Optimal Singular Solutions for Linear Multi-Input Systems

1966 ◽  
Vol 88 (2) ◽  
pp. 323-328 ◽  
Author(s):  
R. A. Rohrer ◽  
M. Sobral
Keyword(s):  
Sufficient Conditions ◽  
Singular Control ◽  
Open Loop ◽  
The State ◽  
Singular Solutions ◽  
Linear Feedback ◽  
State Variables ◽  
Performance Indices ◽  
Explicit Formulae ◽  
Necessary And Sufficient

Linear, stationary systems with multiple inputs when subject to performance indices quadratic in the state variables, but explicitly independent of the control variables, may be optimally governed by singular control. Necessary and sufficient conditions for the optimality of both partially singular control and totally singular control are obtained. Moreover, explicit formulae are presented for both open-loop and linear-feedback implementations of the optimal singular control.

scholarly journals Zeroing of state variables in fractional descriptor electrical circuits by state-feedbacks

2014 ◽  
Vol 63 (3) ◽  
pp. 321-333
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Closed Loop ◽  
Sufficient Conditions ◽  
The State ◽  
Necessary And Sufficient Conditions ◽  
State Variables ◽  
Electrical Circuits ◽  
Closed Loop Systems ◽  
Necessary And Sufficient

Abstract The problem of zeroing of the state variables in fractional descriptor electrical circuits by state-feedbacks is formulated and solved. Necessary and sufficient conditions for the existence of gain matrices such that the state variables of closed-loop systems are zero for time greater zero are established. The procedure of choice of the gain matrices is demonstrated on simple descriptor electrical circuits with regular pencils

System Properties of One-Dimensional Distributed Systems

1977 ◽  
Vol 99 (2) ◽  
pp. 85-90 ◽  
Author(s):  
L. S. Bonderson
Keyword(s):  
Distributed Systems ◽  
Sufficient Conditions ◽  
State Variables ◽  
One Dimensional ◽  
First Order ◽  
Lumped Element ◽  
Order Form ◽  
Power Product ◽  
System Properties ◽  
Necessary And Sufficient

The system properties of passivity, losslessness, and reciprocity are defined and their necessary and sufficient conditions are derived for a class of linear one-dimensional multipower distributed systems. The utilization of power product pairs as state variables and the representation of the dynamics in first-order form allows results completely analogous to those for lumped-element systems.

Positive fractional continuous-time linear systems with singular pencils

2012 ◽  
Vol 60 (1) ◽  
pp. 9-12 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Variables ◽  
Algebraic Constraints ◽  
Necessary And Sufficient ◽  
Time Linear

Positive fractional continuous-time linear systems with singular pencils A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

2020 ◽  
Vol 42 (10) ◽  
pp. 1871-1881 ◽  
Author(s):  
Morteza Motahhari ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Linear Matrix ◽  
Time Interval ◽  
State Variables ◽  
L2 Gain

This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.

scholarly journals Simulation of Performance Response of State Variables of a Chemical Boiler Process

2018 ◽  
pp. 1-5
Author(s):  
Donatus O. Njoku ◽  
Asagba P. O ◽  
Chilaka U. Longinus ◽  
Amaefule I. A. ◽  
Igwe S. Onyema
Keyword(s):  
Transfer Function ◽  
Closed Loop ◽  
Control Process ◽  
Open Loop ◽  
The State ◽  
Feedback Gain ◽  
State Variables ◽  
Simulink Model ◽  
Performance Response ◽  
Optimal Regulator

This paper has presented simulation of performance response of state variables of a chemical boiler process. The transfer function of a boiler flow control process of a chemical plant was obtained. The transfer function was transformed into state space form to study the state variables of the system. An optimal regulator was designed using MATLAB programme. The developed optimal regulator was added to the loop of the system to form a closed loop system. A Simulink model was developed and used to study performance response of the system. Simulation was carried out for two conditions, open loop and closed loop. The simulation results indicated that the performance responses of the state variables were improved and better stability achieved with the inclusion of the designed feedback gain matrix of the optimal regulator.

Generalized semi-Markov decision processes

1979 ◽  
Vol 16 (03) ◽  
pp. 618-630
Author(s):  
Bharat T. Doshi
Keyword(s):  
Markov Decision Processes ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
The State ◽  
Service Rate ◽  
Storage Model ◽  
Sample Paths ◽  
Markov Decision ◽  
Sufficient Conditions For Optimality ◽  
Necessary And Sufficient

Various authors have derived the necessary and sufficient conditions for optimality in semi-Markov decision processes in which the state remains constant between jumps. In this paper similar results are presented for a generalized semi-Markov decision process in which the state varies between jumps according to a Markov process with continuous sample paths. These results are specialized to a general storage model and an application to the service rate control in a GI/G/1 queue is indicated.

scholarly journals Lagrangian for Circuits with Higher-Order Elements

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1059 ◽  
Author(s):  
Zdenek Biolek ◽  
Dalibor Biolek ◽  
Viera Biolkova
Keyword(s):  
Variational Principle ◽  
Equations Of Motion ◽  
Sufficient Conditions ◽  
Higher Order ◽  
The State ◽  
Even Order ◽  
Independent Variable ◽  
Necessary And Sufficient ◽  
Derivatives Of ◽  
State Functions

The necessary and sufficient conditions of the validity of Hamilton’s variational principle for circuits consisting of (α,β) elements from Chua’s periodical table are derived. It is shown that the principle holds if and only if all the circuit elements lie on the so-called Σ-diagonal with a constant sum of the indices α and β. In this case, the Lagrangian is the sum of the state functions of the elements of the L or +R types minus the sum of the state functions of the elements of the C or −R types. The equations of motion generated by this Lagrangian are always of even-order. If all the elements are linear, the equations of motion contain only even-order derivatives of the independent variable. Conclusions are illustrated on an example of the synthesis of the Pais–Uhlenbeck oscillator via the elements from Chua’s table.

SYNCHRONIZATION CRITERIA FOR TWO BOOLEAN NETWORKS BASED ON LOGICAL CONTROL

2013 ◽  
Vol 23 (11) ◽  
pp. 1350178 ◽  
Author(s):  
HONGWEI CHEN ◽  
YANG LIU ◽  
JIANQUAN LU
Keyword(s):  
Sufficient Conditions ◽  
Open Loop ◽  
Boolean Networks ◽  
Space Representation ◽  
Complete Synchronization ◽  
Loop Control ◽  
State Space Representation ◽  
Logic Control ◽  
Logical Control ◽  
Necessary And Sufficient

This paper investigates the complete synchronization of two Boolean networks via logic control. Both feedback control and open-loop control are proposed to make the slave network completely synchronized with the master Boolean network. Using the algebraic state-space representation of Boolean networks, we derive several necessary and sufficient conditions for complete synchronization between two Boolean networks. Two examples are given to illustrate the obtained results.

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