159 research outputs found
Robust stabilization of nonlinear systems via stable kernel representations with L2-gain bounded uncertainty
The approach to robust stabilization of linear systems using normalized left coprime factorizations with H∞ bounded uncertainty is generalized to nonlinear systems. A nonlinear perturbation model is derived, based on the concept of a stable kernel representation of nonlinear systems. The robust stabilization problem is then translated into a nonlinear disturbance feedforward H∞ optimal control problem, whose solution depends on the solvability of a single Hamilton-Jacobi equation
An example of interplay between Physics and Mathematics: Exact resolution of a new class of Riccati Equations
A novel recipe for exactly solving in finite terms a class of special
differential Riccati equations is reported. Our procedure is entirely based on
a successful resolution strategy quite recently applied to quantum dynamical
time-dependent SU(2) problems. The general integral of exemplary differential
Riccati equations, not previously considered in the specialized literature, is
explicitly determined to illustrate both mathematical usefulness and easiness
of applicability of our proposed treatment. The possibility of exploiting the
general integral of a given differential Riccati equation to solve an SU(2)
quantum dynamical problem, is succinctly pointed out.Comment: 10 page
A Result on Output Feedback Linear Quadratic Control
In this note we consider the static output feedback linear quadratic control problem.We present both necessary and sufficient conditions under which this problem has a solution in case the involved cost depend only on the output and control variables.This result is used to present both necessary and sufficient conditions under which the corresponding linear quadratic differential game has a Nash equilibrium in case the players use static output feedback control.LQ theory;Algebraic Riccati equations;Differential games
Grassmannian flows and applications to nonlinear partial differential equations
We show how solutions to a large class of partial differential equations with
nonlocal Riccati-type nonlinearities can be generated from the corresponding
linearized equations, from arbitrary initial data. It is well known that
evolutionary matrix Riccati equations can be generated by projecting linear
evolutionary flows on a Stiefel manifold onto a coordinate chart of the
underlying Grassmann manifold. Our method relies on extending this idea to the
infinite dimensional case. The key is an integral equation analogous to the
Marchenko equation in integrable systems, that represents the coodinate chart
map. We show explicitly how to generate such solutions to scalar partial
differential equations of arbitrary order with nonlocal quadratic
nonlinearities using our approach. We provide numerical simulations that
demonstrate the generation of solutions to
Fisher--Kolmogorov--Petrovskii--Piskunov equations with nonlocal
nonlinearities. We also indicate how the method might extend to more general
classes of nonlinear partial differential systems.Comment: 26 pages, 2 figure
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