77 research outputs found
Control systems of zero curvature are not necessarily trivializable
A control system is said to be trivializable if there
exists local coordinates in which the system is feedback equivalent to a
control system of the form . In this paper we characterize
trivializable control systems and control systems for which, up to a feedback
transformation, and commute. Characterizations are
given in terms of feedback invariants of the system (its control curvature and
its centro-affine curvature) and thus are completely intrinsic. To conclude we
apply the obtained results to Zermelo-like problems on Riemannian manifolds
Microlocal normal forms for regular fully nonlinear two-dimensional control systems
In the present paper we deal with fully nonlinear two-dimensional smooth
control systems with scalar input \dot{q} = \bs{f}(q,u), , , where and are differentiable smooth manifolds of respective
dimensions two and one. For such systems, we provide two microlocal normal
forms, i.e., local in the state-input space, using the fundamental necessary
condition of optimality for optimal control problems: the Pontryagin Maximum
Principle. One of these normal forms will be constructed around a regular
extremal and the other one will be constructed around an abnormal extremal.
These normal forms, which in both cases are parametrized only by one scalar
function of three variables, lead to a nice expression for the control
curvature of the system. This expression shows that the control curvature, a
priori defined for normal extremals, can be smoothly extended to abnormals
Luenberger observers for discrete-time nonlinear systems
In this paper, we consider the problem of designing an asymptotic observer for a nonlin-ear dynamical system in discrete-time following Luenberger's original idea. This approach is a two-step design procedure. In a first step, the problem is to estimate a function of the state. The state estimation is obtained by inverting this mapping. Similarly to the continuous-time context, we show that the first step is always possible provided a linear and stable discrete-time system fed by the output is introduced. Based on a weak observ-ability assumption, it is shown that picking the dimension of the stable auxiliary system sufficiently large, the estimated function of the state is invertible. This approach is illustrated on linear systems with polynomial output. The link with the Luenberger observer obtained in the continuous-time case is also investigated
Avoiding observability singularities in output feedback bilinear systems
Control-affine output systems generically present observability singularities, i.e. inputs that make the system unobservable. This proves to be a difficulty in the context of output feedback stabilization, where this issue is usually discarded by uniform observability assumptions for state feedback stabilizable systems. Focusing on state feedback stabilizable bilinear control systems with linear output, we use a transversality approach to provide perturbations of the stabilizing state feedback law, in order to make our system observable in any time even in the presence of singular inputs
Generalized Lyapunov conditions for k-contraction: analysis and feedback design
Recently, the concept of k-contraction has been introduced as a promising
generalization of contraction for dynamical systems. However, the study of
k-contraction properties has faced significant challenges due to the reliance
on complex mathematical objects called matrix compounds. As a result, related
control design methodologies have yet to appear in the literature. In this
paper, we overcome existing limitations and propose new sufficient conditions
for k-contraction which do not rely on matrix compounds. Our design-oriented
conditions stem from a strong geometrical interpretation and establish a
connection between kcontraction and p-dominance. Notably, these conditions are
also necessary in the linear time-invariant framework. Leveraging on these
findings, we propose a feedback design methodology for both the linear and the
nonlinear scenarios
Dynamic Output Feedback Stabilization of Non-uniformly Observable Dissipative Systems
Output feedback stabilization of control systems is a crucial issue in engineering. Most of these systems are not uniformly observable, which proves to be a difficulty to move from state feedback stabilization to dynamic output feedback stabilization. In this paper, we present a methodology to overcome this challenge in the case of dissipative systems by requiring only target detectability. These systems appear in many physical systems and we provide various examples and applications of the result
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