Data-Driven Synthesis of Robust Positively Invariant Sets: From State Feedback to Output Feedback

Data-Driven Output Feedback based Analysis and Control for Unknown Discrete-Time Linear System

Using the notion of data informativity, the existing results have given conditions under which the data are informative for controller designs for various control problems of unknown linear discrete-time systems, and have developed methods to compute such controllers from data. Nevertheless, the existing conditions for computing a dynamic output feedback control law based on the input and output data are somehow stringent. In this paper, we first focus on developing data informativity analysis and control for an unknown system with a known input matrix. It turns out that the informativity conditions for such a system are much milder and the methods for computing state feedback control laws for stabilization, deadbeat control, and the linear-quadratic regulator (LQR) for such a system are much more straightforward. Further, based on the parameterized observer, we show that the problem of computing a dynamic output feedback control law for an unknown system can be converted to the problem of designing a state feedback control law for an ancillary system whose input matrix is known. Therefore, the results of the first part of this paper can be directly used to compute a dynamic output feedback control law for stabilization and deadbeat control for unknown linear discrete-time systems based on the input and output data. Moreover, we present a dynamic output feedback control law which will asymptotically approach a state feedback LQR solution to the original unknown system.

Data-Driven Inference of Passivity Properties via Gradient Flows and Finite-Time Stabilization

In this paper, we address the problem of computing passivity indices-quantitative measures of a system's passivity-due to their significance in controller design. In practical scenarios, the explicit input-output relationship of a system is often unavailable, and only input-output data from simulations or experiments can be accessed. We focus on determining the passivity indices of a discrete linear time-invariant system using optimal input-output samples tailored to the specific property being assessed. Here, passivity indices are formulated as an objective function of an optimization problem. To compute these indices, we introduce prescribed-time gradient flows, which has the property of guaranteed convergence, within a prior chosen time. Notably, the proposed method is data-driven and does not require knowledge of the system's mathematical model, as it relies solely on gradients computed from data. Furthermore, we leverage the feedback interconnection properties of passive systems to ensure both asymptotic and finite-time stability of the discrete-time system, using only the computed passivity indices. Specifically, stabilization is achieved by employing input feedforward passive and output feedback passive systems as controllers, again without requiring the explicit model of the system. Simulation results for the coupled tank system shows the effectiveness of the proposed approach.

A subspace approach to data-driven predictive control for linear parameter-varying systems

This paper presents a subspace data-driven predictive control method for linear parameter-varying (LPV) systems. Starting from an affine LPV state-space model in innovation form, we derive a multi-step predictor that separates the effects of past data, future inputs, scheduling trajectories, and innovations. By projecting this representation onto the row span of lifted input-output-scheduling data, we obtain an asymptotically unbiased data-driven predictor that can be embedded directly in a receding-horizon control problem, without explicitly identifying an LPV model. To make the resulting LPV data-driven predictive control (DDPC) formulation tractable, we introduce an LPV extension of $\gamma$-DDPC based on an LQ factorization. This formulation fixes the number of online decision variables independently of the length of the dataset. A reduced-order predictor is then proposed to curb the exponential growth of scheduling-dependent regressors, which also relaxes the persistence-of-excitation condition. Simulation studies, including an unbalanced-disk example, show that the proposed controller achieves good tracking performance and, compared to existing LPV DDPC schemes, achieves better robustness to measurement noise and reduced computational cost, making multi-step LPV DDPC practically deployable, even with longer past horizons.

Learning Input-Constrained Funnel Controllers from State Trajectory Data

Designing feedback controllers that satisfy predefined performance specifications while enforcing hard input constraints is a challenging task. Our work is motivated by the idea that state trajectory data, e.g., obtained from an expert controller, often implicitly encode feasible performance attributes and input limitations. We propose an optimization-based framework that uses state trajectory data to jointly learn: (i) a performance funnel that mimics the transient and steady-state behavior encoded within the observed trajectories, and (ii) a feedback controller that enforces the learned performance specifications under hard input constraints. Unlike imitation learning methods, the proposed approach does not rely on control input data and does not reconstruct an expert policy. Instead, it synthesizes a prescribed performance controller by combining nominal model compensation with a learned state-dependent feedback gain. The resulting synthesis problem is nonconvex, for which we develop a feasibility-driven active-set synthesis procedure. Finally, we establish two complementary guarantees: a semi-global conservative actuator-authority-based certificate for prescribed performance and input satisfaction, and a local data-driven certificate ensuring these properties near sufficiently dense demonstrated trajectories.

Koopman-based model predictive control for nonlinear systems with bounded model uncertainty

Data-Driven Stability and Performance Analysis of Lurye Systems

This paper develops data-driven conditions for certifying internal stability and induced-$\ell_2$ performance of discrete-time Lurye systems. The Lurye system is an interconnection of a nominal LTI system in feedback with a static, memoryless nonlinearity. The nonlinearity satisfies a known set of quadratic constraints on the inputs and outputs. Existing conditions for Lurye systems require a state-space realization of the nominal LTI dynamics. Our first data-driven result instead formulates the stability and performance conditions using finite input, output, and state trajectories of the nominal LTI block. Our second condition removes the need for measured state trajectories by reconstructing the state sequence, up to a similarity transformation, from input/output data. This state reconstruction is performed using deterministic subspace-identification techniques. Both data-driven conditions are expressed as convex semidefinite programs. These conditions, given sufficiently exciting inputs, recover the corresponding model-based Lurye condition in the noiseless setting. The proposed methods are illustrated via a simple example with a sector-bounded nonlinearity. Both proposed methods obtain the same induced-$\ell_2$ gain bound as the model-based approach while using only trajectory data from the nominal system.