Related papers: Time-Optimal Control of Linear Fractional Systems
We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders $s \in (0,1)$ and $\gamma \in (0,1]$, respectively. The spatial fractional…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
We present the conditions under which the time-optimal control problem for a nonlinear non-autonomous linearizable system can be solved by the method of successive approximations, at each step of which a power Markov moment min-problem is…
In this study, we consider an optimal control problem driven by a stochastic differential system with a stopping time terminal cost functional. We establish the stochastic maximum principle for this new kind of an optimal control problem by…
It has recently been shown that the minimum energy solution of the control problem for a linear system produces a control trajectory that is nonlocal. An issue then arises when the dynamics represents a linearization of the underlying…
This paper deals with time-optimal control of nonlinear continuous-time systems based on direct collocation. The underlying discretization grid is variable in time, as the time intervals are subject to optimization. This technique differs…
In this paper, a finite-horizon optimal control problem involving a dynamical system described by a linear Caputo fractional differential equation and a quadratic cost functional is considered. An explicit formula for the value functional…
This paper addresses the optimal control problem for a class of nonlinear fractional systems involving Caputo derivatives and nonlocal initial conditions. The system is reformulated as an abstract Hammerstein-type operator equation,…
We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some…
The minimum-time control problem consists in finding a control policy that will drive a given dynamic system from a given initial state to a given target state (or a set of states) as quickly as possible. This is a well-known challenging…
From economics point of view, we investigate a new optimal control problem driven by a stochastic differential equation with a multi-time states cost functional. By constructing a series of first-order adjoint equations, we establish the…
In the present paper, we study the existence and optimal controllability of a multi-term time-fractional stochastic system with non-instantaneous impulses. Using semigroup theory, stochastic analysis theory, and Krasnoselskii's fixed point…
We consider a terminal control problem for processes governed by a nonlinear system of fractional ODEs. In order to show existence of the control, we first consider the linear counterpart of the system and reprove a number of classical…
This paper investigates the problem of regulating in real time a linear dynamical system to the solution trajectory of a time-varying constrained convex optimization problem. The proposed feedback controller is based on an adaptation of the…
In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…
We study the time-inconsistent linear quadratic optimal control problem for forward-backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research…
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…
We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
In this work, we introduce a new three-dimensional chaotic differential dynamical system. We find equilibrium points of this system and provide the stability conditions for various fractional orders. Numerical simulations will be used to…