Lyapunov’s indirect methodLyapunovindirect method is one of the oldest and most popular approaches to model-based controller design for nonlinear systemsNonlinearsystem. When the explicit model of the nonlinear systemNonlinearsystem is unavailable for designing such a linear controller, finite-length off-line data is used to obtain a data-based representation of the closed-loop system, and a data-driven linear control law is designed to render the considered equilibrium locally asymptotically stable. This work presents a systematic approach for data-driven linear stabilizer design for continuous-time and discrete-time general nonlinear systemsNonlinearsystem. Moreover, under mild conditions on the nonlinear dynamics, we show that the region of attractionRegion of attraction of the resulting locally asymptotically stable closed-loop system can be estimated using data.

In this paper, we analyze the regret incurred by a computationally efficient exploration strategy, known as naive exploration, for controlling unknown partially observable systems within the Linear Quadratic Gaussian (LQG) framework. We introduce a two-phase control algorithm called LQG-NAIVE, which involves an initial phase of injecting Gaussian input signals to obtain a system model, followed by a second phase of an interplay between naive exploration and control in an episodic fashion. We show that LQG-NAIVE achieves a regret growth rate of Õ(√T), i.e., O(√T) up to logarithmic factors after T time steps, and we validate its performance through numerical simulations. Additionally, we propose LQG-IF2E, which extends the exploration signal to a 'closed-loop' setting by incorporating the Fisher Information Matrix (FIM). We provide compelling numerical evidence of the competitive performance of LQG-IF2E compared to LQG-NAIVE.

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 technique to design controllers for nonlinear systems from data consists of letting the controllers learn the nonlinearities, cancel them out and stabilize the closed-loop dynamics. When control and nonlinearities are unmatched, the technique leads to an approximate cancellation and local stability results are obtained. In this paper, we show that, if the system has some structure that the designer can exploit, an iterative use of the data leads to a globally stabilizing controller even when control and nonlinearities are unmatched.