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Motion planning, i.e., steering a system from one state to another, is a basic question in automatic control. For a certain class of systems described by ordinary differential equations and called flat systems (Fliess et al. 1995; 1999a), motion planning admits simple and explicit solutions. This stems from an explicit description of the trajectories by an arbitrary time function, the flat output, and a finite number of its time derivatives. Such explicit descriptions are related to old problems...
The problem of invariant output tracking is considered: given a control system admitting a symmetry group , design a feedback such that the closed-loop system tracks a desired output reference and is invariant under the action of . Invariant output errors are defined as a set of scalar invariants of ; they are calculated with the Cartan moving frame method. It is shown that standard tracking methods based on input-output linearization can be applied to these invariant errors to yield the required...
The problem of invariant output tracking is considered: given a control system
admitting a symmetry group , design a feedback such that the
closed-loop system tracks a desired output reference and is invariant under the action of .
Invariant output errors are defined as a set
of scalar invariants of ; they are calculated with the Cartan moving frame
method. It is shown that standard tracking methods based on input-output linearization can be applied to
these invariant errors to yield the...
In this paper we consider a free boundary problem for a nonlinear parabolic partial differential equation. In particular, we are concerned with the inverse problem, which means we know the behavior of the free boundary a priori and would like a solution, e.g. a convergent series, in order to determine what the trajectories of the system should be for steady-state to steady-state boundary control. In this paper we combine two issues: the free boundary (Stefan) problem with a quadratic nonlinearity....
We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman's controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra which suits well to the fact that, in accordance with Willems' standpoint, flatness and defect are best defined without...
In this paper we consider a free boundary problem for a nonlinear
parabolic partial differential equation. In particular, we are
concerned with the inverse problem, which means we know the
behavior of the free boundary and would like a solution,
a convergent series, in order to determine what the
trajectories of the system should be for steady-state to
steady-state boundary control. In this paper we combine two
issues: the free boundary (Stefan) problem with a quadratic
nonlinearity. We prove...
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