Behrad Samari

Behrad Samari, Henrik Sandberg, Karl H. Johansson et al.

Model order reduction techniques simplify high-dimensional dynamical systems by deriving lower-dimensional models that retain essential system characteristics. These techniques are crucial for the controller design of complex systems while significantly reducing computational costs. Nevertheless, constructing effective reduced-order models (ROMs) poses considerable challenges, particularly for nonlinear dynamical systems. These challenges are further exacerbated when the actual system model is unavailable, a scenario frequently encountered in real-world applications. In this work, we propose a data-driven framework for constructing ROMs of nonlinear dynamical systems with unknown mathematical models, enabling controller synthesis directly from the resulting ROMs. We establish similarity relations between the output trajectories of the original systems and those of their ROMs by employing the notion of simulation functions (SFs), thereby enabling a formal characterization of their closeness. To achieve this, we collect one set of noise-corrupted input-state data from the system during a finite-time experiment, upon which we propose conditions to construct both ROMs and SFs simultaneously. These conditions are formulated as data-dependent semidefinite programs. We demonstrate that the data-driven ROMs obtained can be employed to synthesize controllers for the original unknown systems, ensuring that they satisfy high-level logic specifications. This is accomplished by first designing controllers for the data-driven ROMs and then translating the results back to the original systems via interface functions, designed directly from the proposed data-dependent conditions. We evaluate the efficacy of our data-driven framework through two case studies, including a challenging benchmark from the model reduction literature: a circuit of chained inverter gates with 20 state variables.

Behrad Samari, Gian Paolo Incremona, Antonella Ferrara et al.

This paper proposes a data-driven approach to designing adaptive suboptimal second-order sliding mode (ASSOSM) controllers for a class of single-input nonlinear systems with partially unknown dynamics, subject to both matched and unmatched disturbances. We first view the system as comprising two coupled dynamics, referred to as the upper and lower dynamics, with the last state serving as a virtual input to the upper dynamics. The proposed control-design methodology then follows a two-stage procedure: (i) designing a virtual state-feedback control law for the upper dynamics and (ii) synthesizing an ASSOSM controller for the full-order system. To this end, we collect noise-corrupted data from the system throughout a finite-time experiment. We then formulate a data-dependent condition, whose feasibility enables the design of a virtual state-feedback control law that renders the closed-loop upper dynamics input-to-state stable with respect to the unmatched disturbance. Building on this virtual state-feedback control law, we subsequently propose a data-driven nonlinear sliding variable, based on which an ASSOSM controller is designed for the full-order system. The state trajectories of the resulting closed-loop system are semiglobally ultimately bounded (S-GUB), with the ultimate bound explicitly depending on the magnitude of the unmatched disturbance. In particular, the control design parameters can be selected for any prescribed bounded set of initial conditions so that the state trajectories of the closed-loop system are S-GUB. Moreover, the effect of the matched disturbance is totally rejected after a finite time. The effectiveness of the proposed method is satisfactorily demonstrated in the simulation.

Behrad Samari, Henrik Sandberg, Karl H. Johansson et al.

This paper develops a direct data-driven framework for constructing reduced-order models (ROMs) of discrete-time linear dynamical systems with unknown dynamics and process disturbances. The proposed scheme enables controller synthesis on the ROM and its refinement to the original system by an interface function designed using noisy data. To achieve this, the notion of simulation functions (SFs) is employed to establish a formal relation between the original system and its ROM, yielding a quantitative bound on the mismatch between their output trajectories. To construct such relations and interface functions, we rely on data collected from the unknown system. In particular, using noise-corrupted input-state data gathered along a single trajectory of the system, and without identifying the original dynamics, we propose data-dependent conditions, cast as a semidefinite program, for the simultaneous construction of ROMs, SFs, and interface functions. Through a case study, we demonstrate that data-driven controller synthesis on the ROM, combined with controller refinement via the interface function, enables the enforcement of complex specifications beyond stability.