Sufficient Conditions For Local Controllability Research Articles

Local controllability and semigroups of diffeomorphisms

The local structure of orbits of semigroups, generated by families of diffeomorphisms, is studied by Lie theory methods. New sufficient conditions for local controllability are obtained which take into account ordinary, as well as fast-switching variations.

A sufficient condition for local controllability of nonlinear systems along closed orbits

A computable sufficient condition for determining local controllability of a differential nonlinear control system along a reference closed orbit is presented. Comparisons to other results on local controllability along a reference trajectory are made.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

SYMPLECTIC GEOMETRY AND NECESSARY CONDITIONS FOR OPTIMALITY

With the help of a symplectic technique the concept of a field of extremals in the classical calculus of variations is generalized to optimal control problems. This enables us to get new optimality conditions that are equally suitable for regular, bang-bang, and singular extremals. Special attention is given to systems of the form with a scalar control. New pointwise conditions for optimality and sufficient conditions for local controllability are obtained as a consequence of the general theory.

Linear control systems with additive disturbances: constrained controllability to a subset

The paper studies constrained controllability to a subset of linear discrete-time systems with additive disturbances. Several necessary and sufficient conditions for local controllability to a subset of linear infinite-dimensional systems with constraints on both control and state are given. The results are applied to study the pursuit problem in linear discrete-time game

An application of implicit function theorems to controllability problems of nonstationary discrete-time systems

Pshenichnyi's implicit function theorem for multivalued mappings is applied to controllability problems for some classes of nonstationary discrete-time systems. New necessary and sufficient conditions of local controllability are obtained for linear discrete-time systems with control constraints.

Graded Approximations and Controllability Along a Trajectory

Graded approximations of an affine control system are defined and their properties are investigated. In particular, it is proved that the local controllability along a reference trajectory of an approximating system implies the local controllability along the corresponding reference trajectory of the original system. Using graded approximations, sufficient conditions of local controllability along a reference trajectory that generalize some known results are given.

Decomposition of the Roesser model and new conditions for local controllability and local observability

Abstract It is shown that the Roesser model (satisfying rank conditions (9)) can be de- composed into two equivalent one-dimensional systems having dynamics in different directions connected in a feedback system. For this class of Roesser models of two- dimensional systems, new necessary and sufficient conditions for local controllability and local observability are established.

Decomposition of the Roesser model and new conditions for local controllability and local observability

Abstract It is shown that the Roesser model (satisfying rank conditions (9)) can be de- composed into two equivalent one-dimensional systems having dynamics in different directions connected in a feedback system. For this class of Roesser models of two- dimensional systems, new necessary and sufficient conditions for local controllability and local observability are established.

On local controllability of nondifferentiame discrete-time system with nonconvex constraints on controls

In this paper a sufficient condition for local controllability of discrete-time systems of the following form will be established: where are closed subsets of are locally-Lipschitz functions. Some corollaries including a controllability condition for linear discrete-time systems with nonconvex constraints on controls are also obtained.

Controllability of nonlinear discrete systems without differentiability assumption

The paper gives another approach to studying controllability of nonlinear discrete systems, which is based on proving the support principle for some boundary problems involving locally Lipschitzian set-valued maps. The approach enables us to develop sufficient conditions for various types of local controllability of nonlinear non-stationary discrete systems without differentiability assumption. For linear discrete systems with constrained states and controls, necessary and sufficient conditions for local controllability are given.

Sufficient Conditions for Local Controllability with Unbounded Controls

Local controllability of analytic affine control systems $\Sigma $ with an arbitrary number of controls is studied, without any restriction on the dimension of the Lie algebra ${\bf T}'$ generated by the input vector fields.A sufficient condition for local controllability at a point is obtained, first for scalar input systems and then generalized in two different ways to the multi-input case. In all versions, this involves the computation of Lie brackets at the point under consideration and the verification of a criterion of the type considered by Sussmann (this Journal, 16 (1978), pp. 790–802).As an application, controllability of systems defined on $\mathbb{R}^n $ and with constant input vector fields is studied.

New necessary and sufficient conditions for local controllability and local observability of 2-D separable denominator systems

New necessary and sufficient conditions for local controllability and observability of 2-D separable denominator systems (SDS's) are presented on the basis of the reduced-dimensional decomposition of 2-D SDS's. It is proved that local controllability of a 2-D SDS is equivalent to controllability of two 1-D systems which are a special decomposition pair of the 2-D SDS. Furthermore, local observability of a 2-D SDS is equivalent to a full rank condition of the coefficient matrices of the 2-D SDS in addition to observability of two 1-D systems which are another special decomposition pair of the 2-D SDS. Thus, these new conditions which use only 1-D controllability matrices, 1-D observability matrices, and coefficient matrices of the 2-D SDS are much simpler than any previous conditions which use complex 2-D controllability and observability matrices.

A General Theorem on Local Controllability

We prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point. Earlier results of Brunovsky, Hermes, Jurdjevic, Crouch and Byrnes, Sussmann and Grossmann, are shown to be particular cases of this result. Also, a number of new sufficient conditions are obtained. All these results follow from one simple general principle, namely, that local controllability follows whenever brackets with certain symmetries can be “neutralized,” in a suitable way, by writing them as linear combinations of brackets of a lower degree. Both the class of symmetries and the definition of “degree” can be chosen to suit the problem.

Minimum energy control of 2-D linear systems with variable coefficients

The definition of the state-transition matrix for Roesser's model of 2-D systems with variable coefficients is introduced and the general response formula is derived. Necessary and sufficient conditions for local controllability are formulated. The minimum energy control problem for Roesser's model of 2-D systems with variable coefficients is formulated and solved.

Controllability of piecewise linear systems

The paper deals with a discontinuous control system that consists of two finite-dimensional linear systems; the first describes the motion in a given half-space, the second in the complementary half-space. Necessary and sufficient conditions for local controllability are obtained.

Local controllability of nonlinear systems

The local controllability of control systems with an arbitrary number of controls is considered, first on an open set and then at a given point; necessary conditions are derived concerning the Lie algebra T′ generated by the input vector fields, and applied to gradient systems. The main results are a geometric sufficient condition for local controllability at a point, and an equivalent condition based on the computation of Lie brackets, assuming T′ to be ( n − 1)-dimensional.

A note on the controllability of nonlinear systems

In this paper a question of the controllability of nonlinear systems is considered. On the basis of theorems due to Graves, a new sufficient condition for local controllability is established.

Local Controllability and Bilinearization

In this paper a sufficient condition for local controllability of a finite family of analytic vector fields is established. This condition is stable under second order perturbations of the vector fields.

Local controllability of multivalued differential equations

In this paper we give sufficient conditions for local controllability of multivalued differential equations. Some results are obtained without the assumption that the origin is an interior point of the multivalued function. From these, we give sufficient conditions for the local controllability of certain classes of nonlinear control systems where the control appear linearly.

A Sufficient Condition for Local Controllability

A system S of vector fields is locally controllable at point p if, for every positive time t, the set of points reachable from p by an S-trajectory in time $ \leqq t$ contains p in its interior. Let K be the convex hull of the values $X(p)$ of those $X \in S$ for which $X(p) \ne 0$. It is well known that S is l.c. at p if $0 \in \operatorname{interior} (K)$, and that S is not l.c. at p if $0 \notin K$. We prove that these are the only cases in which it is possible to determine if S is l.c. at p by just looking at the values at p of the elements of S. We prove a sufficient condition for local controllability which gives new information for the case when $0 \in K$ but $0 \notin \operatorname{interior}(K)$.