Constrained Control of Input Delayed Systems With Partially Compensated Input Delays

Control Barrier Functions (CBFs) have become popular for enforcing — via barrier constraints — the safe operation of nonlinear systems within an admissible set. For systems with input delay(s) of the same length, constrained control has been achieved by combining a CBF for the delay free system with a state predictor that compensates the single input delay. Recently, this approach was extended to multi input systems with input delays of different lengths. One limitation of this extension is that barrier constraint adherence can only be guaranteed after the longest input delay has been compensated and all input channels become available for control. In this paper, we consider the problem of enforcing constraint adherence when only a subset of input delays have been compensated. In particular, we propose a new barrier constraint formulation that ensures that when possible, a subset of input channels with shorter delays will be utilized for keeping the system in the admissible set even before longer input delays have been compensated. We include a numerical example to demonstrate the effectiveness of the proposed approach.

Continuity and monotonicity of solutions to a greedy maximization problem

Motivated by an application to resource sharing network modelling, we consider a problem of greedy maximization (i.e., maximization of the consecutive minima) of a vector in $${\mathbb {R}}^n$$ R n , with the admissible set indexed by the time parameter. The structure of the constraints depends on the underlying network topology. We investigate continuity and monotonicity of the resulting maximizers with respect to time. Our results have important consequences for fluid models of the corresponding networks which are optimal, in the appropriate sense, with respect to handling real-time transmission requests.

Reference Governors Based on Online Learning of Maximal Output Admissible Set

Reference governors are add-on control schemes that modify the reference commands, if it becomes necessary, in order to avoid constraint violations. To implement a reference governor, explicit knowledge of a model of the system and its constraints is typically required. In this paper, a reference governor which does not require an explicit model of the system or constraints is presented. It constructs an approximation of the maximal output admissible set, as the system operates, using online neural network learning. This approximation is used to modify the reference command in order to satisfy the constraints. The potential of the algorithm is demonstrated through simulations for an electric vehicle and an agile positioning system.

(C , Ψ * , G ) Class of Contractions and Fixed Points in a Metric Space Endowed with a Graph

In this paper, we introduce the ( C , Ψ * , G ) class of contraction mappings using C-class functions and some improved control functions for a pair of set valued mappings as well as a pair of single-valued mappings, and prove common fixed point theorems for such mappings in a metric space endowed with a graph. Our results unify and generalize many important fixed point results existing in literature. As an application of our main result, we have derived fixed point theorems for a pair of α -admissible set valued mappings in a metric space.