Extension Of State Space Research Articles

Co‐design of memorized controllers for global sampled‐data stabilization a class of nonlinear system with input delay

AbstractGlobal sampled‐data stabilization for a class of nonlinear continuous system with input delay has been investigated directly in the discrete‐time domain due to challenges confronted in dealing with infinite‐dimensional system under input delay. Memorized state feedback controllers and output feedback controllers based on dynamic extension of state space have been constructed within the framework of co‐design between sampling period and scaling gain. Upon this compensation scheme, global sampled‐data stabilization a class of nonlinear system has been successfully realized no matter the input delay is smaller than the sampling period or not. Compared with memory‐less sampled‐data controllers, not only sampled‐data stabilization under large input delay has been realized but also transient performance of closed‐loop system has been further improved. Simulation results under different input delays and sampling periods have illustrated the effectiveness of results obtained.

Multipath Wireless Network Coding: A Scheduling Constraint in Game Perspective

This paper considers wireless networks in which various paths are obtainable involving each source and destination. It is allowing each source to tear traffic among all of its existing paths, and it may conquer the lowest achievable number of transmissions per unit time to sustain a prearranged traffic matrix. Traffic bound in contradictory instructions in excess of two wireless hops can utilize the “reverse carpooling” advantage of network coding in order to decrease the number of transmissions used. These call such coded hops “hyper-links.” With the overturn carpooling procedure, longer paths might be cheaper than shorter ones. However, convenient is an irregular situation among sources. The network coding advantage is realized only if there is traffic in both directions of a shared path. This project regard as the problem of routing amid network coding by egotistic agents (the sources) as a potential game and develop a method of state-space extension in which extra agents (the hyper-links) decouple sources’ choices from each other by declaring a hyper-link capacity, allowing sources to split their traffic selfishly in a distributed fashion, and then altering the hyper-link capacity based on user actions. Furthermore, each hyper-link has a scheduling constraint in stipulations of the maximum number of transmissions authorized per unit time. Finally these project show that our two-level control scheme is established and verify our investigative insights by simulation.

Tracking Problem with Consideration of Physical Constraints on Phase Variables and Control. Method of State Space Extension

The paper proposes a method for the synthesis of nonlinear systems invariant to the output variable, under the conditions of parametric and external perturbations, taking into account the constraints on phase variables and control. To solve the problem, the ideology of the block method using sat-functions as local feedback, and the disturbances observer on the sliding modes are applied.

Extension of State Space and Lyapunov Matrices

One of the main problems in the application of the theory of Lyapunov-Krasovskii functionals is the construction of corresponding Lyapunov matrices. Recently, it was noted that systems with distributed delay and exponential kernel may be rewritten by the introduction of auxiliary variables as systems with one delay. A suggestion was made that one can use the Lyapunov matrix of the latter system to obtain the Lyapunov matrix of the original system. In this article, we establish precise relationships between these two systems and their Lyapunov matrices. We show that if there exists a Lyapunov matrix of the extended system then it can be used to compute a Lyapunov matrix of the nominal system. We demonstrate that this method fails for certain systems and establish necessary and sufficient conditions for the extended system to admit a Lyapunov matrix.

Numerical-Analytical Method for Analyzing the Behavior of a Dynamical System Using Incorrect Observations without State Space Extension

Various continuous linear functionals of integral curves of a dynamical system are optimally estimated using incorrect additive observations of this system. A numerical-analytical method for analyzing the behavior of the system is developed in the case when observations contain not only counts of an integral curve and fluctuation noise, but also counts of singular disturbance. The method yields optimal unbiased and invariant (with respect to the given noise) estimates without using conventional state space extension. The random and systematic errors are analyzed, and illustrative examples are given.

Estimation of proximity of controls synthesized on basis of maximum principle and ADAR method

Introduction. A special case of synthesizing the same electromechanical control system by the Pontryagin maximum principle and by the synergetic synthesis method is considered. The task was to solve the synthesis problem of the time optimal electromechanical position control system; herewith the travel resistance modulus linearly depended on the output coordinate of the system. This approach to the selection of the synthesis problem was because the synthesis of time optimal systems is one of the most widespread problems, and it is solved by increasing the efficiency of the existing control systems.Materials and Methods. Synthesis of the time optimal linear control system based on the maximum principle is a widely accepted problem in the modern control theory. However, the procedure of synergistic synthesis does not have such formalization. This being the case, the paper suggests an approach that brings together these two methods, which, in our opinion, will increase the efficiency of the synergistic synthesis method through adding some features of the synthesis methodology for optimal systems.Research Results. The paper formulates two key concepts. The first one is as follows: the application of the maximum principle for an object of the DC motor class when synthesizing the positioning algorithm under the conditions of linear loading functionally dependent on the engine rotation angle allows the time optimal system to be optimized. The second concept states that synthesis of a control system based on the synergistic approach enables to obtain a system close to optimal (quasioptimal), but after modifying the synergetic synthesis method itself. A hypothesis is formulated on the possible connection between the introduced (when implementing the procedure of state space extension in the synergetic synthesis method) time constants with the optimal switching time of control defined in the maximum method.Discussion and Conclusions. The synthesis through the maximum control technique and the ADAR method is performed. In virtue of the comparison of efficiency of these methods, a hypothesis is put forward on the possible compatibility of the studied methods.

Модель живучести сложного объекта в условиях нанесения массированного авиационного удара

The article describes the main provisions of a mathematical model of the survivability of a complex object in a drawing massive air strike, reflecting the process of leaving drums of aviation complexes of the enemy in a given area and to overcome them multifunctional air defense system under cover of objects by means of an integrated (electronic and fire), and taking into account the two-way nature of the conduct EW. The model is based on the representation of these processes in the form of semi-Markov processes described by direct integral-differential equations of the principle of state space extension and application of the Laplace transform.

A scheme for study of linear stochastic time-delay dynamical systems under continuous and impulsive fluctuations

The paper deals with linear stochastic systems perturbed by both continuous and jump random noises. A presence of the lasts leads to the fact that at random times the state vector of the system receives random finite increments. But compound jump processes may have different pulse distributions describing time intervals between the impulses and their magnitudes that brings to a more complex time history of the systems than in the case of continuous noises only. We consider a problem of calculation of the first-order moment functions and the second-order central moment functions (hereinafter referred to as the first moment functions) for the state vectors of linear stochastic difference-differential systems excited by random continuous Wiener and jump Poisson processes. The technique combining the classic method of steps and a scheme of state space extension is used to derive a sequence of jump-diffusion stochastic differential equations (DEs) without delays satisfied by extended state vectors and then a chain of ordinary DEs’ systems governing the first moment functions. A usage of vector-matrix notation allows to obtain this chain in a form that is suitable for a practical computer program implementation. Finally an example of analysis of a stochastic SDOF system demonstrates an application of the scheme.

A MOP based constructive reflective state metamodel

Construction, management and extension of state space is crucial for many applications, Combining with frequent change of requirement of state space, these applications are rather complicated. Synthesizing techniques of refection architecture, MOP mechanism and metamodel, this paper advances a MOP(Meta Object Protocol) based constructive state metamodel, which defines construct and rules for building models with extensible structure for state space. Based on this metamodel, modeling with extension of state space that adopts decorator pattern and role object pattern is discussed. An implementation of modeling based on this metamodel is presented. With appropriate extension, models based on this metamodel can dynamically adapt state space change.

State Space Extension Method in the Theory of Absolute Stability

State space extension method is applied to construct new quadratic constraints and derive new frequency domain criteria for absolute stability.

The state space extension method in the theory of absolute stability

This paper shows how the state space extension method can be used to derive frequency domain criteria for stability of systems with different kinds of uncertainties. The main result is illustrated by a number of examples.

Decoupling and Pole Assignment by Dynamic Compensation

Previous article Next article Decoupling and Pole Assignment by Dynamic CompensationA. S. Morse and W. M. WonhamA. S. Morse and W. M. Wonhamhttps://doi.org/10.1137/0308022PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] W. M. Wonham and , A. S. Morse, Decoupling and pole assignment in linear multivariable systems: A geometric approach, SIAM J. Control, 8 (1970), 1–18 10.1137/0308001 MR0270771 0206.16404 LinkISIGoogle Scholar[2] Elmer G. Gilbert, The decoupling of multivariable systems by state feedback, SIAM J. Control, 7 (1969), 50–63 10.1137/0307004 MR0260443 0175.10301 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Disturbance Decoupling for Descriptor Systems by State FeedbackSIAM Journal on Control and Optimization, Vol. 38, No. 6 | 26 July 2006AbstractPDF (242 KB)Sufficient Conditions for Dynamic State Feedback LinearizationSIAM Journal on Control and Optimization, Vol. 29, No. 1 | 14 July 2006AbstractPDF (1558 KB)A Complete Optimality Condition in the Inverse Problem of Optimal ControlSIAM Journal on Control and Optimization, Vol. 22, No. 2 | 17 February 2012AbstractPDF (1664 KB)Causal Factorization and Linear FeedbackSIAM Journal on Control and Optimization, Vol. 19, No. 4 | 17 February 2012AbstractPDF (3098 KB)Linear Feedback—An Algebraic ApproachSIAM Journal on Control and Optimization, Vol. 16, No. 1 | 18 July 2006AbstractPDF (2478 KB)Generic Solvability of the Decoupling ProblemSIAM Journal on Control, Vol. 12, No. 4 | 1 August 2006AbstractPDF (490 KB)Regulation and Internal Stabilization in Linear Multivariable SystemsSIAM Journal on Control, Vol. 12, No. 1 | 18 July 2006AbstractPDF (961 KB)Tracking and Regulation in Linear Multivariable SystemsSIAM Journal on Control, Vol. 11, No. 3 | 18 July 2006AbstractPDF (915 KB)Structural Invariants of Linear Multivariable SystemsSIAM Journal on Control, Vol. 11, No. 3 | 18 July 2006AbstractPDF (1383 KB)Input–Output Structure of Linear Systems with Application to the Decoupling ProblemSIAM Journal on Control, Vol. 9, No. 2 | 18 July 2006AbstractPDF (3055 KB)Output Controllability and System SynthesisSIAM Journal on Control, Vol. 9, No. 2 | 18 July 2006AbstractPDF (489 KB) Volume 8, Issue 3| 1970SIAM Journal on Control305-440 History Submitted:11 December 1969Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0308022Article page range:pp. 317-337ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics