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The considered optimal control problem of a stochastic power system, is to select the set of power supply vectors which infimizes the probability that the phase-angle differences of any power flow of the network, endangers the transient…
The maximum hands-off control is the optimal solution to the L0 optimal control problem. It has the minimum support length among all feasible control inputs. To avoid computational difficulties arising from its combinatorial nature, the…
We consider the problem of finite-horizon optimal control design under uncertainty for imperfectly observed discrete-time systems with convex costs and constraints. It is known that this problem can be cast as an infinite-dimensional convex…
This work presents new sufficient conditions for the absence of a gap corresponding to Young measure and occupation measure relaxations for constrained optimal control problems. Unlike existing conditions, these sufficient conditions do not…
The modelling of linear quadratic Gaussian optimal control problems on large complex networks is intractable computationally. Graphon theory provides an approach to overcome these issues by defining limit objects for infinite sequences of…
To achieve control objectives for extremely large-scale complex networks using standard methods is essentially intractable. In this work a theory of the approximate control of complex network systems is proposed and developed by the use of…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…
We consider the optimal control problem associated with a general version of the well known shallow lake model, and we prove the existence of an optimum in the class $L_{loc}^{1}\left(0,+\infty\right)$. Any direct proof seems to be missing…
This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…
A general maximum principle (necessary and sufficient conditions) for an optimal control problem governed by a stochastic differential equation driven by an infinite dimensional martingale is established. The solution of this equation takes…
A key idea in convex optimization theory is to use well-structured affine functions to approximate general functions, leading to impactful developments in conjugate functions and convex duality theory. This raises the question: what are the…
The optimization problems with simple bounds are an important class of problems. To facilitate the computation of such problems, an unconstrained-like dynamic method, motivated by the Lyapunov control principle, is proposed. This method…
We establish lower semi-continuity and strict convexity of the energy functionals for a large class of vector equilibrium problems in logarithmic potential theory. This in particular implies the existence and uniqueness of a minimizer for…
In this paper we prove a weak necessary and sufficient maximum principle for Markovian regime switching stochastic optimal control problems. Instead of insisting on the maximum condition of the Hamiltonian, we show that 0 belongs to the sum…
This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS)…
A large collection of financial contracts offering guaranteed minimum benefits are often posed as control problems, in which at any point in the solution domain, a control is able to take any one of an uncountable number of values from the…
Probabilistic control design is founded on the principle that a rational agent attempts to match modelled with an arbitrary desired closed-loop system trajectory density. The framework was originally proposed as a tractable alternative to…
This paper considers the stochastic linear quadratic optimal control problem in which the control domain is nonconvex. By the functional analysis and convex perturbation methods, we establish a novel maximum principle. The application of…
In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…