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This paper studies several problems related to quadratic matrix inequalities (QMI's), i.e., inequalities in the Loewner order involving quadratic functions of matrix variables. In particular, we provide conditions under which the solution…
We consider the problem of designing a stabilizing and optimal static controller with a pre-specified sparsity pattern. Since this problem is NP-hard in general, it is necessary to resort to approximation approaches. In this paper, we…
Aiming at the difficulty of stability analysis in practical application of existing control methods, a controller strategy based on lyapunov stability theory is proposed to realize stable control for any control method. In order to…
This paper introduces a novel approach to evaluating the asymptotic stability of equilibrium points in both continuous-time (CT) and discrete-time (DT) nonlinear autonomous systems. By utilizing indirect Lyapunov methods and linearizing…
We consider the feedback design for stabilizing a rigid body system by making and breaking multiple contacts with the environment without prespecifying the timing or the number of occurrence of the contacts. We model such a system as a…
In this paper, we design nonlinear state feedback controllers for discrete-time polynomial dynamical systems via the occupation measure approach. We propose the discrete-time controlled Liouville equation, and use it to formulate the…
We initiate a formal study on the use of low-dimensional latent representations of dynamical systems for verifiable control synthesis. Our main goal is to enable the application of verification techniques -- such as Lyapunov or barrier…
This work provides a framework for data-driven control of discrete time systems with unknown input-output dynamics and outputs controllable by the inputs. This framework leads to stable and robust real-time control of the system such that a…
This paper addresses the robust stability of a boundary controlled system coupling two partial differential equations (PDEs), namely beam and string equations, in the presence of boundary and in-domain disturbances under the framework of…
Modern control systems must operate in increasingly complex environments subject to safety constraints and input limits, and are often implemented in a hierarchical fashion with different controllers running at multiple time scales. Yet…
We consider the data-driven stabilization of discrete-time linear time-varying systems. The controller is defined as a linear state-feedback law whose gain is adapted to the plant changes through a data-based event-triggering rule. To do…
While stability analysis is a mainstay for control science, especially computing regions of attraction of equilibrium points, until recently most stability analysis tools always required explicit knowledge of the model or a high-fidelity…
While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stability regions remain challenging due to the curse of…
Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…
We propose new methods for learning control policies and neural network Lyapunov functions for nonlinear control problems, with provable guarantee of stability. The framework consists of a learner that attempts to find the control and…
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…
In this paper the existence of a quadratic control Lyapunov function for bilinear systems is considered. The existence of a control Lyapunov function ensures the existence of a control law which ensures the global asymptotic stability of…
This paper deals with the finite-time stabilization of a class of nonlinear infinite-dimensional systems. First, we consider a bounded matched perturbation in its linear form. It is shown that by using a set-valued function, both the…
This paper proposes a control design approach for stabilizing nonlinear control systems. Our key observation is that the set of points where the decrease condition of a control Lyapunov function (CLF) is feasible can be regarded as a safe…
This paper addresses three complex control challenges related to input-saturated systems from a data-driven perspective. Unlike the traditional two-stage process involving system identification and model-based control, the proposed approach…