相关论文: Sum-of-Squares Stability Verification on Manifolds…
In this paper, we present a novel approach to determine the stability of switched linear and nonlinear systems using Sum of Squares optimisation. Particularly, we use Sum of Squares optimisation to search for a Lyapunov function that…
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…
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…
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…
Reliable quasi-static object manuipulation and robotic locomotion require verification of the stability of equilibria under rigid contacts and friction. In a recent paper, M. Posa, M. Tobenkin, and R. Tedrake demonstrated that…
This note is concerned with the stability and stabilization of the linearized spacecraft attitude control system. Necessary and sufficient conditions are respectively provided to guarantee that the considered systems are polynomially stable…
This paper examines the global convergence problem of SLAM algorithms, an issue that faces topological obstructions. This is because the state-space of attitude dynamics is defined on a non-contractible manifold: the special orthogonal…
We present a new data-driven method to provide probabilistic stability guarantees for black-box switched linear systems. By sampling a finite number of observations of trajectories, we construct approximate Lyapunov functions and deduce the…
The spacecraft attitude tracking problem is addressed with actuator faults and uncertainties among inertias, external disturbances, and, in particular, state estimates. A continuous sliding mode attitude controller is designed using…
Managing uncertainty is a fundamental and critical issue in spacecraft entry guidance. This paper presents a novel approach for uncertainty propagation during entry, descent and landing that relies on a new sum-of-squares robust…
This paper studies formation control of an arbitrary number of spacecraft based on a serial network structure. The leader controls its absolute position and absolute attitude with respect to an inertial frame, and the followers control its…
The natural trajectory tracking problem is studied for generic quantum states represented by density operators. A control design based on the Hilbert-Schmidt distance as a Lyapunov function is considered. The control dynamics is redefined…
We consider the problem of global stability of nonlinear sampled-data systems. Sampled-data systems are a form of hybrid model which arises when discrete measurements and updates are used to control continuous-time plants. In this paper, we…
The general objective of this Ph.D. thesis is to study the dynamics and control of rigid and flexible spacecraft supported by a high-fidelity numerical simulation environment. The demand for greater attitude pointing precision, attitude…
In this work feedback control laws are designed for achieving three-axis attitude stabilization of inertial pointing spacecraft using only magnetic torquers. The designs are based on an almost periodic model of geomagnetic field along the…
This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to search for a partially quadratic Lyapunov Function (LF). The…
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 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…
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…
We provide a computer-assisted approach to ensure that a given continuous or discrete-time polynomial system is (asymptotically) stable. Our framework relies on constructive analysis together with formally certified sums of squares Lyapunov…