Related papers: Using Ellipsoidal Domains to Analyze Control Syste…
This paper presents a method to stabilize state and input constrained nonlinear systems using an offline optimization on variable triangulations of the set of admissible states. For control-affine systems, by choosing a continuous piecewise…
Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…
We propose a new matrix pencil based approach for design of state-feedback and output-feedback stabilizing controllers for a general class of uncertain nonlinear strict-feedback-like systems. While the dynamic controller structure is based…
In this paper, we present a methodology for stability analysis of a general class of systems defined by coupled Partial Differential Equations (PDEs) with spatially dependent coefficients and a general class of boundary conditions. This…
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…
The problem of safely learning and controlling a dynamical system - i.e., of stabilizing an originally (partially) unknown system while ensuring that it does not leave a prescribed 'safe set' - has recently received tremendous attention in…
This technical note is concerned with boundary stabilization of multi-dimensional discrete-velocity kinetic models. By exploiting a certain stability structure of the models and adapting an appropriate Lyapunov functional, we derive…
While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $ N $ variables, as binary neural networks and cellular automata. The main difficulty is the…
Verifying stability and safety guarantees for nonlinear systems has received considerable attention in recent years. This property serves as a fundamental building block for specifying more complex system behaviors and control objectives.…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
Stability analysis plays a crucial role in studying the behavior of dynamical systems with theoretical and engineering applications. Among various kinds of stability, the stability of equilibrium points is of the greatest importance which…
interpretation is a general methodology for building static analyses of programs. It was introduced by P. and R. Cousot in \cite{cc}. We present, in this paper, an application of a generic abstract interpretation to domain of…
In this work, we continue our study on discrete abstractions of dynamical systems. To this end, we use a family of partitioning functions to generate an abstraction. The intersection of sub-level sets of the partitioning functions defines…
At the intersection of dynamical systems, control theory, and formal methods lies the construction of symbolic abstractions: these typically represent simpler, finite-state models whose behavior mimics that of an underlying concrete system…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
Sensor and actuator selection problems (SASP) are some of the core problems in dynamic systems design and control. These problems correspond to determining the optimal selection of sensors (measurements) or actuators (control nodes) such…
A controller synthesis method for state- and input-constrained nonlinear systems is presented that seeks continuous piecewise affine (CPA) Lyapunov-like functions and controllers simultaneously. Non-convex optimization problems are…
Ensuring the safety and efficacy of Cyber-Physical Systems (CPSs) is challenging due to the large variability of their operating environment. Model checking has been proposed for validation of CPSs, but the models of the environment are…
We develop a method to control discrete-time systems with constant but initially unknown parameters from linear temporal logic (LTL) specifications. We introduce the notions of (non-deterministic) parametric and adaptive transition systems…
We introduce a method for learning provably stable deep neural network based dynamic models from observed data. Specifically, we consider discrete-time stochastic dynamic models, as they are of particular interest in practical applications…