Model-Free Plant Tuning

Given a static plant described by a differentiable input-output function, which is completely unknown, but whose Jacobian takes values in a known polytope in the matrix space, this paper considers the problem of tuning (i.e., driving to a desired value) the output, by suitably choosing the input. It is shown that, if the polytope is robustly nonsingular (or has full rank, in the nonsquare case), then a suitable tuning scheme drives the output to the desired point. The proof exploits a Lyapunov-like function and applies a well-known game-theoretic result, concerning the existence of a saddle point for a min-max zero-sum game. When the plant output is represented in an implicit form, it is shown that the same result can be obtained, resorting to a different Lyapunov-like function. The case in which proper input or output constraints must be enforced during the transient is considered as well. Some application examples are proposed to show the effectiveness of the approach

Model-free cable robot control

This paper proposes a technique to control a cable robot in the total absence of a model and its parameters. The cable robot is actuated by three motors whose data, including exact positions, pulley diameters, and nominal cable length, are unknown. We just assume to have a very rough knowledge of lower and upper bounds for the partial derivatives of the relation between the cable lengths and the end-effector space coordinates. A structured-light sensor measures the end-effector position, and the goal is to drive it to a designated point. An algorithm is proposed with guaranteed convergence based on the so-called model-free plant tuning approach. No learning stage is required. Experimental results are reported

Data-driven computation of invariant sets of discrete time-invariant black-box systems

We consider the problem of computing the maximal invariant set of discrete-time black-box nonlinear systems without analytic dynamical models. Under the assumption that the system is asymptotically stable, the maximal invariant set coincides with the domain of attraction. A data-driven framework relying on the observation of trajectories is proposed to compute almost-invariant sets, which are invariant almost everywhere except a small subset. Based on these observations, scenario optimization problems are formulated and solved. We show that probabilistic invariance guarantees on the almost-invariant sets can be established. To get explicit expressions of such sets, a set identification procedure is designed with a verification step that provides inner and outer approximations in a probabilistic sense. The proposed data-driven framework is illustrated by several numerical examples.Comment: A shorter version with the title "Scenario-based set invariance verification for black-box nonlinear systems" is published in the IEEE Control Systems Letters (L-CSS

Data Driven Stability Analysis of Black-box Switched Linear Systems

Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of observations, one can give probabilistic stability guarantees. The probabilistic nature of these guarantees implies a trade-off between their quality and the desired level of confidence. We provide an explicit way of computing the best stability-like guarantee, as a function of both the number of observations and the required level of confidence. Our proof techniques rely on geometrical analysis, chance-constrained optimization, and stability analysis tools for switched systems, including the joint spectral radius

Free-electron laser spectrum evaluation and automatic optimization

The radiation generated by a seeded free-electron laser (FEL) is characterized by a high temporal coherence, which is close to the Fourier limit in the ideal case. The setup and optimization of a FEL is a non-trivial and challenging operation. This is due to the plethora of highly sensitive machine parameters and to the complex correlations between them. The fine tuning of the FEL process is normally supervised by physicists and is carried out by scanning various parameters with the aim of optimizing the spectrum of the emitted pulses in terms of intensity and line-width. In this article we introduce a novel quantitative method for the evaluation of the FEL spectrum via a quality index. Moreover, we investigate the possibility of optimization of the FEL parameters using this index as the objective function of an automatic procedure. We also present the results of the preliminary tests performed in the FERMI FEL focused on the effectiveness and ability of the automatic procedure to assist in the task of machine tuning and optimization