Related papers: Neural Lyapunov Control for Discrete-Time Systems
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
Deep neural networks are increasingly used as an effective parameterization of control policies in various learning-based control paradigms. For continuous-time optimal control problems (OCPs), which are central to many decision-making…
This paper is concerned with stability analysis and synthesis for discrete-time linear systems with stochastic dynamics. Equivalence is first proved for three stability notions under some key assumptions on the randomness behind the…
Recently, a number of counter examples have surfaced where Linear Parameter-Varying (LPV) control synthesis applied to achieve asymptotic output tracking and disturbance rejection for a nonlinear system, fails to achieve the desired…
In this paper, we present Lyapunov-based robust and adaptive controllers for the finite time stabilization of a perturbed chain of integrators with bounded uncertainties. The proposed controllers can be designed for integrator chains of any…
Learned models and policies can generalize effectively when evaluated within the distribution of the training data, but can produce unpredictable and erroneous outputs on out-of-distribution inputs. In order to avoid distribution shift when…
In this paper, we propose a novel nonlinear observer based on neural networks, called neural observer, for observation tasks of linear time-invariant (LTI) systems and uncertain nonlinear systems. In particular, the neural observer designed…
In a recent paper we have shown how to learn controllers for unknown linear systems using finite-sized noisy data by solving linear matrix inequalities. In this note we extend this approach to deal with unknown nonlinear polynomial systems…
In this work, we study finite-time stability of switched and hybrid systems in the presence of unstable modes. We present sufficient conditions in terms of multiple Lyapunov functions for the origin of the system to be finite time stable.…
This paper presents new results that allow one to address the discrete-time general nonlinear robust control problem. The uncertain system is described by a general nonlinear function set characterized by the nominal model and the…
Most of nonlinear robust control methods just consider the affine nonlinear nominal model. When the nominal model is assumed to be affine nonlinear, available information about existing non-affine nonlinearities is ignored. For non-affine…
We study asymptotic stability of continuous-time systems with mode-dependent guaranteed dwell time. These systems are reformulated as special cases of a general class of mixed (discrete-continuous) linear switching systems on graphs, in…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
This paper investigates the robust stabilisation of a class of fractional-order non-linear systems via fixed-order dynamic output feedback controller in terms of linear matrix inequalities (LMIs). The systematic stabilisation algorithm…
This paper introduces a novel approach to evaluating the asymptotic stability of equilibrium points in both continuous-time (CT) and discrete-time (DT) nonlinear autonomous systems. By utilizing indirect Lyapunov methods and linearizing…
In this paper quotients of control systems which are generalizations of system reductions are used to study the stabilizability property of non-linear systems. Given a control system and its quotient we study under what conditions…
Control Lyapunov functions are traditionally used to design a controller which ensures convergence to a desired state, yet deriving these functions for nonlinear systems remains a complex challenge. This paper presents a novel,…
We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…
In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an…
The feedback linearization method is further developed for the controller design on general nonlinear systems. Through the Lyapunov stability theory, the intractable nonlinear implicit algebraic control equations are effectively solved, and…