Related papers: How Deduction Systems Can Help You To Verify Stabi…
In order to guarantee stability, known results for MPC without additional terminal costs or endpoint constraints often require rather large prediction horizons. Still, stable behavior of closed loop solutions can often be observed even for…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of…
Human posture control models are used to analyse neurological experiments and control of humanoid robots. This work focuses on a well-known nonlinear posture control model, the DEC (Disturbance estimate and Compensation). In order to…
Studying the reliability of complex systems using machine learning techniques involves facing a series of technical and practical challenges, ranging from the intrinsic nature of the system and data to the difficulties in modeling and…
Teaching proofs is a crucial component of any undergraduate-level program that covers formal reasoning. We have developed a calculational reasoning format and refined it over several years of teaching a freshman-level course, "Logic and…
In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs will be studied at three levels: syntactical, semantical and pragmatical. Computer-assisted proofs will be give a special…
Assume-guarantee reasoning is a technique for compositional model checking in which system specifications are checked under certain assumptions on system parameters or inputs, and provide guarantees on observations of system state. We…
In this paper we present tableau proof systems for various justification logics. We show that the tableau systems are sound and complete with respect to Mkrtychev models. In order to prove the completeness of the tableaux, we give a…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
Lyapunov's theorem provides a fundamental characterization of the stability of dynamical systems. This paper presents a categorical framework for Lyapunov theory, generalizing stability analysis with Lyapunov functions categorically. Core…
We present a technique for learning control Lyapunov-like functions, which are used in turn to synthesize controllers for nonlinear dynamical systems that can stabilize the system, or satisfy specifications such as remaining inside a safe…
The material presented in this paper contributes to establishing a basis deemed essential for substantial progress in Automated Deduction. It identifies and studies global features in selected problems and their proofs which offer the…
This article presents novel methods for synthesizing distributionally robust stabilizing neural controllers and certificates for control systems under model uncertainty. A key challenge in designing controllers with stability guarantees for…
For Hilbert, the consistency of a formal theory T is an infinite series of statements "D is free of contradictions" for each derivation D and a consistency proof is i) an operation that, given D, yields a proof that D is free of…
Stability, reachability, and safety are crucial properties of dynamical systems. While verification and control synthesis of reach-avoid-stay objectives can be effectively handled by abstraction-based formal methods, such approaches can be…
Explainability is needed to establish confidence in machine learning results. Some explainable methods take a post hoc approach to explain the weights of machine learning models, others highlight areas of the input contributing to…
In dealing with nonlinear systems, it is common to use numerical solutions. Unlike the careful behavior towards the numerical results in chaotic regions, the validity of numerical results in regions of transient chaos might not always be…
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…
Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been…