The concentration-compactness principle in the calculus of variations. The locally compact case, part 1
The Euler derivative. An intrinsic approach to the calculus of variations.
The existence of gaps in minimal foliations.
The existence theorem for one class of optimal problems in Banach space.
The gradient projection method for solving an optimal control problem
A gradient method for solving an optimal control problem described by a parabolic equation is considered. The gradient projection method is applied to solve the problem. The convergence of the projection algorithm is investigated.
The linear-quadratic optimal control problem for delay differential equations
In questo lavoro si considera il problema del controllo ottimo per un'equazione lineare con ritardo in uno spazio di Hilbert, con costo quadratico. Si dimostra che il problema della sintesi si traduce in una equazione di Riccati in uno opportuno spazio prodotto e si prova che tale equazione ammette un’unica soluzione.
The problem of the number of switches in parabolic equations with control
The regularity of the trace for minimal surfaces
The spectrum of the damped wave operator for a bounded domain in .
The SQP method for control constrained optimal control of the Burgers equation
A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...
The SQP method for control constrained optimal control of the Burgers equation
A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...
Theoretical analysis and control results for the Fitzhugh-Nagumo equation.
Time dependent Dirichlet space, mixed Dirichlet problem and pseudo-differential operators
Time optimal control of the heat equation with pointwise control constraints
Time optimal control problems for an internally controlled heat equation with pointwise control constraints are studied. By Pontryagin’s maximum principle and properties of nontrivial solutions of the heat equation, we derive a bang-bang property for time optimal control. Using the bang-bang property and establishing certain connections between time and norm optimal control problems for the heat equation, necessary and sufficient conditions for the optimal time and the optimal control are obtained....
Time-dependent Stokes equations with measure data.
Time-optimal boundary control of a parabolic system with time lags given in integral form
In this paper, the time-optimal boundary control problem for a distributed parabolic system in which time lags appear in integral form in both the state equation and the boundary condition is presented. Some particular properties of optimal control are discussed.
Time-optimal boundary control of an infinite order parabolic system with time lags
In this paper the time-optimal boundary control problem is presented for a distributed infinite order parabolic system in which time lags appear in the integral form both in the state equation and in the boundary condition. Some specific properties of the optimal control are discussed.
Time-optimal control of infinite order hyperbolic systems with time delays
In this paper, the time-optimal control problem for infinite order hyperbolic systems in which time delays appear in the integral form both in state equations and in boundary conditions is considered. Optimal controls are characterized in terms of an adjoint system and shown to be unique and bang-bang. These results extend to certain cases of nonlinear control problems. The particular properties of optimal control are discussed.
Time-optimal control of nonlinear parabolic systems with constrained derivative of control, existence theorem
Two Dimensional Variational Problems with Thin Obstacles.