scholarly journals On the necessity of the constant rank condition for L p estimates

2021 ◽  
Vol 358 (9-10) ◽  
pp. 1091-1095
Author(s):  
André Guerra ◽  
Bogdan Raiţă
Keyword(s):  
Constant Rank ◽  
Rank Condition

A weak maximum principle for optimal control problems with mixed constraints under a constant rank condition

2020 ◽  
Vol 37 (3) ◽  
pp. 1021-1047
Author(s):  
Roberto Andreani ◽  
Valeriano Antunes de Oliveira ◽  
Jamielli Tomaz Pereira ◽  
Geraldo Nunes Silva
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Equality Constraints ◽  
Control Problems ◽  
Constant Rank ◽  
Rank Condition ◽  
Weak Maximum Principle

Abstract Necessary optimality conditions for optimal control problems with mixed state-control equality constraints are obtained. The necessary conditions are given in the form of a weak maximum principle and are obtained under (i) a new regularity condition for problems with mixed linear equality constraints and (ii) a constant rank type condition for the general non-linear case. Some instances of problems with equality and inequality constraints are also covered. Illustrative examples are presented.

scholarly journals CONSTANT RANK CONSTRAINT QUALIFICATIONS: A GEOMETRIC INTRODUCTION

2014 ◽  
Vol 34 (3) ◽  
pp. 481-494 ◽  
Author(s):  
Roberto Andreani ◽  
Paulo J.S. Silva
Keyword(s):  
Constraint Qualifications ◽  
Constant Rank ◽  
Rank Constraint

Graphical Minimax Game and Off-Policy Reinforcement Learning for Heterogeneous MASs with Spanning Tree Condition

2021 ◽  
pp. 2150011
Author(s):  
Wei Dong ◽  
Jianan Wang ◽  
Chunyan Wang ◽  
Zhenqiang Qi ◽  
Zhengtao Ding
Keyword(s):  
Reinforcement Learning ◽  
Spanning Tree ◽  
Learning Algorithm ◽  
Control Policy ◽  
Game Problem ◽  
Algebraic Riccati Equation ◽  
Multi Agent Systems ◽  
Rank Condition ◽  
Minimax Game ◽  
Tree Condition

In this paper, the optimal consensus control problem is investigated for heterogeneous linear multi-agent systems (MASs) with spanning tree condition based on game theory and reinforcement learning. First, the graphical minimax game algebraic Riccati equation (ARE) is derived by converting the consensus problem into a zero-sum game problem between each agent and its neighbors. The asymptotic stability and minimax validation of the closed-loop systems are proved theoretically. Then, a data-driven off-policy reinforcement learning algorithm is proposed to online learn the optimal control policy without the information of the system dynamics. A certain rank condition is established to guarantee the convergence of the proposed algorithm to the unique solution of the ARE. Finally, the effectiveness of the proposed method is demonstrated through a numerical simulation.

scholarly journals Controllability and Observability of a Large Scale Thermodynamical System via Connectability Approach

2010 ◽  
Author(s):  
Virdiansyah Permana ◽  
Rahmat Shoureshi
Keyword(s):  
Graph Theory ◽  
Lie Algebra ◽  
Large Scale ◽  
Point Of View ◽  
Rank Condition ◽  
Computational Point ◽  
New Approach ◽  
Class System ◽  
Necessary And Sufficient ◽  
Controllability And Observability

This study presents a new approach to determine the controllability and observability of a large scale nonlinear dynamic thermal system using graph-theory. The novelty of this method is in adapting graph theory for nonlinear class and establishing a graphic condition that describes the necessary and sufficient terms for a nonlinear class system to be controllable and observable, which equivalents to the analytical method of Lie algebra rank condition. The directed graph (digraph) is utilized to model the system, and the rule of its adaptation in nonlinear class is defined. Subsequently, necessary and sufficient terms to achieve controllability and observability condition are investigated through the structural property of a digraph called connectability. It will be shown that the connectability condition between input and states, as well as output and states of a nonlinear system are equivalent to Lie-algebra rank condition (LARC). This approach has been proven to be easier from a computational point of view and is thus found to be useful when dealing with a large system.

scholarly journals NONPARAMETRIC IDENTIFICATION OF ACCELERATED FAILURE TIME COMPETING RISKS MODELS

2013 ◽  
Vol 29 (5) ◽  
pp. 905-919 ◽  
Author(s):  
Sokbae Lee ◽  
Arthur Lewbel
Keyword(s):  
Competing Risks ◽  
Failure Time ◽  
Nonparametric Identification ◽  
Accelerated Failure Time ◽  
Rank Condition ◽  
Survivor Function ◽  
Auction Models ◽  
Regression Functions ◽  
Accelerated Failure ◽  
Identification Strategy

We provide new conditions for identification of accelerated failure time competing risks models. These include Roy models and some auction models. In our setup, unknown regression functions and the joint survivor function of latent disturbance terms are all nonparametric. We show that this model is identified given covariates that are independent of latent errors, provided that a certain rank condition is satisfied. We present a simple example in which our rank condition for identification is verified. Our identification strategy does not depend on identification at infinity or near zero, and it does not require exclusion assumptions. Given our identification, we show estimation can be accomplished using sieves.

scholarly journals Controllability of Flow-Conservation Transportation Networks with Fractional-Order Dynamics

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Wei Chen ◽  
Bo Zhou
Keyword(s):  
Theoretical Analysis ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Fractional Order ◽  
Location Problem ◽  
Transportation Networks ◽  
Qr Decomposition ◽  
Rank Condition ◽  
Numerical Examples ◽  
Flow Conservation

In this paper, we adapt the fractional derivative approach to formulate the flow-conservation transportation networks, which consider the propagation dynamics and the users’ behaviors in terms of route choices. We then investigate the controllability of the fractional-order transportation networks by employing the Popov-Belevitch-Hautus rank condition and the QR decomposition algorithm. Furthermore, we provide the exact solutions for the full controllability pricing controller location problem, which includes where to locate the controllers and how many controllers are required at the location positions. Finally, we illustrate two numerical examples to validate the theoretical analysis.

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