Constrained Controllability of Nonlinear Systems (original) (raw)

Controllability of Nonlinear Systems

2000

In the paper, infinite-dimensional, continuous-time control systems described by nonlinear abstract differential equations are considered. Using methods of functional analysis sufficient conditions for constrained exact local controllability are formulated and proved. It is generally assumed that the values of controls are in a convex and closed cone with vertex at zero. Illustrative examples are also given. Moreover, some remarks and

Local constrained controllability of second order dynamical systems with delay

2011 16th International Conference on Methods & Models in Automation & Robotics, 2011

The paper considers finite-dimensional dynamical control systems described by second order semilinear stationary ordinary differential state equations with delay in control. Using a generalized open mapping theorem, sufficient conditions for constrained local controllability in a given time interval are formulated and proved. These conditions require verification of constrained global controllability of the associated linear first-order dynamical control system. It is generally assumed that the values of admissible controls are in a convex and closed cone with vertex at zero. Moreover, several remarks and comments on the existing results for controllability of semilinear dynamical control systems are also presented. Finally, a simple numerical example which illustrates theoretical considerations is also given. It should be pointed out that the results given in the paper extend for the case of semilinear second-order dynamical systems constrained controllability conditions, which were previously known only for linear second-order systems.

Controllability of nonlinear systems with multiple delays

Proceedings of 2011 International Conference on Modelling, Identification and Control, 2011

In the present paper local constrained controllability problems for nonlinear system with constant delays in the control are formulated and discussed. Using some mapping theorems taken from functional analysis and linear approximation methods sufficient conditions for relative and absolute local constrained controllability in a given time interval are derived and proved. The present paper extends controllability conditions with unconstrained controls given in the literature to cover the case of nonlinear systems with delays in control and with constrained controls.

Constrained controllability of semilinear systems

Nonlinear Analysis: Theory, Methods & Applications, 2001

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 a semilinear hyperbolic type distributed parameter dynamical system is solved in details. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.

Constrained controllability of semilinear systems with variable delay in control”

2006

Abstract. In the present paper finite-dimensional dynamical control systems described by semilinear ordinary differential state equations with multiple point delays in control are considered. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Using so-called generalized open mapping theorem, sufficient conditions for constrained local relative controllability near the origin are formulated and proved. Roughly speaking, it will be proved that under suitable assumptions constrained global relative controllability of a linear associated approximated dynamical system implies constrained local relative controllability near the origin of the original semilinear dynamical system. This is generalization to the constrained controllability case some previous results concerning controllability of linear dynamical systems with multiple point delays in the control and with unconstrained controls. Moreover, necessary and sufficient...

Constrained controllability of semilinear systems with delayed controls

2000

In the present paper finite-dimensional dynamical control systems described by semilinear ordinary differential state equations with multiple point delays in control are considered. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Using so-called generalized open mapping theorem, sufficient conditions for constrained local relative controllability near the origin

Controllability of delayed dynamical systems

IFAC Proceedings Volumes, 1999

The main purpose of the present paper is to study the concept of constrained approximate relative and approximate absolute controllability for linear stationary abstract delayed dynamical systems defined in infinite-dimensional Hilbert spaces. It is generally assumed, that the admissible controls are nonnegative square integrable functions. Using the methods taken from the spectral theory of linear unbounded operators necessary and sufficient conditions for constrained approximate relative controllability are formulated and proved. These conditions are generalization for infinite-dimensional delayed dynamical systems the results derived recently for finitedimensional dynamical systems with delays. Finally, as the simple illustrative examples, necessary and sufficient conditions for constrained approximate relative controllability with nonnegative controls for delayed distributed parameter parabolic type dynamical systems with constant delays and \vith homogeneous Dirichlet boundary conditions are presented.

Controllability of Infinite-Dimensional Systems with Delays in Control

1980

T his p a p e r considers th e vario u s types of co n tro llab ility of lin e a r infinite-dim ensional d ynam ical system s defined in a B an ach space, w ith m u ltip le tim e-v ary in g delays in control. N ecessary an d su fficien t conditions fo r ap p ro x im a ­ te co n tro llab ility , ap p ro x im ate re la tiv e co n tro llab ility an d ap p ro x im ate absolute- co n tro llab ility of th ese system s a re obtained. S pecial cases of system s defined in a H ilb e rt space a re also considered.

Existence and Uniqueness for the Controllability of a Dynamical System

Academic Journal of Applied Mathematical Sciences, 2019

In this paper, we consider the existence and uniqueness for the controllability of a dynamical system. Here, measure of non-compactness of set was employed to examine the conditions for darbo’s fixed point theorem which is used to established the existence and uniqueness solution for nonlinear integro-differential equation with implicit derivatives.