Related papers: Backstepping Mean-Field Density Control for Large-…
Stability is arguably one of the core concepts upon which our understanding of dynamical and control systems has been built. The related notion of incremental stability, however, has received much less attention until recently, when it was…
This work studies distributed (probability) density estimation of large-scale systems. Such problems are motivated by many density-based distributed control tasks in which the real-time density of the swarm is used as feedback information,…
A PDE-based control concept is developed to deploy a multi-agent system into desired formation profiles. The dynamic model is based on a coupled linear, time-variant parabolic distributed parameter system. By means of a particular coupling…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…
The stabilization of unstable nonlinear systems and tracking control are challenging engineering problems due to the encompassed nonlinearities in dynamic systems and their scale. In the past decades, numerous observer-based control designs…
Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting exponential (AdEx) and quartic integrate and fire (QIF), among others. Unfortunately, the…
Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…
Incremental stability of dynamical systems ensures the convergence of trajectories from different initial conditions towards each other rather than a fixed trajectory or equilibrium point. Here, we introduce and characterize a novel class…
To stabilize PDEs, feedback controllers require gain kernel functions, which are themselves governed by PDEs. Furthermore, these gain-kernel PDEs depend on the PDE plants' functional coefficients. The functional coefficients in PDE plants…
In this paper, we propose a deterministic diffusion-based framework for controlling the probability density of nonlinear control-affine systems, with theoretical guarantees for drift-free and linear time-invariant (LTI) dynamics. The…
We consider output-feedback stabilization problems for a class of two-component linear parabolic systems with boundary actuation and measurement. The state-feedback control laws are obtained using backstepping method and require measurement…
In this paper, we study the feedback synthesis problem for steering the joint state density or ensemble subject to multi-input state feedback linearizable dynamics. This problem is of interest to many practical applications including that…
This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…
A control design for error reduction in the tracking control for a class of non-lower triangular nonlinear systems is presented by combining techniques of Variable Power Surface Error Function (VPSEF), backstepping, and dynamic surface…
We propose a fully backward representation of semilinear PDEs with application to stochastic control. Based on this, we develop a fully backward Monte-Carlo scheme allowing to generate the regression grid, backwardly in time, as the value…
Low-frequency oscillations remain a major challenge in bulk power systems with high renewable penetration, long lines, and large loads. Existing damping strategies based on power modulation of high voltage DC (HVDC) or energy storage, are…
In this paper, we introduce a decentralized optimization-based density controller designed to enforce set invariance constraints in multi-robot systems. By designing a decentralized control barrier function, we derived sufficient conditions…
Backward stochastic differential equation (BSDE)-based deep learning methods provide an alternative to Physics-Informed Neural Networks (PINNs) for solving high-dimensional partial differential equations (PDEs), offering potential…
The paper investigates dynamical systems for which the derivative of some positive-definite function along the solutions of this system depends on so-called density function. In turn, such dynamical systems are called density systems. The…
We develop a control design for stabilization of traffic flow in congested regime, based on an Aw-Rascle-Zhang-type (ARZ-type) Partial Differential Equation (PDE) model, for traffic consisting of both ACC-equipped (Adaptive Cruise…