Related papers: A Noether Theorem on Unimprovable Conservation Law…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
The present paper represents a continuation of our previous one. There, a continuous dependence result for the solution of an elliptic variational-hemivariational inequality was obtained and then used to prove the existence of optimal pairs…
For nonsmooth Euler-Lagrange extremals, Noether's conservation laws cease to be valid. We show that Emmy Noether's theorem of the calculus of variations is still valid in the wider class of Lipschitz functions, as long as one restrict the…
Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…
Noether's theorem, which connects continuous symmetries to exact conservation laws, remains one of the most fundamental principles in physics and dynamical systems. In this work, we draw a conceptual parallel between two paradigms: the…
A multi-variable PI (proportional integrating) controller is proved to be optimal for an important class of control problems where performance is specified in terms of frequency weighted H-infinity norms. The problem class includes…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
We propose a variational formulation of an inverse problem in continuous-time stochastic control, aimed at identifying control costs consistent with a given distribution over trajectories. The formulation is based on minimizing the…
In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional (exact/approximate) controllability. Some equivalent…
A general maximum principle is proved for optimal controls of abstract semilinear stochastic evolution equations. The control variable, as well as linear unbounded operators, acts in both drift and diffusion terms, and the control set need…
In this paper, we focus on a method based on optimal control to address the optimization problem. The objective is to find the optimal solution that minimizes the objective function. We transform the optimization problem into optimal…
The general maximum principle is proved for an infinite dimensional controlled stochastic evolution system. The control is allowed to take values in a nonconvex set and enter into both drift and diffusion terms. The operator-valued backward…
The paper is concerned with an optimal control problem governed by the equations of elasto plasticity with linear kinematic hardening and the inertia term at small strain. The objective is to optimize the displacement field and plastic…
We consider cost minimising control problems, in which the dynamical system is constrained by higher order differential equations of Euler-Lagrange type. Following ideas from a previous paper by the first and the third author, we prove that…
We prove existence of optimal control for the deterministic and stochastic shallow lake problem without any restrictions on the parameter space and we establish a generalization of the Arrhenius Law in the case of noise-dependent…
We introduce a novel notion of invariance feedback entropy to quantify the state information that is required by any controller that enforces a given subset of the state space to be invariant. We establish a number of elementary properties,…
We consider controllability for divergence-free systems that have a conserved quantity and satisfy a H\"ormander condition. It is shown that such systems are controllable, provided that the conserved quantity is a proper function. The proof…
We investigate a control process described by a linear system of ordinary differential equations with a noise of special type acting to the control parameter. As the cost functional the probability of the final state vector to enter to a…
We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a variational discrete approach for the control. Based on a…
We extend the DuBois-Reymond necessary optimality condition and Noether's first theorem to variational problems of Herglotz type with time delay. Our results provide, as corollaries, the DuBois-Reymond necessary optimality condition and the…