Guaranteed Avoidance Control and Holding Control

1982 ◽  
Vol 104 (2) ◽  
pp. 166-172 ◽  
Author(s):  
W. E. Schmitendorf ◽  
B. R. Barmish ◽  
B. S. Elenbogen
Keyword(s):  
Control Problem ◽  
State Space ◽  
The State ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Avoidance Control ◽  
Avoidance Problem

This paper considers the problem of steering the state of a system, in the presence of disturbances, so that it avoids a specified subset of the state space. This subset is called the avoidance set and the problem is called the avoidance control problem. An avoidance control is a control which guarantees that the system does not enter the avoidance set regardless of the disturbance. A necessary condition and a sufficient condition for the existence of an avoidance control are given when the disturbance is subject to magnitude constraints. Closely related to the avoidance problem is the holding problem which is concerned with guaranteeing that the state of the system remains within a specified set. We also reinterpret our conditions for the existence of an avoidance control within the context of the holding problem.

scholarly journals Optimal control theory with general constraints

1981 ◽  
Vol 23 (2) ◽  
pp. 115-126 ◽  
Author(s):  
John M. Blatt
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Theory ◽  
Time Dependent ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
General Constraints ◽  
Elementary Methods ◽  
And Control

AbstractWe consider an optimal control problem with, possibly time-dependent, constraints on state and control variables, jointly. Using only elementary methods, we derive a sufficient condition for optimality. Although phrased in terms reminiscent of the necessary condition of Pontryagin, the sufficient condition is logically independent, as can be shown by a simple example.

CHUA'S SINGULARITIES: GREAT MIRACLE IN CIRCUIT THEORY

2010 ◽  
Vol 20 (10) ◽  
pp. 2993-3006 ◽  
Author(s):  
VIKTOR ŠPÁNY ◽  
PAVOL GALAJDA ◽  
MILAN GUZAN ◽  
LADISLAV PIVKA ◽  
MARTIN OLEJÁR
Keyword(s):  
State Space ◽  
Stable Manifold ◽  
Saddle Points ◽  
Circuit Theory ◽  
The State ◽  
The Other ◽  
Sufficient Condition ◽  
State Equations ◽  
Chua's Circuit ◽  
The Subject

In the work [Chua, 1992], a deep intuition of its author gave rise to the choice of singularities corresponding to Chua's circuit. Therefore, it is the only one probably exhibiting three saddle points named Chua's singularities in this paper. One of the singularities is a saddle in forward time (dt > 0) of integration, whereas the other two are saddles in backward time (dt < 0) of integration. In the following, the term Chua's Chaos denotes chaos related to Chua's singularities. These singularities are the source of all special surfaces that are the subject of this contribution. We named the surface to which all other surfaces are bound as the Double-Arm Stable Manifold (DASM). The beauty and multifunctionality of this surface represents the unfathomable Intelligence in the sense of [Tolle, 2003]. The presence of the DASM in the state space is a sufficient condition for the generation of Chua's chaos or corresponding periodic windows. Since Chua's singularities are not limited by circuit morphology or the order of state equations, the research on Chua's chaos seems to be still very promising.

A Note on Avoidance Control

1981 ◽  
Vol 103 (1) ◽  
pp. 69-70 ◽  
Author(s):  
B. R. Barmish ◽  
W. E. Schmitendorf ◽  
G. Leitmann
Keyword(s):  
State Space ◽  
Existence Theorem ◽  
The State ◽  
Avoidance Control

This note points out some technical difficulties which can arise when attempting to determine the existence of a control which guarantees avoidance of a given set in the state space. It is concluded that the hypotheses of the existence theorem in [1] require strengthening.

scholarly journals Sum of Squares Approach for Nonlinear H∞ Control

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Ai-ping Pang ◽  
Zhen He ◽  
Ming-han Zhao ◽  
Guang-xiong Wang ◽  
Qin-mu Wu ◽  
...  
Keyword(s):  
Control Problem ◽  
State Space ◽  
Nonlinear Problem ◽  
Design Process ◽  
Synthesis Method ◽  
Sum Of Squares ◽  
Space Region ◽  
Sufficient Condition ◽  
Set Containment ◽  
Reasonable Result

A proper Hamilton-Jacobi-Isaacs (HJI) inequality must be solved in a nonlinear H∞ control problem. The sum of squares (SOS) method can now be used to solve an analytically unsolvable nonlinear problem. A HJI inequality suitable for SOS approach is derived in the paper. The SOS algorithm for solving the HJI inequality is also provided. Conservativeness of the SOS method is then discussed in the paper. The conservativeness of the SOS approach is caused by the method itself, because it is really a synthesis method over the entire state space. To reduce the conservativeness, a local H∞ design on a restricted state-space region is proposed. But the SOS approach for the local H∞ design also suffers from the conservativeness problem, because the S-procedure for solving the set-containment constraint provides only a sufficient condition. The above-mentioned sources of conservativeness are peculiar for the SOS approaches. So a proper approach must be carefully selected in the design process to get a reasonable result. A design example is also given in the paper.

scholarly journals Structural Analysis and Control of a Model of Two-Site Electricity and Heat Supply

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Hikaru Hoshino ◽  
Yoshihiko Susuki ◽  
T. John Koo ◽  
Takashi Hikihara
Keyword(s):  
Control Problem ◽  
Equilibrium Point ◽  
State Space ◽  
Heat Supply ◽  
State Space Model ◽  
The State ◽  
Model Parameters ◽  
Space Model ◽  
Energy Flows

This paper introduces a control problem of regulation of energy flows in a two-site electricity and heat supply system, where two combined heat and power (CHP) plants are interconnected via electricity and heat flows. The control problem is motivated by recent development of fast operation of CHP plants to provide ancillary services of power system on the order of tens of seconds to minutes. Due to the physical constraint that the responses of the heat subsystem are not necessary as fast as those of the electric subsystem, the target controlled state is not represented by any isolated equilibrium point, implying that stability of the system is lost in the long-term sense on the order of hours. In this paper, we first prove in the context of nonlinear control theory that the state-space model of the two-site system is nonminimum phase due to nonexistence of isolated equilibrium points of the associated zero dynamics. Instead, we locate a one-dimensional (1D) invariant manifold that represents the target controlled flows completely. Then, by utilizing a virtual output under which the state-space model becomes minimum phase, we synthesize a controller that achieves not only the regulation of energy flows in the short-term regime but also stabilization of an equilibrium point in the long-term regime. Effectiveness of the synthesized controller is established with numerical simulations with a practical set of model parameters.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

Modeling of CCLP in koryo extract production

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ji Chol ◽  
Ri Jun Il
Keyword(s):  
Process Control ◽  
Medical Care ◽  
State Space ◽  
State Space Model ◽  
The State ◽  
Space Model ◽  
Effective Components ◽  
Counter Current

Abstract The modeling of counter-current leaching plant (CCLP) in Koryo Extract Production is presented in this paper. Koryo medicine is a natural physic to be used for a diet and the medical care. The counter-current leaching method is mainly used for producing Koryo medicine. The purpose of the modeling in the previous works is to indicate the concentration distributions, and not to describe the model for the process control. In literature, there are no nearly the papers for modeling CCLP and especially not the presence of papers that have described the issue for extracting the effective components from the Koryo medicinal materials. First, this paper presents that CCLP can be shown like the equivalent process consisting of two tanks, where there is a shaking apparatus, respectively. It allows leachate to flow between two tanks. Then, this paper presents the principle model for CCLP and the state space model on based it. The accuracy of the model has been verified from experiments made at CCLP in the Koryo Extract Production at the Gang Gyi Koryo Manufacture Factory.

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