An Extended Pontryagin Principle for Control Systems whose Control Laws Contain Measures

1965 ◽  
Vol 3 (2) ◽  
pp. 191-205 ◽  
Author(s):  
Raymond W. Rishel
Keyword(s):  
Control Systems ◽  
Control Laws ◽  
Pontryagin Principle

scholarly journals On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sendren Sheng-Dong Xu ◽  
Chih-Chiang Chen
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Switched Systems ◽  
The Other ◽  
Linear Control ◽  
Linear Control Systems ◽  
Problem Statement ◽  
Theoretical Derivation ◽  
Control Laws ◽  
Numerical Examples

The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among unstable linear systems and unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.

scholarly journals A Nonlinear Systems Framework for Cyberattack Prevention for Chemical Process Control Systems †

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 169 ◽  
Author(s):  
Helen Durand
Keyword(s):  
Nonlinear Systems ◽  
Control Systems ◽  
Chemical Process ◽  
Property A ◽  
Control Laws ◽  
Industrial Control Systems ◽  
Plant Safety ◽  
And Control ◽  
Systems Framework ◽  
Control Designs

Recent cyberattacks against industrial control systems highlight the criticality of preventing future attacks from disrupting plants economically or, more critically, from impacting plant safety. This work develops a nonlinear systems framework for understanding cyberattack-resilience of process and control designs and indicates through an analysis of three control designs how control laws can be inspected for this property. A chemical process example illustrates that control approaches intended for cyberattack prevention which seem intuitive are not cyberattack-resilient unless they meet the requirements of a nonlinear systems description of this property.

Computing the closed-loop characteristics of a generalized multi-threshold knock controller

2017 ◽  
Vol 19 (9) ◽  
pp. 952-962 ◽  
Author(s):  
Saeed Shayestehmanesh ◽  
James C Peyton Jones ◽  
Jesse Frey
Keyword(s):  
Steady State ◽  
Control Systems ◽  
Closed Loop ◽  
Single Experiment ◽  
Informative Feedback ◽  
Control Laws ◽  
Knock Control ◽  
Transient And Steady State ◽  
Steady State Performance

Most knock controllers respond to knock events which are defined according to some threshold knock intensity. Multi-threshold knock events offer more informative feedback since they encode not just the occurrence of knock events but also some measure of their intensity. While this has the potential for improved control, it is hard to assess the extent to which any benefits are truly realized because (in common with all knock control systems) the results of any single experiment or simulation depends on the random arrival of knock events in that instance. In this article, methods are developed instead to compute the statistical properties of the closed-loop response of a general multi-threshold knock controller, thereby providing a much more complete and rigorous characterization of its performance than has previously been possible. The method is applied to single- and dual-threshold knock controllers and used to provide a rigorous comparison of the transient and steady-state performance of these different control laws. The method can also be used as a calibration aid to assess the effects of different controller gains in reliable, repeatable fashion.

scholarly journals Finite-Horizon Optimal Control of Discrete-Time Switched Linear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Qixin Zhu ◽  
Guangming Xie
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Discrete Time ◽  
Finite Horizon ◽  
Linear Control ◽  
Linear Control Systems ◽  
Control Input ◽  
Optimal Switching ◽  
Control Laws ◽  
Control Factors

Finite-horizon optimal control problems for discrete-time switched linear control systems are investigated in this paper. Two kinds of quadratic cost functions are considered. The weight matrices are different. One is subsystem dependent; the other is time dependent. For a switched linear control system, not only the control input but also the switching signals are control factors and are needed to be designed in order to minimize cost function. As a result, optimal design for switched linear control systems is more complicated than that of non-switched ones. By using the principle of dynamic programming, the optimal control laws including both the optimal switching signal and the optimal control inputs are obtained for the two problems. Two examples are given to verify the theory results in this paper.

scholarly journals ALGORITHM FOR SYNTHESIZING PARAMETERS OF CONTROL LAWS OF TECHNICAL SYSTEMS UNDER POLYNOMIAL APPROXIMATION OF NONLINEARITIES

2018 ◽  
pp. 97-102
Author(s):  
V. F. Shishlakov ◽  
E. Yu. Vataeva ◽  
I. G. Krivolapchuk ◽  
N. V. Reshetnikova
Keyword(s):  
Automatic Control ◽  
Control Systems ◽  
Polynomial Approximation ◽  
Nonlinear Characteristics ◽  
Control Laws ◽  
Software Complex ◽  
Automatic Control Systems ◽  
New Class ◽  
Advantages And Disadvantages ◽  
Direct Variational Method

The paper considers the algorithm for solving the problem of synthesis of automatic control systems (ACS) with nonlinear characteristics for polynomial approximation. As a mathematical apparatus, the inversion of the direct variational method of analysis, Galerkin generalized method, is applied to the solution of the problem. Recurrence relations are obtained that make it possible to extend this method to a new class of dynamical systems with nonlinear elements whose characteristics are approximated polynomially. The advantages and disadvantages of various methods of approximation of automatic control systems with nonlinear characteristics are analyzed. The presented algorithm of the software complex is universal and allows solving the synthesis problem for control systems of different classes and structures from unified mathematical, methodological and algorithmic positions.

scholarly journals Design of Composite Feedback and Feedforward Control Law for Aircraft Inertially Stabilized Platforms

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Valerii Azarskov ◽  
Anatoly Tunik ◽  
Olha Sushchenko
Keyword(s):  
Control Systems ◽  
Feedforward Control ◽  
Design Method ◽  
Synergetic Effect ◽  
Measurement Unit ◽  
Control Law ◽  
Control Laws ◽  
Robustness Criterion ◽  
Two Stages ◽  
Invariance Theory

The design of the control systems of the inertially stabilized platforms (ISPs) as part of airborne equipment for the majority of aircraft has its peculiarity. The presence of rate gyros in the inertial measurement unit gives the possibility to measure the rotation rate of the ISP base, which is the main disturbance interfering with the ISP accuracy. Inclusion of the feedforward disturbance gain in the control law with the simplest PI feedback significantly improves the accuracy of stabilization by the invariance theory. A combination of feedback and feedforward controllers produces a synergetic effect, thus, improving ISP accuracy. This article deals with the design of the airborne ISP control systems consisting of two stages: the parametric optimization of the PI feedback control based on composite “performance-robustness” criterion and the augmentation of the obtained system with feedforward gain. To prove the efficiency of the proposed control laws, the simulation of the ISP was undertaken. We have used a simulation of the heading-hold system of the commuter aircraft Beaver and the yaw rate output of this closed-loop system we have used as a source of the disturbance. The results of modeling proved the efficiency of the proposed design method.

scholarly journals Self-Oscillations of The Free Turbine Speed in Testing Turboshaft Engine with Hydraulic Dynamometer

Aerospace ◽  
2021 ◽  
Vol 8 (4) ◽  
pp. 114
Author(s):  
Oleksandr Lytviak ◽  
Vasyl Loginov ◽  
Sergii Komar ◽  
Yevhen Martseniuk
Keyword(s):  
Automatic Control ◽  
Control Systems ◽  
Control Laws ◽  
Automatic Control Systems ◽  
First Case ◽  
Calculation Results ◽  
Nonlinear Features ◽  
Turbine Speed ◽  
Turboshaft Engine ◽  
Helicopter Main Rotor

Self-oscillations are one of the common problems in the complex automatic system, that can occur due to the features of the workflow and the design of the governor. The development of digital control systems has made it possible to damp self-oscillations by applying complex control laws. However, for hydromechanical systems, such way is unacceptable due to the design complexity and the governor cost. The objective of this work is to determine the parameters of the hydromechanical free turbine speed controller, ensuring the absence of self-oscillations during ground tests of the turboshaft engine with a hydraulic dynamometer. The TV3-117VM engine (Ukraine) with the NR-3VM regulator pump (Ukraine) was selected as the object of the study. However, self-oscillations can also occur in any modifications of the TV3-117 engine with any NR-3 regulator pump. The results of the research may be of interest to engineers and scientists who investigate the dynamics of automatic control systems for similar engines. The paper analyses the nonlinear features of the empirical characteristics of the FTSC leading to self-oscillations of the engine speed. The authors propose the mathematical model of the automatic control system dynamics, which takes into account all the features of the engine and regulator pump. It is shown that the load characteristics of the water brake and the helicopter main rotor can differ significantly. Research of the dynamic characteristics of the TV3-117VM engine was carried out. The analysis showed a good agreement between the calculation results and the field test results, and made it possible to determine the parameters of the controller, which lead to self-oscillations during test. Two cases are considered. The first case includes ground tests of the engine with a water brake; the second case—flight tests of the engine as part of the helicopter’s power plant. The data obtained make it possible to develop recommendations for adjusting the hydromechanical governor without testing it on the engine.

Intelligent Cruise Control Systems and Traffic Flow Behavior

1999 ◽  
Author(s):  
Darbha Swaroop ◽  
K. R. Rajagopal
Keyword(s):  
Control Systems ◽  
Traffic Flow ◽  
Adaptive Cruise Control ◽  
Flow Behavior ◽  
Flow Stability ◽  
Traffic Density ◽  
Cruise Control ◽  
String Stability ◽  
Control Laws ◽  
Traffic Flow Stability

Abstract In analogy to the flow of fluids, it is expected that the aggregate density and the velocity of vehicles in a section of a freeway adequately describe the traffic flow dynamics. The conservation of mass equation together with the aggregation of the vehicle following dynamics of controlled vehicles describes the evolution of the traffic density and the aggregate speed of a traffic flow. There are two kinds of stability associated with traffic flow problems — string stability (or car-following stability) and traffic flow stability. We make a clear distinction between traffic flow stability and string stability, and such a distinction has not been recognized in the literature, thus far. String stability is stability with respect to intervehicular spacing; intuitively, it ensures the knowledge of the position and velocity of every vehicle in the traffic, within reasonable bounds of error, from the knowledge of the position and velocity of a vehicle in the traffic. String stability is analyzed without adding vehicles to or removing vehicles from the traffic. On the other hand, traffic flow stability deals with the evolution of traffic velocity and density in response to the addition and/or removal of vehicles from the flow. Traffic flow stability can be guaranteed only if the velocity and density solutions of the coupled set of equations is stable, i.e., only if stability with respect to automatic vehicle following and stability with respect to density evolution is guaranteed. Therefore, the flow stability and critical capacity of any section of a highway is dependent not only on the vehicle following control laws and the information used in their synthesis, but also on the spacing policy employed by the control system. Such a dependence has practical consequences in the choice of a spacing policy for adaptive cruise control laws and on the stability of the traffic flow consisting of vehicles equipped with adaptive cruise control features on the existing and future highways. This critical dependence is the subject of investigation in this paper. This problem is analyzed in two steps: The first step is to understand the effect of spacing policy employed by the Intelligent Cruise Control (ICC) systems on traffic flow stability. The second step is to understand how the dynamics of ICC system affects traffic flow stability. Using such an analysis, it is shown that cruise control systems that employ a constant time headway policy lead to unacceptable characteristics for the traffic flows.

Output Regulation of the Liu Chaotic System

2011 ◽  
Vol 110-116 ◽  
pp. 3982-3989 ◽  
Author(s):  
Vaidyanathan Sundarapandian
Keyword(s):  
Feedback Control ◽  
Control Systems ◽  
Chaotic System ◽  
State Feedback ◽  
Output Regulation ◽  
State Feedback Control ◽  
Nonlinear Control Systems ◽  
Control Laws ◽  
Reference Signals ◽  
Simulation Results

This paper investigates the problem of regulating the output of the Liu chaotic system (2004). Explicitly, we construct state feedback control laws to regulate the Liu chaotic system so as to track constant reference signals. The control laws are derived using the regulator equations of Byrnes and Isidori (1990), who have solved the output regulation of nonlinear control systems using neutrally stable exosystem dynamics. The simulation results are also discussed in detail.

Sign in / Sign up

Export Citation Format

Share Document