Related papers: Secondary Controller Design for the Safety of Nonl…
We consider the problem of safety verification and safety-aware controller synthesis for systems with sector bounded nonlinearities. We aim to keep the states of the system within a given safe set under potential actuator and sensor…
Safety is closely related to set invariance for dynamical systems. However, synthesizing a safe invariant set and at the same time synthesizing the associated safe controller still remains challenging. In this note we introduce a simple…
We propose a novel approach to certify closed-loop stability and safety of a constrained polynomial system based on the combination of Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs). For polynomial systems that are…
Stability analysis tools are essential to understanding and controlling any engineering system. Recently sum-of-squares (SOS) based methods have been used to compute Lyapunov based estimates for the region-of-attraction (ROA) of polynomial…
Neural network controllers have the potential to improve the performance of feedback systems compared to traditional controllers, due to their ability to act as general function approximators. However, quantifying their safety and…
Recently sum-of-squares (SOS) based methods have been used for the stability analysis and control synthesis of polynomial dynamical systems. This analysis framework was also extended to non-polynomial dynamical systems, including power…
One of the desirable objectives in feedback control design is to formulate and solve the design problem as an optimisation problem that is convex, so that an optimal solution can be found efficiently. Unfortunately many control design…
Recent advances in learning techniques have enabled the modelling of unknown dynamical systems directly from data. However, in many contexts, these learning-based methods are short of safety guarantee and strict stability verification. To…
We present a method for synthesizing dynamic, reduced-order output-feedback polynomial control policies for control-affine nonlinear systems which guarantees runtime stability to a goal state, when using visual observations and a learned…
Sum of Squares programming has been used extensively over the past decade for the stability analysis of nonlinear systems but several questions remain unanswered. In this paper, we show that exponential stability of a polynomial vector…
In this paper, we present a computational approach to certify almost sure reachability for discrete-time polynomial stochastic systems by turning drift--variant criteria into sum-of-squares (SOS) programs solved with standard semidefinite…
This work estimates safe invariant subsets of the Region of Attraction (ROA) for a seven-state vehicle-with-driver system, capturing both asymptotic stability and the influence of state-safety bounds along the system trajectory. Safe sets…
For the class of nonlinear input-affine systems with polynomial dynamics, we consider the problem of designing an input-to-state stabilizing controller with respect to typical exogenous signals in a feedback control system, such as actuator…
The dynamics of many systems from physics, economics, chemistry, and biology can be modelled through polynomial functions. In this paper, we provide a computational means to find positively invariant sets of polynomial dynamical systems by…
This work presents a computationally efficient approach to data-driven robust contracting controller synthesis for polynomial control-affine systems based on a sum-of-squares program. In particular, we consider the case in which a system…
Sum-of-squares (SOS) methods have been shown to be very useful in computing polynomial Lyapunov functions for systems of reasonably small size. However for large scale systems it is necessary to use a scalable alternative using vector…
Control systems often need to satisfy strict safety requirements. Safety index provides a handy way to evaluate the safety level of the system and derive the resulting safe control policies. However, designing safety index functions under…
This paper presents an approach to systematically design sliding mode control and manifold to stabilize nonlinear uncertain systems. The objective is also accomplished to enlarge the inner bound of region of attraction for closed-loop…
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…
We present a control design procedure for nonlinear control systems in which we represent a potentially high dimensional system with a low dimensional continuous-state abstraction. The abstraction generates a reference which the original…