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In this paper, we consider the infinite horizon optimal control problem for nonlinear systems. Under the conditions of controllability of the linearized system around the origin, and nonlinear controllability of the system to a terminal set…
The optimal control of passive systems in equilibrium typically favours quasistatic (infinite-time) protocols. We show that a breakdown of quasistatic optimality occurs when the controller itself is dissipative. Concretely, we study a…
In this paper we study affine and bilinear systems on Lie groups. We show that there is an intrinsic connection between the solutions of both systems. Such relation allows us to obtain some preliminary controllability results of affne…
The paper introduces and solves a structural controllability problem for continuum ensembles of linear time-invariant systems. All the individual linear systems of an ensemble are sparse, governed by the same sparsity pattern.…
We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…
We introduce discontinuous solutions to nonlinear impulsive control systems with state time delays in the dynamics and derive necessary optimality conditions in the form of a Maximum Principle for associated optimal control problems. In the…
The optimal time for the controllability of linear hyperbolic systems in one dimensional space with one-side controls has been obtained recently for time-independent coefficients in our previous works. In this paper, we consider linear…
We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…
In the present contribution we consider a singular phase field system located in a smooth and bounded three-dimensional domain. The entropy balance equation is perturbed by a logarithmic nonlinearity and by the presence of an additional…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
Optimal unbounded control problems with affine control dependence may fail to have minimizers in the class of absolutely continuous state trajectories. For this reason, extended impulsive versions --which cannot be of measure-theoretical…
We investigate the singularities and boundedness of a special kind of algebraic varieties so-called stable minimal models, which are constructed and studied by Birkar. Given a klt stable minimal model with bounded relative volume, if we fix…
In this paper approximations of the set of trajectories and integral funnel of the control system described by nonlinear ordinary differential equation with integral constraint on the control functions are considered. The set of admissible…
We deal with a singularly perturbed optimal control problem with slow and fast variable depending on a parameter {\epsilon}. We study the asymptotic, as {\epsilon} goes to 0, of the corresponding value functions, and show convergence, in…
In this paper, we discuss our recent works on the null-controllability, the exact controllability, and the stabilization of linear hyperbolic systems in one dimensional space using boundary controls on one side for the optimal time. Under…
Singular arcs emerge in the solutions of Optimal Control Problems (OCPs) when the optimal inputs on some finite time intervals cannot be directly obtained via the optimality conditions. Solving OCPs with singular arcs often requires…
We generalize the notions of singularities and ordinary points from linear ordinary differential equations to D-finite systems. Ordinary points of a D-finite system are characterized in terms of its formal power series solutions. We also…
In this letter, we derive minimum-energy controls for a broad class of control-affine systems using a Lagrange multiplier fixed-point equation and a generally non-symmetric Gramian-like matrix. In feasible coercivity classes, this fixed…
This note is concerned with the study of the initial boundary value problem for systems of conservation laws from the point of view of control theory, where the initial data is fixed and the boundary data are regarded as control functions.…
Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin…