Related papers: Continuous Abstraction of Nonlinear Systems using …
In this paper, we investigate the problem of unified prescribed performance tracking for a class of non-square strict-feedback nonlinear systems under relaxed controllability conditions. By using a skillful matrix decomposition and…
Approximate simulation, an extension of simulation relations from formal methods to continuous systems, is a powerful tool for hierarchical control of complex systems. Finding an approximate simulation relation between the full "concrete"…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
This paper studies formal synthesis of controllers for continuous-space systems with unknown dynamics to satisfy requirements expressed as linear temporal logic formulas. Formal abstraction-based synthesis schemes rely on a precise…
General purpose correct-by-construction synthesis methods are limited to systems with low dimensionality or simple specifications. In this work we consider highly symmetrical counting problems and exploit the symmetry to synthesize provably…
This paper presents a general framework for the design of linear controllers for linear systems subject to time-domain constraints. The design framework exploits sums-of-squares techniques to incorporate the time-domain constraints on…
The design of embedded control systems is mainly done with model-based tools such as Matlab/Simulink. Numerical simulation is the central technique of development and verification of such tools. Floating-point arithmetic, that is well-known…
The paper presents a nonlinear state-feedback control design approach for long-time average cost control, where the control effort is assumed to be expensive. The approach is based on sum-of-squares and semi-definite programming techniques.…
This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS)…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
We present a lazy version of multi-layered abstraction-based controller synthesis (ABCS) for continuous-time nonlinear dynamical systems against safety specifications. State-of-the-art multi-layered ABCS uses pre-computed finite-state…
A key question that arises in rigorous analysis of cyberphysical systems under attack involves establishing whether or not the attacked system deviates significantly from the ideal allowed behavior. This is the problem of deciding whether…
Safety is critical in robotic tasks. Energy function based methods have been introduced to address the problem. To ensure safety in the presence of control limits, we need to design an energy function that results in persistently feasible…
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be…
In this paper, we introduce a compositional method for the construction of finite abstractions of interconnected discrete-time switched systems. Particularly, we use a notion of so-called alternating simulation function as a relation…
Sum-of-squares (SOS) optimization provides a computationally tractable framework for certifying polynomial nonnegativity. If the considered problem is convex, the SOS problem can be transcribed into and solved by semi-definite programs.…
Verification of numerical accuracy properties in modern software remains an important and challenging task. This paper describes an original framework combining different solutions for numerical accuracy. First, we extend an existing…
This paper presents a control synthesis algorithm for dynamical systems to satisfy specifications given in a fragment of linear temporal logic. It is based on an abstraction-refinement scheme with nonuniform partitions of the state space. A…
In this paper, we propose a novel controller design approach for unknown nonlinear systems using the Koopman operator. In particular, we use the recently proposed stability- and feedback-oriented extended dynamic mode decomposition…
Abstraction is a commonly used process to represent some low-level system by a more coarse specification with the goal to omit unnecessary details while preserving important aspects. While recent work on abstraction in the situation…