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We propose a general variance reduction strategy for diffusion processes. Our approach does not require the knowledge of the measure that is sampled, which may indeed be unknown as for nonequilibrium dynamics in statistical physics. We show…
With the increasing penetration of Inverter-Based Resources (IBRs) and their impact on power system stability and operation, the concept of stability-constrained optimization has drawn significant attention from researchers. In order to…
In this paper, we present Robust Model Predictive Control (MPC) problems with adjustable uncertainty sets. In contrast to standard Robust MPC problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional…
A joint characterisation of the controllability and observability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…
We investigate a class of higher-order nonlinear dispersive equations posed on the circle, subject to additive forcing by a finite-dimensional control. Our main objective is to establish approximate controllability by using the…
In this paper, we consider the problem of computing robust controlled invariants for discrete-time monotone dynamical systems. We consider different classes of monotone systems depending on whether the sets of states, control inputs and…
The diffusion model has shown success in generating high-quality and diverse solutions to trajectory optimization problems. However, diffusion models with neural networks inevitably make prediction errors, which leads to constraint…
We analyze the dynamics of multi-agent collective behavior models and their control theoretical properties. We first derive a large population limit to parabolic diffusive equations. We also show that the non-local transport equations…
With the wide application of diffusion model, the high cost of inference resources has became an important bottleneck for its universal application. Controllable generation, such as ControlNet, is one of the key research directions of…
Often, the unknown diffusivity in diffusive processes is structured by piecewise constant patches. This paper is devoted to efficient methods for the determination of such structured diffusion parameters by exploiting shape calculus. A…
We discuss a class of linear control problems in a Hilbert space setting, which covers diverse systems such as hyperbolic and parabolic equations with boundary control and boundary observation even including memory terms. We introduce…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…
A conditional diffusion model has been developed to analyze intricate conductance fluctuations called universal conductance fluctuations or quantum fingerprints appearing in quantum transport phenomena. The model reconstructs impurity…
For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset Q of the state space with respect to a quasi-stationary measure obtained by endowing the control range with a probability measure.…
Lyapunov functions are popularly used to investigate the stabilization problem of systems of hyperbolic conservation laws with boundary controls. In real life applications often not every boundary value can be observed. In this work, we…
We design observer-based controllers to stabilise abstract linear boundary control systems on Hilbert spaces. Our main results introduce conditions for exponential, strong, and polynomial stability, and establish external well-posedness of…
In this paper we study the global approximate multiplicative controllability for nonlinear degenerate parabolic Cauchy problems. In particular, we consider a one-dimensional semilinear degenerate reaction-diffusion equation in divergence…
The author studies the diffusion problem $u_t=u_{xx},\ 0<x<1,\ t>0; \ u(x,0)=0,$ and $-u_x(0,t)=u_x(1,t)=\phi(t),$ where $\phi(t)$ is a control function that ensures that the total mass $\int_0^1 u(x,t_k)dx$ stays between two predetermined…
Recent work by Mania et al. has proved that certainty equivalent control achieves nearly optimal regret for linear systems with quadratic costs. However, when parameter uncertainty is large, certainty equivalence cannot be relied upon to…
In this work, we propose a robust optimization approach to mitigate the impact of uncertainties in particle precipitation. Our model incorporates partial differential equations, more particular nonlinear and nonlocal population balance…