Related papers: Locally optimal controllers and globally inverse o…
This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
Safety and stability are common requirements for robotic control systems; however, designing safe, stable controllers remains difficult for nonlinear and uncertain models. We develop a model-based learning approach to synthesize robust…
This paper investigates the robust stabilisation of a class of fractional-order non-linear systems via fixed-order dynamic output feedback controller in terms of linear matrix inequalities (LMIs). The systematic stabilisation algorithm…
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…
In this paper quotients of control systems which are generalizations of system reductions are used to study the stabilizability property of non-linear systems. Given a control system and its quotient we study under what conditions…
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…
In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and…
Optimization plays a central role in intelligent systems and cyber-physical technologies, where speed and reliability of convergence directly impact performance. In control theory, optimization-centric methods are standard: controllers are…
We propose a novel flexible-step model predictive control algorithm for unknown linear time-invariant discrete-time systems. The goal is to asymptotically stabilize the system without relying on a pre-collected dataset that describes its…
This paper studies the problem of constructing control Lyapunov functions (CLFs) and feedback stabilization strategies for deterministic nonlinear control systems described by ordinary differential equations. Many numerical methods for…
Finding a control Lyapunov function (CLF) in a dynamical system with a controller is an effective way to guarantee stability, which is a crucial issue in safety-concerned applications. Recently, deep learning models representing CLFs have…
This paper is concerned with establishing global asymptotic stability results for a class of non-linear PDE which have some similarity to the PDE of the Lifschitz-Slyozov-Wagner model. The method of proof does not involve a Lyapounov…
Learning from expert demonstrations to flexibly program an autonomous system with complex behaviors or to predict an agent's behavior is a powerful tool, especially in collaborative control settings. A common method to solve this problem is…
Quantum Lyapunov control was developed in order to transform a quantum system from arbitrary initial states to a target state. The idea is to find control fields that steer the Lyapunov function to zero as $t\rightarrow \infty$, meanwhile…
Deep learning methods have demonstrated significant potential for addressing complex nonlinear control problems. For real-world safety-critical tasks, however, it is crucial to provide formal stability guarantees for the designed…
Quadratic-bilinear (QB) systems arise in many areas of science and engineering. In this paper, we present a scalable approach for designing locally stabilizing state-feedback control laws and certifying the local stability of QB systems.…
We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some…
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…
In this paper, we solve the long-standing fundamental problem of irregular linear--quadratic (LQ) optimal control, which has received significant attention since the 1960s. We derive the optimal controllers via the key technique of finding…