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Incremental stability is a property of dynamical systems ensuring the uniform asymptotic stability of each trajectory rather than a fixed equilibrium point or trajectory. Here, we introduce a notion of incremental stability for stochastic…
Stability is arguably one of the core concepts upon which our understanding of dynamical and control systems has been built. The related notion of incremental stability, however, has received much less attention until recently, when it was…
Incremental stability of dynamical systems ensures the convergence of trajectories from different initial conditions towards each other rather than a fixed trajectory or equilibrium point. Here, we introduce and characterize a novel class…
Lyapunov stability theory is the bedrock of direct adaptive control. Fundamentally, Lyapunov stability requires constructing a distance-like function which must decrease with time to ensure stability. Feedback linearization, backstepping,…
This work has the goal of briefly surveying some key stabilization techniques for general nonlinear systems, for which, as it is well known, a smooth control Lyapunov function may fail to exist. A general overview of the situation with…
Learning controllers merely based on a performance metric has been proven effective in many physical and non-physical tasks in both control theory and reinforcement learning. However, in practice, the controller must guarantee some notion…
A dynamic backstepping method is proposed to design controllers for nonlinear systems in the pure-feedback form, for which the traditional backstepping method suffers from solving the implicit nonlinear algebraic equation. The idea of this…
In this paper, we report several new geometric and Lyapunov characterizations of incrementally stable systems on Finsler and Riemannian manifolds. A new and intrinsic proof of an important theorem in contraction analysis is given via the…
Incremental stability is a property of dynamical systems that ensures the convergence of trajectories with respect to each other rather than a fixed equilibrium point or a fixed trajectory. In this paper, we introduce a related stability…
Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results…
In this work, we propose the design and analysis of a novel continuous robust controller for a class of multi--input multi--output (MIMO) nonlinear uncertain systems. The systems under consideration contains unstructured uncertainties in…
In this paper, we provide for the first time an automated, correct-by-construction, controller synthesis scheme for a class of infinite dimensional stochastic systems, namely, retarded jump-diffusion systems. First, we construct finite…
In the article$^a$, the authors introduced a time-varying Lyapunov function for the stability analysis of nonlinear systems whose motion is governed by standard Newton-Euler equations. The authors established asymptotic stability with the…
This paper develops an adaptive tracking controller for a class of nonlinear systems with parametric uncertainty subject to state constraints. The system is characterized by a strict-feedback structure with unknown parameters entering both…
Incremental input-to-state stability (delta-ISS) offers a robust framework to ensure that small input variations result in proportionally minor deviations in the state of a nonlinear system. This property is essential in practical…
This paper presents a constraint-lifting control framework for designing stabilizing controllers that guarantee the forward invariance of a prescribed safe set. State-of-the-art safety-enforcing methods, such as control barrier functions…
In this paper, an asymptotic stability proof for a class of methods for inexact nonlinear model predictive control is presented. General Q-linearly convergent online optimization methods are considered and an asymptotic stability result is…
Stability and safety are two important aspects in safety-critical control of dynamical systems. It has been a well established fact in control theory that stability properties can be characterized by Lyapunov functions. Reachability…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
Control Lyapunov function is a central tool in stabilization. It generalizes an abstract energy function -- a Lyapunov function -- to the case of controlled systems. It is a known fact that most control Lyapunov functions are non-smooth --…