Linearization and Boundary Trajectories of Nonsmooth Control Systems

1988 ◽  
Vol 40 (3) ◽  
pp. 589-609 ◽  
Author(s):  
H. Frankowska ◽  
B. Kaśkosz
Keyword(s):  
Control System ◽  
Control Systems ◽  
Differential Inclusions ◽  
Necessary Condition ◽  
Time Interval ◽  
Control Pair ◽  
Smooth Control ◽  
First Order ◽  
Image Position ◽  
Nonsmooth Control Systems

This paper deals with boundary trajectories of non-smooth control systems and differential inclusions.Consider a control system(1.1)and denote by R(t) its reachable set at time t. Let (z, u*) be a trajectory-control pair. If for every t from the time interval [0, 1], z(t) lies on the boundary of R(t) then z is called a boundary trajectory. It is known that for systems with Lipschitzian in x right-hand side, z is a boundary trajectory if and only if z(1) belongs to the boundary of the set R(1). If z is not a boundary trajectory, that is, z(1) ∊ Int R(1) then the system is said to be locally controllable around z at time 1.A first-order necessary condition for boundary trajectories of smooth systems comes from the Pontriagin maximum principle, (see e.g. [12]).

Analysis and control of differential inclusions with anti-periodic conditions

2014 ◽  
Vol 144 (3) ◽  
pp. 591-602 ◽  
Author(s):  
Z. H. Liu ◽  
S. Migórski
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Optimal Control Problem ◽  
Control Systems ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Topological Properties ◽  
Control Pair ◽  
Control Variables ◽  
And Control

We deal with the optimal control of systems driven by differential inclusions with anti-periodic conditions in Banach spaces. The operators in the differential inclusions, describing the control system, all depend on control variables. By a solution of the control system we mean a ‘trajectory-control’ pair. We first prove that, for fixed control variables, the set of solutions is non-empty for the corresponding differential inclusion with anti-periodic conditions. We then show the functional-topological properties of the set of solutions. Finally, we investigate the existence of solutions to the optimal control problem. These abstract results can be used to study optimal control systems of evolutionary hemi-variational inequalities.

On Uniqueness of Filippov’s Solutions for Non-Smooth Systems Having Multiple Discontinuity Surfaces With Applications to Control Engineering

2004 ◽  
Author(s):  
Qiong Wu ◽  
Hairong Zeng ◽  
Nariman Sepehri
Keyword(s):  
Control System ◽  
State Space ◽  
Control Systems ◽  
Convex Sets ◽  
Discontinuity Surface ◽  
Control Engineering ◽  
Smooth Control ◽  
Discontinuity Surfaces ◽  
Uniqueness Of The Solution

The analysis of the uniqueness of Filippov’s solutions to non-smooth control systems is important before the solutions can be sought. Such an analysis is extremely challenging when the discontinuity surface is the intersecting discontinuity surfaces. The key step is to study the intersections of the convex sets from Filippov’s inclusions and the sets containing vectors tangent to the discontinuity surfaces. Due to the fact that all the elements of these sets are functions of the states and time and their numerical values can not be obtained before the uniqueness of the solution is analyzed, the determination of such intersections, symbolically, is extremely difficult. In this paper, we propose to firstly transform the control system to a new state space where the discontinuity surfaces can be written in special forms. Secondly, we expand the sets associated with Filippov’s inclusion such that the determinations of the intersections become feasible. Two examples of practical non-smooth control systems are presented to demonstrate the efficacy of the method.

INTERVAL LOGIC FOR PROCESS CONTROL SYSTEM SPECIFICATION

1991 ◽  
Vol 01 (03) ◽  
pp. 303-326
Author(s):  
PETER P.K. CHIU ◽  
Y.S. CHEUNG
Keyword(s):  
Control System ◽  
Process Control ◽  
Control Systems ◽  
Process Control System ◽  
Time Interval ◽  
System Specification ◽  
Time Intervals ◽  
Process Control Systems ◽  
Sequential Processes ◽  
Interval Logic

A new methodology for the specification of process control systems involving time interval information and verification of their design is proposed. The specification is based on interval logic and a time-interval operator is defined. By means of this operator, time interval information is incorporated in the specification. Thus properties that involve time intervals can be verified. Moreover, combinational and sequential processes can be specified. An application example for a process control system is demonstrated.

scholarly journals Optimization of nonlinear pulse systems of automatic control with astatic objects

2020 ◽  
pp. 61-70
Author(s):  
O. Sinyavsky ◽  
◽  
V. Kisten ◽  
N. Solomko ◽  
◽  
...  
Keyword(s):  
Control System ◽  
Automatic Control ◽  
Control Systems ◽  
Pulse Duration ◽  
Automatic Control System ◽  
Linear Element ◽  
Optimal Parameters ◽  
First Order ◽  
Automatic Control Systems ◽  
In Series

Currently, nonlinear pulse automatic control systems have become widespread, so there is a need to develop methods for their study. Pulse regulators are created on the basis of positional with the addition of pulse breakers. They can be represented as a non-linear element, a simple impulse element and a forming circle connected in series. The aim of the study was to determine the optimal parameters for setting up a relay-pulse controller for an astatic object with a delay. When determining the parameters of adjustment of the relay-pulse regulator for the quality indicator in the optimization of the automatic control system was taken as the total square deviation. Applying this criterion, the pulse duration of the regulator was determined. The time quantization interval is determined from the condition of ensuring the absolute stability of the automatic control system. Analytical dependences were obtained to determine the pulse duration and time quantization interval, which make it possible to determine the debugging parameters of the relay-pulse controller for a first-order astatic object with a delay. This ensures a minimum control error, and the control system is stable.

scholarly journals LOCALMINIMUM PRINCIPLE FOR OPTIMIZATION PROBLEMS WITH DIFFERENT TYPES OF CONTROL SYSTEMS SUBJECT TO MIXED STATE-CONTROL CONSTRAINTS

2018 ◽  
Vol 14 (2) ◽  
pp. 57-64 ◽  
Author(s):  
Andrey V. Dmitruk ◽  
Nikolay P. Osmolovskii
Keyword(s):  
Control Systems ◽  
Optimal Control Problems ◽  
Optimization Problems ◽  
Fixed Time ◽  
Time Interval ◽  
State Control ◽  
First Order ◽  
Type Integral ◽  
Different Types ◽  
Interval Systems

This paper discusses the first-order optimality conditions for optimal control problems with two different types of control systems, considered on a fixed time interval: systems of ordinary differential equations and systems of Volterra-type integral equations

scholarly journals On Determining the Optimal Sampling Frequency for Feedback Quality Control Systems

2014 ◽  
Vol 61 (1) ◽  
pp. 54-65
Author(s):  
C. P. Kartha
Keyword(s):  
Quality Control ◽  
Control System ◽  
Control Systems ◽  
Cost Model ◽  
Moving Average ◽  
Sampling Frequency ◽  
Optimal Sampling ◽  
First Order ◽  
Feedback Quality ◽  
The Cost

Abstract This paper considers the choice of the most profitable sampling frequency for a feedback quality control system. It is assumed that the disturbance can be adequately modeled by a first-order Integrated Moving Average (IMA (0, 1, 1)) process. The cost model includes two terms, one for the cost of being off-target and one for the cost of sampling and adjustment. An analytical solution is obtained and the sensitivity of parameters examined

Pengaruh Sistem Pengendalian Internal Pemerintah dan Kompetensi Pegawai Terhadap Kinerja Instansi Pemerintah Kabupaten Karimun

2020 ◽  
Vol 5 (1) ◽  
pp. 101-106
Author(s):  
Doni Putra Utama
Keyword(s):  
Control System ◽  
Control Systems ◽  
Internal Control ◽  
Statistical Tests ◽  
Government Agencies ◽  
Government Performance ◽  
Significant Positive Effect ◽  
Internal Control System ◽  
Employee Competencies ◽  
Positive Effect

This research is a causality study with the title "Effect of Government Internal Control Systems and Employee Competence on the Performance of Government Agencies in Karimun Regency." The purpose of this study was to determine the effect of the implementation of the Government's Internal Control System on the performance of Karimun Regency government agencies and to determine the effect of employee competence on the performance of Karimun Regency government agencies. Data collection using a questionnaire where the questionnaire contained questions about the Government's Internal Control System, employee competencies and agency performance. Data were tested using multiple linear regression statistical tests. Based on the results of the study, it can be concluded that the governmental internal control system has a significant positive effect on Government Agency Performance with the results of statistical tests that show a sig value of 0.016 <0.05 (alpha 5%). Employee Competency has a significant positive effect on Government Performance with the results of statistical tests showing a sig value of 0,000.

Coercion and the Nature of Law

2020 ◽  
Author(s):  
Kenneth Einar Himma
Keyword(s):  
Conceptual Analysis ◽  
Existence Condition ◽  
Necessary Condition ◽  
First Order ◽  
Normative System ◽  
Motivating Reasons

COERCION AND THE NATURE OF LAW argues that it is a conceptually necessary condition for something to count as a system of law according to our conceptual practices that it authorizes the imposition of coercive sanctions for violations of some mandatory norms governing non-official behavior (the Coercion Thesis). The book begins with an explication of the modest approach to conceptual analysis that is deployed throughout. The remainder of the book is concerned to show that an institutional normative system is not reasonably contrived to do anything that law must be able to do for us to make sense of why we adopt systems of law to regulate non-official behavior unless we assume that mandatory norms governing that behavior are backed by the threat of a sovereign; an institutional normative system that satisfies every other plausible existence condition for law is not reasonably contrived to give rise to either objective or subjective first-order motivating reasons to comply with mandatory norms governing non-official behavior unless they are backed by the threat of a coercive sanction. Law’s presumed conceptual normativity can be explained only by the Coercion Thesis.

scholarly journals Coordination of Lateral Vehicle Control Systems Using Learning-Based Strategies

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1291
Author(s):  
Balázs Németh
Keyword(s):  
Control System ◽  
Control Systems ◽  
Coordinated Control ◽  
Front Wheel ◽  
Steering Angle ◽  
Conventional Model ◽  
Linear Parameter Varying ◽  
Coordination Strategy ◽  
Torque Vectoring ◽  
Performance Specifications

The paper proposes a novel learning-based coordination strategy for lateral control systems of automated vehicles. The motivation of the research is to improve the performance level of the coordinated system compared to the conventional model-based reconfigurable solutions. During vehicle maneuvers, the coordinated control system provides torque vectoring and front-wheel steering angle in order to guarantee the various lateral dynamical performances. The performance specifications are guaranteed on two levels, i.e., primary performances are guaranteed by Linear Parameter Varying (LPV) controllers, while secondary performances (e.g., economy and comfort) are maintained by a reinforcement-learning-based (RL) controller. The coordination of the control systems is carried out by a supervisor. The effectiveness of the proposed coordinated control system is illustrated through high velocity vehicle maneuvers.

Sign in / Sign up

Export Citation Format

Share Document