We consider a system which is assumed to be affected by an expanding disturbance which occurs at the initial time. The compensation of the disturbance is accomplished by extending the concept of remediability to a class of nonlinear systems. The results are implemented and illustrated with a nonlinear distributed model.

Let $A_0$ be a possibly unbounded positive operator on the Hilbert space $H$, which is boundedly invertible. Let $C_0$ be a bounded operator from $𝒟\left(A_0^{\frac{1}{2}}\right)$ to another Hilbert space $U$. We prove that the system of equations$$\ddot{z}\left(t\right)+A_{0}z\left(t\right)+\frac{1}{2}{C}_0^{*}{C}_0\dot{z}\left(t\right)=C_0^{*}u\left(t\right)$$$$y\left(t\right)...$$

Let A0 be a possibly unbounded positive operator on the Hilbert space H, which is boundedly invertible. Let C0 be a bounded operator from $𝒟\left(A_0^{\frac{1}{2}}\right)$ to another Hilbert space U. We prove that the system of equations $$\ddot{z}\left(t\right)+A_{0}z\left(t\right)+\frac{1}{2}{C}_0^{*}{C}_0\dot{z}\left(t\right)=C_0^{*}u\left(t\right)$$$$y\left(t\right)...$$

The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: ${\displaystyle \underset{{\displaystyle (u,v)\in {𝒰}_{ad}}}{inf}{\int }_0^{1}f\left(t,u\left({\theta }_v\left(t\right)\right),u^{\text{'}}\left(t\right),v\left(t\right)\right)\mathrm{d}t}$, (1) where ${𝒰}_{ad}$ is a set of admissible controls and ${\theta }_v$ is the solution of the following equation: $\{\frac{\mathrm{d}\theta \left(t\right)}{\mathrm{d}t}=g(t,\theta \left(t\right),v\left(t\right)),t\in [0,1]$ ; ${\displaystyle \theta \left(0\right)={\theta }_0,\theta \left(t\right)\in [0,1]\forall t}$. (2). The results are nonlocal and new.

We consider stabilizing a discrete-time LTI (linear time-invariant) system via state feedback where both the quantized state and control input signals are involved. The system under consideration is stabilizable and stabilizing state feedback has been designed without considering quantization, but the system's stability is not guaranteed due to the quantization effect. For this reason, we propose a hybrid quantized state feedback strategy asymptotically stabilizing the system, where the values of...

Haar's Lemma (1918) deals with the algebraic characterization of the inclusion of polyhedral sets. This Lemma has been involved many times in automatic control of linear dynamical systems via positive invariance of polyhedrons. More recently, it has been used to characterize stochastic comparison w.r.t. linear/integral ordering of Markov (reward) chains. In this paper we develop a state space oriented approach to the control of Discrete Event Systems (DES) based on the remark that most of control...

We study the identification of the nonlinearities A,(→)b and c appearing in the quasilinear parabolic equation y_t − div(A(y)∇y + (→)b(y)) + c(y) = u inΩ × (0,T), assuming that the solution of an associated boundary value problem is known at the terminal time, y(x,T), over a (probably small) subset of Ω, for each source term u. Our work can be divided into two parts. Firstly, the uniqueness of A,(→)b and c is proved under appropriate assumptions. Secondly, we consider a finite-dimensional optimization...