Effective, simulation-based trajectory optimization algorithms adapted to heterogeneous computers are studied with reference to the problem taken from alpine ski racing (the presented solution is probably the most general one published so far). The key idea behind these algorithms is to use a grid-based discretization scheme to transform the continuous optimization problem into a search problem over a specially constructed finite graph, and then to apply dynamic programming to find an approximation...

We prove the continuity and the Hölder equivalence w.r.t. an Euclidean distance of the value function associated with the L1 cost of the control-affine system q̇ = f0(q) + ∑j=1m ujfj(q), satisfying the strong Hörmander condition. This is done by proving a result in the same spirit as the Ball–Box theorem for driftless (or sub-Riemannian) systems. The techniques used are based on a reduction of the control-affine system to a linear but time-dependent one, for which we are able to define a generalization...

This paper is concerned with the construction of local observers for nonlinear systems without inputs, satisfying an observability rank condition. The aim of this study is, first, to define an homogeneous approximation that keeps the observability property unchanged at the origin. This approximation is further used in the synthesis of a local observer which is proven to be locally convergent for Lyapunov-stable systems. We compare the performance of the homogeneous approximation observer with the...

We are concerned with the asymptotic analysis of optimal control problems for $1$-D partial differential equations defined on a periodic planar graph, as the period of the graph tends to zero. We focus on optimal control problems for elliptic equations with distributed and boundary controls. Using approaches of the theory of homogenization we show that the original problem on the periodic graph tends to a standard linear quadratic optimal control problem for a two-dimensional homogenized system, and...

We are concerned with the asymptotic analysis of optimal control problems for 1-D partial differential equations defined on a periodic planar graph, as the period of the graph tends to zero. We focus on optimal control problems for elliptic equations with distributed and boundary controls. Using approaches of the theory of homogenization we show that the original problem on the periodic graph tends to a standard linear quadratic optimal control problem for a two-dimensional homogenized system,...

We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary conditions depend on parameters ε, α, β and the...

We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...

We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...

A four-dimensional hyperchaotic Lü system with multiple time-delay controllers is considered in this paper. Based on the theory of Hopf bifurcation in delay system, we obtain a simple relationship between the parameters when the system has a periodic solution. Numerical simulations show that the assumption is a rational condition, choosing parameter in the determined region can control hyperchaotic Lü system well, the chaotic state is transformed to the periodic orbit. Finally, we consider the differences...

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.

HIV infection is multi-faceted and a multi-step process. The virus-induced pathogenic mechanisms are manifold and mediated through a range of positive and negative feedback regulations of immune and physiological processes engaged in virus-host interactions. The fundamental questions towards understanding the pathogenesis of HIV infection are now shifting to ‘dynamic’ categories: (i) why is the HIV-immune response equilibrium finally disrupted? (ii)...

The paper proposes a design procedure for the creation of a robust and effective hybrid algorithm, tailored to and capable of carrying out a given design optimisation task. In the course of algorithm creation, a small set of simple optimisation methods is chosen, out of which those performing best will constitute the hybrid algorithm. The simplicity of the method allows implementing ad-hoc modifications if unexpected adverse features of the optimisation problem are found. It is postulated to model...