Related papers: On some systems controlled by the structure of the…
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…
We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We…
We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…
The effectiveness of a robot manipulation to a large extent is determined by the speed of making this or that movement needed for carrying out the task. Accordingly to this the problem of optimal robot control is often subdivided into two…
To better understand the structure and function of complex systems, researchers often represent direct interactions between components in complex systems with networks, assuming that indirect influence between distant components can be…
How can the stability and efficiency of Artificial Neural Networks (ANNs) be ensured through a systematic analysis method? This paper seeks to address that query. While numerous factors can influence the learning process of ANNs, utilizing…
In this paper, we present some properties of time optimal controls for linear ODEs with the ball-type control constraint. More precisely, for an optimal control, we build up an upper bound for the number of its switching points; show that…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
Many techniques originally developed in the context of deterministic control theory have been recently applied to the quest for optimal protocols in stochastic processes. Given a system subject to environmental fluctuations, one may ask…
We consider optimal control problems where the state equation is an elliptic PDE of a Schr\"odinger type, governed by the Laplace operator $-\Delta$ with the addition of a potential V, and the control is the potential V itself, that may…
Autonomous systems often have logical constraints arising, for example, from safety, operational, or regulatory requirements. Such constraints can be expressed using temporal logic specifications. The system state is often partially…
This article is devoted to studying the null controllability of evolution equations with memory terms. The problem is challenging not only because the state equation contains memory terms but also because the classical controllability…
We generalize the Maximum Principle for free end point optimal control problems involving sweeping systems derived in [9] to cover the case where the end point is constrained to take values in a certain set. As in [9], an ingenious smooth…
Biological molecular machines convert free energy between different forms in cells, often at high efficiency. Optimal control theory provides a framework to elucidate design principles governing energetically efficient driving. Here, we use…
The emergence of mutant lineages within a viral species has become a public health problem, as the existing treatments and drugs are usually more effective on the original lineages than in the mutant ones. The following manuscript presents…
In this paper the connection between stochastic optimal control and reinforcement learning is investigated. Our main motivation is to apply importance sampling to sampling rare events which can be reformulated as an optimal control problem.…
The way the brain selects and controls actions is still widely debated. Mainstream approaches based on Optimal Control focus on stimulus-response mappings that optimize cost functions. Ideomotor theory and cybernetics propose a different…
The main result of this letter is that SOC naturally arises as a result of memory effects. We show that memory effects provide the mechanism for self organization. A general procedure to investigate this issue in models that display self…
This is mainly a survey on the properties of Strong Metric Regularity (SMR) and Strong Metric subRegularity (SMsR) of mappings representing first order optimality conditions (so-called optimality mappings) of optimization problems in…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…