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We establish a geometric Pontryagin maximum principle for discrete time optimal control problems on finite dimensional smooth manifolds under the following three types of constraints: a) constraints on the states pointwise in time, b)…
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…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
We consider two-dimensional homogeneous shear turbulence within the context of optimal control, a multi-scale turbulence model containing the fluctuation velocity and pressure correlations up to the fourth order; The model is formulated on…
This article deals with a stochastic control problem for certain fluids of non-Newtonian type. More precisely, the state equation is given by the two-dimensional stochastic second grade fluids perturbed by a multiplicative white noise. The…
We apply an extension of the Pontryagin Maximum Principle to derive time-optimal controls of two-level quantum systems by means of piecewise constant pulses. Global optimal solutions are obtained for state-to-state transfer in the cases…
This paper deals with second-order optimality conditions for a quasilinear elliptic control problem with a nonlinear coefficient in the principal part that is countably $PC^2$ (continuous and $C^2$ apart from countably many points). We…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
We consider the minimum-time problem for a multi-input control-affine system, where we assume that the controlled vector fields generate a non-involutive distribution of constant dimension, and where we do not assume a-priori bounds for the…
We explore the dual approach to nonlocal optimal design, specifically for a classical min-max problem which in this study is associated with a nonlocal scalar diffusion equation. We reformulate the optimal design problem utilizing a dual…
Robustness is a basic property of any control system. In the context of linear output regulation, it was proved that embedding an internal model of the exogenous signals is necessary and sufficient to achieve tracking of the desired…
The problem we consider in this work is to minimize the L^q-norm (q > 2) of the semidiscrete controls. As shown in [LT06], under the main approximation assumptions that the discretized semigroup is uniformly analytic and that the degree of…
This paper presents a new and straightforward procedure for solving bilinear quadratic optimal control problem. In this method, first the original optimal control problem is transformed into a nonlinear twopoint boundary value problem…
In this paper, we study linearly constrained policy optimization over the manifold of Schur stabilizing controllers, equipped with a Riemannian metric that emerges naturally in the context of optimal control problems. We provide extrinsic…
Infinite-time nonlinear optimal regulation control is widely utilized in aerospace engineering as a systematic method for synthesizing stable controllers. However, conventional methods often rely on linearization hypothesis, while recent…
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…
A system's configurational state can be manipulated using dynamic variation of control parameters, such as temperature, pressure, or magnetic field; for finite-duration driving, excess work is required above the equilibrium free-energy…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
This paper proposes a robust control method based on sliding mode design for two-level quantum systems with bounded uncertainties. An eigenstate of the two-level quantum system is identified as a sliding mode. The objective is to design a…
This paper discusses the energy optimal control problem for the class of quantum systems that possess dynamical symmetry of SU(1,1), which are widely studied in various physical problems in the quantum theory. Based on the maximum principle…