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A Discrete-Time Linear Complementarity System (DLCS) is a dynamical system in discrete time whose state evolution is governed by linear dynamics in states and algebraic variables that solve a Linear Complementarity Problem (LCP). The DLCS…

The Lyapunov inequality is an indispensable tool for stability analysis in linear control theory. It provides a necessary and sufficient condition for the stability of an autonomous linear-time invariant system in terms of the existence of…

This article presents a novel numerically tractable technique for synthesizing Lyapunov functions for equilibria of nonlinear vector fields. In broad strokes, corresponding to an isolated equilibrium point of a given vector field, a…

Pointwise minimum norm control laws for hybrid dynamical systems are proposed. Hybrid systems are given by differential equations capturing the continuous dynamics or flows, and by difference equations capturing the discrete dynamics or…

Convex functionals are ubiquitous in applied analysis, appearing as value functions, risk measures, super-hedging prices, and loss functionals in machine learning. In many applications, however, the functional is only observed through…

Despite advances in learning-based methods, finding valid Lyapunov functions for nonlinear dynamical systems remains challenging. Current neural network approaches face two main issues: challenges in scalable verification and limited…

Reinforcement learning (RL) in the context of control systems offers wide possibilities of controller adaptation. Given an infinite-horizon cost function, the so-called critic of RL approximates it with a neural net and sends this…

Safety-critical control of piecewise affine (PWA) systems under bounded additive disturbances requires guarantees not for individual states but for entire state sets simultaneously: a single control action must steer every state in the set…

Designing stabilizing controllers is a fundamental challenge in autonomous systems, particularly for high-dimensional, nonlinear systems that can hardly be accurately modeled with differential equations. The Lyapunov theory offers a…

This paper proposes the construction of a coercive ISS-Lyapunov functional for linear regular infinite-dimensional system. Indeed, as already known, Lyapunov functionals for infinite-dimensional systems might be not coercive. Under the…

In this paper, we define and analyze a subclass of (time-invariant) Control Barrier Functions (CBF) that have favorable properties for the construction of uniformly timevarying CBFs and thereby for the satisfaction of uniformly time-varying…

This paper studies data-driven stabilization of a class of unknown polynomial systems using data corrupted by bounded noise. Existing work addressing this problem has focused on designing a controller and a Lyapunov function so that a…

We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear…

Controlling infinite dimensional models remains a challenging task for many practitioners since they are not suitable for traditional control design techniques or will result in a high-order controller too complex for implementation.…

We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are…

This paper addresses the problem of control synthesis for nonlinear optimal control problems in the presence of state and input constraints. The presented approach relies upon transforming the given problem into an infinite-dimensional…

In this paper, we propose a model reduction technique for linear parameter varying (LPV) systems based on available tools for fixed-structure controller synthesis. We start by transforming a model reduction problem into an equivalent…

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 Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are popular tools for enforcing safety and stability of a controlled system, respectively. They are commonly utilized to build constraints that can be incorporated in a…

The vector field of a mixed-monotone system is decomposable via a decomposition function into increasing (cooperative) and decreasing (competitive) components, and this decomposition allows for, e.g., efficient computation of reachable sets…