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In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals depend on the cost…
We geometrically describe optimal control problems in terms of Morse families in the Hamiltonian framework. These geometric structures allow us to recover the classical first order necessary conditions for optimality and the starting point…
In this note, we develop the first-order theory of optimal control problems with box constraints on the control. We emphasize the precise modification of Pontryagin's maximum principle when the admissible control set is compact, the…
Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing tools from H-convergence, we show existence of optimal solutions. First order necessary optimality conditions are obtained after deriving…
We derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ODEs and a PDE of Vlasov-type. Such problems arise naturally as ${\Gamma}$-limits of optimal control problems subject to ODE…
Limited bandwidth and limited saturation in actuators are practical concerns in control systems. Mathematically, these limitations manifest as constraints being imposed on the control actions, their rates of change, and more generally, the…
For periodic linear control systems with bounded control range, an autonomized system is introduced by adding the phase to the state of the system. Here a unique control set (i.e., a maximal set of approximate controllability) with nonvoid…
We study a class of optimal control problems governed by nonlinear stochastic equations of monotone type under certain coercivity and linear growth conditions. We give first order necessary conditions of optimality. A stochastic Pontryagin…
A family of optimal control problems for a single and two coupled spinning particles in the Euler-Lagrange formalism is discussed. A characteristic of such problems is that the equations controlling the system are implicit and a reduction…
Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…
In this article we derive a strong version of the Pontryagin Maximum Principle for general nonlinear optimal control problems on time scales in finite dimension. The final time can be fixed or not, and in the case of general boundary…
We show that mean field optimal controls satisfy a first order optimality condition (at a.e. time) without any a priori requirement on their spatial regularity. This principle is obtained by a careful limit procedure of the Pontryagin…
Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by $r$-th order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone…
An optimal control problem with an infinite horizon quadratic cost functional for a linear system with a known additive disturbance is considered. The feature of this problem is that a weight matrix of the control cost in the cost…
In this paper, we discuss a new general formulation of fractional optimal control problems whose performance index is in the fractional integral form and the dynamics are given by a set of fractional differential equations in the Caputo…
The verification theorem serving as an optimality condition for the optimal control problem, has been expected and studied for a long time. The purpose of this paper is to establish this theorem for control systems governed by stochastic…
The famous proof of the Pontryagin maximum principle for control problems on a finite horizon bases on the needle variation technique, as well as the separability concept of cones created by disturbances of the trajectories. In this…
We present a new geometric unfolding of a prototype problem of optimal control theory, the Mayer problem. This approach is crucially based on the Stokes Theorem and yields to a necessary and sufficient condition that characterizes the…
In this paper we consider the problem of a multi-agent system achieving a formation in the presence of misbehaving or adversarial agents. We introduce a novel continuous time resilient controller to guarantee that normally behaving agents…
In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…