown linear time-varying systems.

This work studies data-driven switched controller design for discrete-time switched linear systems. Instead of having access to the full system dynamics, an initialization phase is performed, during which noiseless measurements of the state and the input are collected for each mode. Under certain conditions on these measurements, we develop a stabilizing switched controller for the switched system. To be precise, the controller switches between identifying the active mode of the system and applying a predetermined stabilizing feedback. We prove that if the system switches according to certain specifications, this controller stabilizes the closed-loop system. Simulations on a network example illustrate our approach.