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Design procedures are proposed for two different classes of observers for systems with unknown inputs. In the first approach, the state of the observed system is decomposed into known and unknown components. The unknown component is a projection, not necessarily orthogonal, of the whole state along the subspace in which the available state component resides. Then, a dynamical system to estimate the unknown component is constructed. Combining the output of the dynamical system, which estimates the...
We consider the problem of state and parameter estimation for a class of nonlinear
oscillators defined as a system of coupled nonlinear ordinary differential equations.
Observable variables are limited to a few components of state vector and an input signal.
This class of systems describes a set of canonic models governing the dynamics of evoked
potential in neural membranes, including Hodgkin-Huxley, Hindmarsh-Rose, FitzHugh-Nagumo,
and Morris-Lecar...
The aim of this paper is to give the proofs of those results that in [4] were only announced, and, at the same time, to propose some possible developments, indicating some of the most significant open problems.
In this paper, we study the motion planning problem for generic sub-riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean [10, 11]), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic case, we study some non-generic generalizations in the analytic case.
In this paper, we study the motion planning problem for
generic sub-Riemannian metrics of co-rank one. We give explicit
expressions for the metric complexity (in the sense of Jean
[CITE]), in terms of the elementary invariants of
the problem. We construct asymptotic optimal syntheses. It turns out
that among the results we show, the most complicated case is the
3-dimensional. Besides the generic C∞ case, we study some
non-generic generalizations in the analytic case.
We deal with the problems of four boundary points conditions for both differential inclusions and differential equations with and without moving constraints. Using a very recent result we prove existence of generalized solutions for some differential inclusions and some differential equations with moving constraints. The results obtained improve the recent results obtained by Papageorgiou and Ibrahim-Gomaa. Also by means of a rather different approach based on an existence theorem due to O. N. Ricceri...
We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.
In questa Nota si continua la discussione iniziata in [4] dell'esistenza di soluzioni ottimali per problemi di ottimo controllo in . Si definiscono problemi generalizzati, e si ottengono estensioni di risultati già presentati in [4]. Si dimostrano anche varie relazioni tra le soluzioni ottimali dei problemi generalizzati e i problemi originali e non convessi di ottimo controllo. Alla fine si considerano problemi lineari nelle variabili di stato anche nel caso di costi funzionali a valori vettoriali...
This paper deals with a multiobjective control problem for nonlinear discrete time systems. The problem consists of finding a control strategy which minimizes a number of performance indexes subject to state and control constraints. A solution to this problem through the Receding Horizon approach is proposed. Under standard assumptions, it is shown that the resulting control law guarantees closed-loop stability. The proposed method is also used to provide a robustly stabilizing solution to the problem...
Let be a smooth connected complete manifold of dimension , and be a smooth nonholonomic distribution of rank on . We prove that if there exists a smooth Riemannian metric on1for which no nontrivial singular path is minimizing, then there exists a smooth repulsive stabilizing section of on . Moreover, in dimension three, the assumption of the absence of singular minimizing horizontal paths can be dropped in the Martinet case. The proofs are based on the study, using specific results of...
In this paper, we look at a model depicting the relationship of cancer cells in different
development stages with immune cells and a cell cycle specific chemotherapy drug. The
model includes a constant delay in the mitotic phase. By applying optimal control theory,
we seek to minimize the cost associated with the chemotherapy drug and to minimize the
number of tumor cells. Global existence of a solution has been shown for this model and
existence...
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