In this paper the problem of time-varying parameter identification is studied. To this aim, two identification algorithms are developed in order to identify time-varying parameters in a finite-time or prescribed time (fixed-time). The convergence proofs are based on a notion of finite-time stability over finite intervals of time, i.e. Short-finite-time stability; homogeneity for time-varying systems; and Lyapunov-based approach. The results are obtained under injectivity of the regressor term, which is related to the classical identifiability condition. The case of bounded disturbances (noise of measurements) is analyzed for both algorithms. Simulation results illustrate the feasibility of the proposed algorithms.

The increase in system complexity paired with a growing availability of operational data has motivated a change in the traditional control design paradigm. Instead of modeling the system by first principles and then proceeding with a (model-based) control design, the data-driven control paradigm proposes to directly characterize the controller from data. By exploiting a fundamental result of Willems and collaborators, this approach has been successfully applied to linear systems, yielding data-based formulas for many classical linear controllers. In the present paper, the data-driven approach is extended to a class of nonlinear systems, namely second-order discrete Volterra systems. Two main contributions are made for this class of systems. At first, we show that -under a necessary and sufficient condition on the input data excitation -a databased system representation can be derived from input-output data and used to replace an explicit system model. That is, the fundamental result of Willems et al. is extended to this class of systems. Subsequently a data-driven internal model control formula for output-tracking is derived. The approach is illustrated via two simulation examples.

In this work, an observer for a linear time-varying system with delayed measurements is developed. The delay is assumed to be unknown, bounded, and it can be time-varying with no restriction on its rate of change. The observer uses auxiliary signals related to the constructibility Gramian of the system and it contains nonlinearities that provide a uniform fixed-time convergence to a bounded region in the estimation error coordinates. This means that the convergence time can be bounded by a positive constant which is independent from the initial conditions and the initial time. This property is new for the addressed class of systems. The ultimate bound of the estimation error depends on the maximum difference between the nominal output and the delayed one, and not directly on the delay size or its time derivative. These properties are illustrated in a numerical simulation.

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