Symmetric piecewise linear bi-dimensional systems are very common in control engineering. They constitute a class of non-differentiable vector fields for which classical Hopf bifurcation theorems are not applicable. For such systems, sufficient and necessary conditions for bifurcation of a limit cycle from the periodic orbit at infinity are given.

This paper is devoted to the general problem of reconstructing the cost from the observation of trajectories, in a problem of optimal control. It is motivated by the following applied problem, concerning HALE drones: one would like them to decide by themselves for their trajectories, and to behave at least as a good human pilot. This applied question is very similar to the problem of determining what is minimized in human locomotion. These starting points are the reasons for the particular classes...

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...