Radiality and semismoothness
Reachability and minimum energy control of positive 2D systems with delays
Receding horizon optimal control for infinite dimensional systems
The receding horizon control strategy for dynamical systems posed in infinite dimensional spaces is analysed. Its stabilising property is verified provided control Lyapunov functionals are used as terminal penalty functions. For closed loop dissipative systems the terminal penalty can be chosen as quadratic functional. Applications to the Navier–Stokes equations, semilinear wave equations and reaction diffusion systems are given.
Receding horizon optimal control for infinite dimensional systems
The receding horizon control strategy for dynamical systems posed in infinite dimensional spaces is analysed. Its stabilising property is verified provided control Lyapunov functionals are used as terminal penalty functions. For closed loop dissipative systems the terminal penalty can be chosen as quadratic functional. Applications to the Navier–Stokes equations, semilinear wave equations and reaction diffusion systems are given.
Reconfigurable control design with integration of a reference governor and reliability indicators
A new approach to manage actuator redundancy in the presence of faults is proposed based on reliability indicators and a reference governor. The aim is to preserve the health of the actuators and the availability of the system both in the nominal behavior and in the presence of actuator faults. The use of reference governor control allocation is a solution to distribute the control efforts among a redundant set of actuators. In a degraded situation, a reconfigured control allocation strategy is...
Regional control problem for distributed bilinear systems: Approach and simulations
This paper investigates the regional control problem for infinite dimensional bilinear systems. We develop an approach that characterizes the optimal control and leads to a numerical algorithm. The obtained results are successfully illustrated by simulations.
Regular syntheses and solutions to discontinuous ODEs
In this paper we analyze several concepts of solution to discontinuous ODEs in relation to feedbacks generated by optimal syntheses. Optimal trajectories are called Stratified Solutions in case of regular synthesis in the sense of Boltyanskii–Brunovsky. We introduce a concept of solution called Krasowskii Cone Robust that characterizes optimal trajectories for minimum time on the plane and for general problems under suitable assumptions.
Regular syntheses and solutions to discontinuous ODEs
In this paper we analyze several concepts of solution to discontinuous ODEs in relation to feedbacks generated by optimal syntheses. Optimal trajectories are called Stratified Solutions in case of regular synthesis in the sense of Boltyanskii-Brunovsky. We introduce a concept of solution called Krasowskii Cone Robust that characterizes optimal trajectories for minimum time on the plane and for general problems under suitable assumptions.
Regular time-optimal syntheses for smooth planar systems
Régularité du problème de Kelvin–Helmholtz pour l’équation d’Euler 2D
Nous prouvons que pour toute solution du problème de Kelvin–Helmholtz des nappes de tourbillons pour l’équation d’Euler bi-dimensionnelle, définie localement en temps, la courbe de saut de et la densité de tourbillon sont analytiques (sous une hypothèse de régularité Holderienne de la courbe de saut). Nous donnons également un résultat de régularité partielle de la trace de sur lorsque est définie sur un demi-interval .
Régularité du problème de Kelvin-Helmholtz pour l’équation d’Euler 2d
Régularité du problème de Kelvin–Helmholtz pour l'équation d'Euler 2d
Nous prouvons que pour toute solution u du problème de Kelvin–Helmholtz des nappes de tourbillons pour l'équation d'Euler bi-dimensionnelle, définie localement en temps, la courbe de saut de u et la densité de tourbillon sont analytiques (sous une hypothèse de régularité Holderienne de la courbe de saut). Nous donnons également un résultat de régularité partielle de la trace de u sur t=0 lorsque u est définie sur un demi-interval [O,T[.
Regularity along optimal trajectories of the value function of a Mayer problem
We consider an optimal control problem of Mayer type and prove that, under suitable conditions on the system, the value function is differentiable along optimal trajectories, except possibly at the endpoints. We provide counterexamples to show that this property may fail to hold if some of our conditions are violated. We then apply our regularity result to derive optimality conditions for the trajectories of the system.
Regularity along optimal trajectories of the value function of a Mayer problem
We consider an optimal control problem of Mayer type and prove that, under suitable conditions on the system, the value function is differentiable along optimal trajectories, except possibly at the endpoints. We provide counterexamples to show that this property may fail to hold if some of our conditions are violated. We then apply our regularity result to derive optimality conditions for the trajectories of the system.
Regularity and stability of optimal controls of nonstationary Navier-Stokes equations
Regularity and variationality of solutions to Hamilton-Jacobi equations. Part I : regularity
We formulate an Hamilton-Jacobi partial differential equationon a dimensional manifold , with assumptions of convexity of and regularity of (locally in a neighborhood of in ); we define the “min solution” , a generalized solution; to this end, we view as a symplectic manifold. The definition of “min solution” is suited to proving regularity results about ; in particular, we prove in the first part that the closure of the set where is not regular may be covered by a countable number...
Regularity and variationality of solutions to Hamilton-Jacobi equations. Part I: Regularity
We formulate an Hamilton-Jacobi partial differential equation H( x, D u(x))=0 on a n dimensional manifold M, with assumptions of convexity of H(x, .) and regularity of H (locally in a neighborhood of {H=0} in T*M); we define the “minsol solution” u, a generalized solution; to this end, we view T*M as a symplectic manifold. The definition of “minsol solution” is suited to proving regularity results about u; in particular, we prove in the first part that the closure of the set where...
Regularity at the free boundary of two-dimensional stationary harmonic maps
Regularity for degenerate elliptic problems via p-harmonic approximation
Regularity for minimizers of functionals with variable growth and discontinuous coefficients
Based on the theory of variable exponent spaces, we study the regularity of local minimizers for a class of functionals with variable growth and discontinuous coefficients. Under suitable assumptions, we obtain local Hölder continuity of minimizers.