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This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…
Learning stable dynamical systems from data is crucial for safe and reliable robot motion planning and control. However, extending stability guarantees to trajectories defined on Riemannian manifolds poses significant challenges due to the…
This work studies robustness to system disturbance and measurement noise of some popular general practical stabilization techniques, namely, Dini aiming, optimization-based stabilization and inf-convolution stabilization. Common to all…
A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an ellipsoidal inner-approximation to the region of attraction…
Learning stable dynamics from observed time-series data is an essential problem in robotics, physical modeling, and systems biology. Many of these dynamics are represented as an inputs-output system to communicate with the external…
A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…
We consider nonlinear stochastic systems that arise in path planning and control of mobile robots. As is typical of almost all nonlinear stochastic systems, the optimally solving problem is intractable. We provide a design approach which…
This paper addresses the safe stabilization problem of stochastic nonlinear time-delay systems. Based on theKrasovskii approach, we first propose a stochastic control Lyapunov-Krasovskii functional to guarantee the stabilization objective…
This paper focuses on the problem of constructing time-varying feedback laws that asymptotically stabilize a given part of the state variables for nonlinear control-affine systems. It is assumed that the class of systems under consideration…
In this paper, a stochastic asymptotic stabilization method is proposed for deterministic input-affine control systems, which are randomized by including Gaussian white noises in control inputs. The sufficient condition is derived for the…
This paper introduces a framework for learning a minimum-norm stabilizing controller for a system with unknown dynamics using model-free policy optimization methods. The approach begins by first designing a Control Lyapunov Function (CLF)…
In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…
This paper studies distributed trajectory tracking for networks of nonholonomic mobile robots under adversarial information exchange. An exact global input--output feedback linearization scheme is developed to regulate planar position…
In this paper, we develop an asymptotic-preserving dynamical low-rank method for the multiscale linear kinetic transport equation. The proposed scheme is unconditionally stable in the diffusive regime while preserving the correct asymptotic…
Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…
This paper addresses the problem of stabilizing a part of variables for control systems described by stochastic differential equations of the Ito type. The considered problem is related to the asymptotic stability property of invariant sets…
This paper presents a framework for stabilizing the Dubins vehicle model to zero in finite time (deadbeat parking) by interpreting distance as a time-like variable. We develop control laws that bring the system to a desired position and…
The robust tracking and model following problem of linear discrete-time systems is investigated in this paper. An approach to design robust tracking controllers is proposed. The system is controlled to track dynamic inputs generated from a…
It is an interesting open problem to achieve adaptive prescribed-time control for strict-feedback systems with unknown and fast or even abrupt time-varying parameters. In this paper we present a solution with the aid of several design and…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…