Exact determinations of the maximal output admissible set for a class of nonlinear systems

Automatica ◽  
2008 ◽  
Vol 44 (2) ◽  
pp. 526-533 ◽  
Author(s):  
Kenji Hirata ◽  
Yoshito Ohta
Keyword(s):  
Nonlinear Systems ◽  
Admissible Set ◽  
Maximal Output

Constrained Control of Input Delayed Systems With Partially Compensated Input Delays

2020 ◽  
Author(s):  
Imoleayo Abel ◽  
Mrdjan Janković ◽  
Miroslav Krstić
Keyword(s):  
Nonlinear Systems ◽  
Input Delay ◽  
Constrained Control ◽  
Admissible Set ◽  
Safe Operation ◽  
Barrier Functions ◽  
Delayed Systems ◽  
Free System ◽  
Single Input ◽  
Input Delays

Abstract 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.

Reference Governors Based on Online Learning of Maximal Output Admissible Set

2019 ◽  
Author(s):  
Manuel Lanchares ◽  
Ilya Kolmanovsky ◽  
Anouck Girard ◽  
Denise Rizzo
Keyword(s):  
Neural Network ◽  
Explicit Knowledge ◽  
Positioning System ◽  
Admissible Set ◽  
Explicit Model ◽  
Neural Network Learning ◽  
Network Learning ◽  
Control Schemes ◽  
Maximal Output ◽  
Reference Governor

Abstract 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.

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