In this article, we give a necessary and sufficient condition of Kalman type for the indirect controllability of systems of groups of linear operators, under some “regularity and locality” conditions on the control operator that will be made precise later and fit very well the case of distributed controls. Moreover, in the case of first order in time systems, when the Kalman rank condition is n...

Optimal feedback control is classically based on linear approximations, whose accuracy drops off rapidly in highly nonlinear dynamics. A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows the dependency of the spacecraft state on initial conditions and environmental p...

The behavior of the run of an impulse differential inclusion, and, in particular, of a hybrid control system, is “summarized” by the “ initialization map” associating with each initial condition the set of new initialized conditions and more generally, by its “substratum”, that is a set-valued map associating with a cadence and a state the next reinitialized state. These maps are characterized ...

The notion of output-input stability, recently proposed in [2], represents a variant of the minimum-phase property for general smooth nonlinear control systems. In the spirit of the input-to-state stability (ISS) philosophy, the definition of output-input stability requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, mo...

Basins of attraction are instrumental to study the effect of input saturation in control systems, as these sets characterise the initial conditions for which the control strategy induces attraction to the desired equilibrium. In this paper, we describe these sets when the open-loop system is exponentially unstable and the system is controlled by a single actuator with both constant time-delays ...

In this paper, we consider an optimal control problem for a linear infinite order hyperbolic system. One from the initial conditions is given by control function. Sufficient conditions for the existence of a unique solution of such hyperbolic equations with the Dirichlet boundary conditions are presented. The performance functional has the quadratic form. The time horizon T is fixed. Finally, w...

(1.1) x(i+ 1) = g(x(i),u(i), i) , with initial condition x(i1) = x at time i1. Here g(x(i),u(i), i) is a random variable with known probability distribution determined by the values of (x(i),u(i), i). Thus we have a set of random variables g(x,u, i) for all possible values of the variables x ∈ R, u ∈ R, i ∈ Z. The process determined by (1.1) is clearly Markovian. For the cost function we take t...

The output behavior of a nonlinear control system depends not only on its input but also on its initial conditions. These two factors have to be considered simultaneously in nonlinear systems design. This paper presents a new definition, called dynamic right factorization, for nonlinear dynamic control systems. This factorization takes the initial conditions as well as the system input into acc...

The problem of closed-loop control of maneuvers between two states for linear dynamical systems, subject to an arbitrarily specified terminal state, is considered. The feedback controller design is based on finite-time quadratic regulator theory. Closed-form expressions for the optimal control law are developed. Solutions are presented for both conventional and smoothed control profiles with fi...

4 Pore fluid chlorinity/salinity data from deep-sea cores related to the salinity maximum 5 of the last glacial maximum (LGM) are analyzed using estimation methods deriving from 6 linear control theory. With conventional diffusion coefficient values and no vertical advection, 7 results show a very strong dependence upon initial conditions at -100 ky. Earlier inferences 8 that the abyssal Southe...