Related papers: Fixed Point Theory Analysis of a Lambda Policy Ite…

This paper discusses generalized weak rigidity theory, and aims to apply the theory to formation control problems with a gradient flow law. The generalized weak rigidity theory is utilized in order that desired formations are characterized…

We propose an approach to design a Model Predictive Controller (MPC) for constrained Linear Time Invariant systems performing an iterative task. The system is subject to an additive disturbance, and the goal is to learn to satisfy state and…

In this paper, we revisit the computation of controlled invariant sets for linear discrete-time systems through a trajectory-based viewpoint. We begin by introducing the notion of convex feasible points, which provides a new…

We are motivated by the real challenges presented in a human-robot system to develop new designs that are efficient at data level and with performance guarantees such as stability and optimality at systems level. Existing…

Fixed-frequency control in robotics imposes a trade-off between the efficiency of low-frequency control and the robustness of high-frequency control, a limitation not seen in adaptable biological systems. We address this with a…

This paper establishes novel fixed point theorems for Kannan-type and Chatterjea-type mappings in probabilistic cone metric spaces. By integrating probabilistic distance functions with cone-valued structures, we generalize classical fixed…

A reinforcement learning (RL) control policy could fail in a new/perturbed environment that is different from the training environment, due to the presence of dynamic variations. For controlling systems with continuous state and action…

This paper introduces a formal notion of fixed point explanations, inspired by the "why regress" principle, to assess, through recursive applications, the stability of the interplay between a model and its explainer. Fixed point…

The naive application of Reinforcement Learning algorithms to continuous control problems -- such as locomotion and manipulation -- often results in policies which rely on high-amplitude, high-frequency control signals, known colloquially…

The Primal-Dual (PD) algorithm is widely used in convex optimization to determine saddle points. While the stability of the PD algorithm can be easily guaranteed, strict contraction is nontrivial to establish in most cases. This work…

We study weak and strong solutions of nonlinear non-compact operator equations in abstract spaces of adapted random points. The main result of the paper is similar to Schauder's fixed-point theorem for compact operators. The illustrative…

We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using…

This paper studies the control synthesis of motion planning subject to uncertainties. The uncertainties are considered in robot motions and environment properties, giving rise to the probabilistic labeled Markov decision process (PL-MDP). A…

Policy iteration is one of the classical frameworks of reinforcement learning, which requires a known initial stabilizing control. However, finding the initial stabilizing control depends on the known system model. To relax this requirement…

In this paper I introduce the property CD which is a more convenient variant of the UC property and show one of the possible relationships between them, I also extend the concept of a fixed point, introducing the concept of a weak fixation…

Fixpoints are ubiquitous in computer science and when dealing with quantitative semantics and verification one often considers least fixpoints of (higher-dimensional) functions over the non-negative reals. We show how to approximate the…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

In this paper, inspired by the concept of generalized weakly contractive mappings in metric spaces, we introduce C-Class function and fixed point theory for weakly contractive in the setting of rectangular $b$-metric spaces and established…

Recent empirical studies have identified fixed point iteration phenomena in deep neural networks, where the hidden state tends to stabilize after several layers, showing minimal change in subsequent layers. This observation has spurred the…

Deep Reinforcement Learning (Deep RL) has had incredible achievements on high dimensional problems, yet its learning process remains unstable even on the simplest tasks. Deep RL uses neural networks as function approximators. These neural…