Constrained exact controllability of semilinear systems

In the paper infinite-dimensional dynamical control systems described by semilinear abstract differential equations are considered. Using a generalized open-mapping theorem, sufficient conditions for constrained exact local controllability are formulated and proved. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Constrained exact local controllability of semilinear abstract second-order dynamical systems are also formulated and proved. As an illustrative example, constrained exact local controllability problem for semilinear hyperbolic type distributed parameters dynamical system is solved in details. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.     

Approximate controllability for abstract measure differential systems

In this paper, we investigate approximate controllability for abstract measure differential systems based on generalizing knowledge for ordinary differential systems. We first introduce new concepts of the reachable set and approximate controllability for abstract measure differential systems. Then based on the nonlinear alternative for α-condensing mapping in Banach space, we present sufficient conditions of approximate controllability for a class of abstract measure differential systems. Our results in dealing with approximate controllability are less conservative than those in the previous literature. Finally, an example is given to illustrate the availability of our results for approximate controllability.     

Constrained approximate controllability

In the paper, constrained approximate controllability for linear dynamical systems described by abstract differential equations with unbounded control operator is considered. Using methods of spectral analysis for linear self-adjoint operators and general constrained controllability results given by Son (1990), necessary and sufficient conditions of the constrained approximate controllability for the piecewise polynomial controls with values in a given cone are formulated and proved. Moreover, as illustrative examples, constrained approximate boundary controllability of one-dimensional distributed parameter dynamical systems described by partial differential equations of parabolic type with Dirichlet and Neumann boundary conditions are investigated. The constrained controllability conditions obtained in the paper represent an extension of the unconstrained controllability results given by Glothin (1974) and Klamka (1991)     

Approximate controllability of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces

Many practical systems in physical and technical sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, we prove the approximate controllability of control systems governed by a class of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces. Sufficient conditions for approximate controllability of the control systems are established under the natural assumption that the corresponding linear system is approximately controllable. The results are obtained by using semigroup theory, stochastic analysis techniques, fixed point approach and abstract phase space axioms. An example is provided to illustrate the application of the obtained results.     

Constrained approximate boundary controllability

In this paper, constrained approximate boundary controllability for linear disturbed parameter dynamical systems described by partial differential equations of parabolic-type with mixed boundary conditions is considered. Using methods of spectral analysis for linear self-adjoint operators and general constrained controllability results, given by Son (1990), necessary and sufficient conditions for constrained approximate boundary controllability are formulated and proved. Moreover, in illustrative examples the constrained approximate boundary controllability of 1D distributed parameter dynamical systems is investigated. The constrained controllability conditions obtained represent an extension of the unconstrained controllability results given by Glothin (1974)     

一种非线性动力系统的开环控制方法及其应用研究

本文研究采用振荡控制方法，来改善非线性动力系统的特性，具体对用Ｄｕｆｆｉｎｇ、Ｒａｙｌｅｉｇｈ及Ｖａｎ ｄｅｒ Ｐｏｌ方程描述的动力系统特性进行了分析，并进行了该系统振荡稳定性、振荡可控性分析，最后引入振荡控制，使原系统特性得到很大改善。     

Approximate controllability of stochastic delay differential systems driven by Poisson jumps with instantaneous and noninstantaneous impulses

Control systems in which instantaneous and noninstantaneous impulses occur simultaneously are difficult to handle. In this article, we investigate the solvability and approximate controllability for a new category of stochastic differential equations steered by Poisson jumps with instantaneous and noninstantaneous impulses. Utilizing the theory of fundamental solution, stochastic analysis, the measure of noncompactness, and the fixed-point approach, we establish the presence of a mild solution for the proposed system. We have also constructed a new set of sufficient constraints that assures approximate controllability of the considered system. Next, we discuss the existence of a solution and approximate controllability for an impulsive deterministic control system in which the nonlinear term contains spatial derivatives. Lastly, two examples are presented to encapsulate the abstract results.     

Approximate controllability of partial neutral functional differential systems of fractional order with state-dependent delay

We prove the approximate controllability of control systems governed by a class of partial neutral functional differential systems of fractional order with state-dependent delay in an abstract space. Sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using the Krasnoselskii–Schaefer type fixed point theorem with the fractional power of operators. An example is provided to illustrate the main results.     

Complete controllability for abstract measure differential systems

In this paper, we investigate the complete controllability for abstract measure differential systems. Firstly, we introduce several new concepts about complete controllability for abstract measure differential systems. Then, on the basis of the Sadovskii fixed‐point theorem, we give sufficient conditions for complete controllability for a class of abstract measure differential systems. The compactness of the semigroup generated by some operator is unnecessary in this paper, and we show that our results, dealing with complete controllability problem for an ordinary differential system in infinite‐dimensional Banach space, are also less conservative than that in the previous literature. Copyright © 2012 John Wiley & Sons, Ltd.     

Approximate controllability of abstract stochastic impulsive systems with multiple time‐varying delays

This paper investigates the approximate controllability of abstract stochastic impulsive systems with multiple time‐varying delays. The class of stochastic impulsive systems consists of ordinary differential equations effected by impulse and noise environment. We focus first on constructing the control function. With this control function, we present sufficient conditions for approximate controllability problems in Hilbert space. The results are then extended to more easily verified conditions. The methods we choose are mainly Nussbaum fixed point theorem and stochastic analysis techniques combined with a strongly continuous semigroup. Finally, an example is given to illustrate the effectiveness of the results. Copyright © 2012 John Wiley & Sons, Ltd.     

Limited Computational Ability and Approximation of Dynamical Systems

This paper addresses problems due to approximation of dynamical systems. Theapproach presented here is based on the notion of the shadowing property ofa dynamical system and on the use of pseudotrajectories to approximate trueorbits. In particular, specific results in the case of attractors and thenotion of generalized shadowing are reviewed. The evidence described may berelevant for a wide range of economic models, whenever agents that havelimited computational ability, such as agents relying on digital computers,are concerned. The final section presents two sample applications to economicmodels.     

基于输出加微分反馈的广义二阶动力学系统跟踪设计

考虑了基于输出及其微分反馈的广义二阶动力学系统输出渐近跟踪设计．主要给出了如下结果： 广义二阶动力学系统基于输出及其微分反馈的特征结构配置;广义二阶动力学系统基于输出及其微分反馈的 输出渐近跟踪控制律存在的充分条件以及该控制律增益阵的完全参数化表达式．仿真结果说明本文所给出的 算法是有效的．     

An approximate inverse system for nonminimum-phase systems and its application to disturbance observer

This paper proposes an approximate inverse system for nonminimum-phase dynamical systems based on the least-square approximation method. The nonminimum-phase systems are approximated by minimum-phase systems. The proposed formulation is applied to the disturbance observation problems for multivariable nonminimum-phase systems with arbitrary relative degrees. The disturbances, which are assumed bounded, are the combination of the external disturbances, the nonlinearities and the model uncertainties of the system. The estimation error of the disturbances is controlled by the design parameters. Furthermore, the accuracy of the estimation also depends on the frequencies of the disturbances. Simulation results show the effectiveness of the proposed method.     

Controllability of non-linear impulsive stochastic systems

In this article, we consider the finite-dimensional dynamical control systems described by non-linear impulsive stochastic differential equations. Sufficient conditions for the complete and approximate controllability of non-linear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable.     

Nonlinearity-aware sub-model combination in trajectory based methods for nonlinear Mor

Trajectory based methods approximate nonlinear dynamical systems by superposition of dimensionally reduced linear systems. The linear systems are obtained by linearisations at multiple points along a state-trajectory. They are combined in a weighted sum and the combinations are switched appropriately to approximate the dynamic behaviour of the nonlinear system. Weights assigned at a specimen point on the trajectory generally depend on the euclidean distance to the linearisation points. In this work, limitations of the conventional weight-assignment scheme are pointed out. It is shown that the procedure is similar across all nonlinearities, and hence ignores the nonlinear vector field curvature for superposition. Additionally, it results in an inadequate assessment of the linear systems when they are equidistant from the specimen point. An improved method for weight-assignment, which uses state-velocities in addition to state-positions is proposed. The method naturally takes into account the system nonlinearity and is hence called Nonlinearity-aware Trajectory Piece-wise Linear (Ntpwl) method. Further, a computationally efficient procedure for estimating the state-velocity is introduced. The new strategy is illustrated and assessed with the help of case studies and it is shown that the Ntpwl model substantially improves the approximation of the nonlinear systems considered. Increased robustness to training and negligible stretching of the computational resources is also obtained.     

Second-order conditions for local controllability

This paper presents second-order (depending on the 2-jet) sufficient conditions for small time local controllability of affine smooth control systems, based on a very simple observation that can also lead to higher-order conditions; a second-order obstruction for a certain class of systems is also discussed, as is the gap between the obstruction and the sufficient condition. The new results are used for deciding local controllability of systems for which a direct application of the usual criteria is not conclusive.     

Controllability and observability of multi-agent systems with heterogeneous and switching topologies

ABSTRACT

This paper focuses on controllability and observability of multi-agent systems with heterogeneous and switching topologies, where the first- and the second-order information interaction topologies are different and switching. First, based on the controllable state set, a controllability criterion is obtained in terms of the controllability matrix corresponding to the switching sequence. Next, by virtue of the subspace sequence, two necessary and sufficient algebraic conditions are established for controllability in terms of the system matrices corresponding to all the possible topologies. Furthermore, controllability is considered from the graphic perspective. It is proved that the system is controllable if the union graph of all the possible topologies is controllable. With respect to observability, two sufficient and necessary conditions are derived by taking advantage of the system matrices and the corresponding invariant subspace, respectively. Finally, some simulation examples are worked out to illustrate the theoretical results.     

Hybrid dynamical systems: robust control synthesis problems

The paper presents a new approach to robust control synthesis problems for hybrid dynamical systems. The hybrid system under consideration is a composite of a continuous plant and a discrete event controller. State and output feedback problems are considered. The main results are given in terms of the existence of suitable solutions to a dynamic programming equation and a Riccati differential equation of the H^∞ filtering type. These results show a connection between the theories of hybrid dynamical systems and robust and nonlinear control.     

Controllability of Multi‐Agent Dynamical Systems with a Broadcasting Control Signal

This paper is concerned with the controllability of a multi‐agent dynamical system in which all identical first‐order dynamical agents receive a common exogenous control signal in addition to their inter‐agent communications. Existing graph theoretic results are used to determine conditions for controllability, and to study the dependency of controllability on the size of network and the number of connections. The fragility of controllability in the presence of hidden or broken connections is also investigated.