Daniele Astolfi, Lorenzo Marconi
In this note we deal with a new observer for nonlinear systems of dimension n in canonical observability form. We follow the standard high-gain paradigm, but instead of having an observer of dimension n with a gain that grows up to power n, we design an observer of dimension 2n-2 with a gain that grows up only to power 2.
Zirui Niu, Daniele Astolfi, Giordano Scarciotti
Motivated by the prevalence of non-smooth, possibly non-periodic signals in real-world applications, the output regulation of linear systems subject to non-smooth non-periodic exogenous signals has emerged as a challenging problem. A fundamental prerequisite for solving this problem is the existence of solutions to the so-called ``quasi-regulator equations''. In this paper, we investigate the solvability of these equations. To this end, we reformulate the quasi-regulator equations as differential-algebraic equations and highlight the critical role played by the system's relative degree. We finally propose a ``non-smooth non-resonance condition'' that, under specific relative degree requirements, provides a necessary and sufficient characterization of the solvability of the quasi-regulator equations.
Tao Chen, Andreu Cecilia, Lei Wang et al.
Replay attacks comprise replaying previously recorded sensor measurements and injecting malicious signals into a physical plant, causing great damage to cyber-physical systems. Replay attack detection has been widely studied for linear systems, whereas limited research has been reported for nonlinear cases. In this paper, the replay attack is studied in the context of a nonlinear plant controlled by an observer-based output feedback controller. We first analyze replay attack detection using an innovation-based detector and reveal that this detector alone may fail to detect such attacks. Consequently, we turn to a watermark-based design framework to improve the detection. In the proposed framework, the effects of the watermark on attack detection and closed-loop system performance loss are quantified by two indices, which exploit the incremental gains of nonlinear systems. To balance the detection performance and control system performance loss, an explicit optimization problem is formulated. Moreover, to achieve a better balance, we generalize the proposed watermark design framework to co-design the watermark, controller and observer. Numerical simulations are presented to validate the proposed frameworks.
Simone Pirrera, Francesco Ripa, Daniele Astolfi et al.
This paper studies the flows of continuous-time dynamics for equality-constrained optimization based on control-theoretic Lagrangian methods. In particular, we consider dynamics induced by proportional-integral and feedback linearization controllers, which have been recently proposed as alternatives to primal-dual gradient methods. Unlike existing convergence results, which rely on strong convexity of the objective function or boundedness assumptions, we exploit the geometric structure induced by the constraints. Specifically, we show global exponential convergence for non-convex problems that satisfy a suitable convexity property when restricted to the constraint manifold.
Clara Lucía Galimberti, Johan Peralez, Daniele Astolfi et al.
The Kazantzis-Kravaris-Luenberger (KKL) observer provides a general framework for nonlinear state estimation by immersing the system dynamics into a stable linear or nonlinear latent dynamics. However, the performance of KKL observers relies heavily on the specific choice of these latent dynamics, which is often heuristic. This paper proposes a methodology to learn a KKL observer that combines global stability guarantees with local optimality. We derive a condition on the latent dynamics such that the observer locally mimics the behavior of a Minimum Energy Estimator (Mortensen observer). We then employ Deep Learning to approximate the KKL transformation and the latent dynamics, using neural network architectures that structurally enforce the contraction property. The proposed strategy is validated through numerical simulations on nonlinear benchmarks, demonstrating a good performance in the presence of state and measurement noise.
Daniele Astolfi, Laurent Praly
We address a particular problem of output regulation for multi-input multi-output nonlinear systems. Specifically, we are interested in making the stability of an equilibrium point and the regulation to zero of an output, robust to (small) unmodelled discrepancies between design model and actual system in particular those introducing an offset. We propose a novel procedure which is intended to be relevant to real life systems, as illustrated by a (non academic) example.