time optimal control problems for an internally controlled heat equation with point-wise control constraints are studied. By Pontryagin's maximum principle and properties of nontrivial solutions of the heat equati...
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time optimal control problems for an internally controlled heat equation with point-wise control constraints are studied. By Pontryagin's maximum principle and properties of nontrivial solutions of the heat equation, we derive a bang-bang property for time optimal control. Using the bang-bang property and establishing certain connections between time and norm optimalcontrol problems for the heat equation, necessary and sufficient conditions for the optimaltime and the optimalcontrol are obtained.
An efficient computational scheme for solving a general class of linear time optimal control problems, where the target set is a compact and convex set with nonempty interior in the state space, is presented. The sche...
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An efficient computational scheme for solving a general class of linear time optimal control problems, where the target set is a compact and convex set with nonempty interior in the state space, is presented. The scheme is applied to solve the ship steering control problem, and excellent results are obtained.
This paper investigates the time optimal control for a class of non-instantaneous impulsive Clarke subdifferential type stochastic evolution inclusions in Hilbert spaces. We focus first on the existence of mild soluti...
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This paper investigates the time optimal control for a class of non-instantaneous impulsive Clarke subdifferential type stochastic evolution inclusions in Hilbert spaces. We focus first on the existence of mild solutions for these systems by using the measure of non-compactness and a fixed-point theorem wth the properties of Clarke subdifferential. Then, the existence of time optimal control of governed by stochastic control systems is also obtained. We do not assume that the evolution operator and the values of multi-valued map are compact. Finally, an example is given to illustrate the effectiveness of the results.
In this paper, we study the time optimal control of a class of partial stochastic impulsive functional differential systems with pseudo almost periodic coefficients in the alpha-norm functional spaces. Firstly, the ex...
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In this paper, we study the time optimal control of a class of partial stochastic impulsive functional differential systems with pseudo almost periodic coefficients in the alpha-norm functional spaces. Firstly, the existence of p-mean piecewise pseudo almost periodic mild solutions for the impulsive stochastic control systems is investigated by utilising stochastic analysis, analytic semigroup, the fixed-point techniques with fractional power arguments. Secondly, the existence of timeoptimal pairs of a system governed by partial stochastic impulsive functional differential equations is also obtained. Finally, two examples are provided to illustrate the time optimal control problems of parabolic control system with pseudo almost periodic coefficients and impulses.
An optimalcontrol approach to a simplified reaction-diffusion system describing cardiac defibrillation is proposed that allows for joint optimization of shape and duration of defibrillation pulses. Within the framewo...
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An optimalcontrol approach to a simplified reaction-diffusion system describing cardiac defibrillation is proposed that allows for joint optimization of shape and duration of defibrillation pulses. Within the framework, optimized multi-phasic pulses with low energy, short duration and/or low amplitude can be designed according to specific needs. The approach is based on a novel time optimal control formulation for the monodomain model, which takes into consideration the dynamical system properties of the uncontrolled equation. The highly complex dynamics requires a consistent discretization of first-and second-order information to guarantee effective optimization schemes leading to successful defibrillation. Numerical examples underline the efficiency of the proposed method.
This paper studies a time optimal control problem for a class of ordinary differential equations. The control systems may have multiple solutions. Based on the properties fulfilled by the solutions of the concerned eq...
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This paper studies a time optimal control problem for a class of ordinary differential equations. The control systems may have multiple solutions. Based on the properties fulfilled by the solutions of the concerned equations, we get both the existence and the Pontryagin maximum principle for optimalcontrols.
In this paper, we study an optimalcontrol problem for the three-dimensional Navier-Stokes-alpha equations in bounded domains with Dirichlet boundary conditions, where the time needed to reach a desired state plays an...
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In this paper, we study an optimalcontrol problem for the three-dimensional Navier-Stokes-alpha equations in bounded domains with Dirichlet boundary conditions, where the time needed to reach a desired state plays an essential role. We first prove the existence of optimal solutions. Then we establish the first-order and second-order necessary optimality conditions, and the second-order sufficient optimality conditions. The second-order optimality ones obtained in the paper seem to be optimal in the sense that the gap between them is minimal.
The paper proposes control design strategies that minimize the time required by a mobile robot to accomplish a certain task (reach a target) while transmitting/receiving a message. The message delivery is done over a ...
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The paper proposes control design strategies that minimize the time required by a mobile robot to accomplish a certain task (reach a target) while transmitting/receiving a message. The message delivery is done over a wireless network, and we account for path-loss while disregarding any shadowing phenomena, i.e., the transmission rate depends only on the distance to the wireless antenna. First, using the Pontryagin maximum principle we design a minimal-timecontrol for the simplified robot dynamics described by a single integrator. Next, we show how we can use these theoretical results to efficiently control more complicated non-holonomic dynamics. Numerical simulations illustrate the effectiveness of the theoretical results.(c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
We study the minimum time to implement an arbitrary two-qubit gate in two heteronuclear spins systems. We give a systematic characterization of two-qubit gates based on the invariants of local equivalence. The quantum...
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We study the minimum time to implement an arbitrary two-qubit gate in two heteronuclear spins systems. We give a systematic characterization of two-qubit gates based on the invariants of local equivalence. The quantum gates are classified into four classes, and for each class the analytical formula of the minimum time to implement the quantum gates is explicitly presented. For given quantum gates, by calculating the corresponding invariants one easily obtains the classes to which the quantum gates belong. In particular, we analyze the effect of global phases on the minimum time to implement the gate. Our results present complete solutions to the optimaltime problem in implementing an arbitrary two-qubit gate in two heteronuclear spins systems. Detailed examples are given to typical two-qubit gates with or without global phases.
In this paper, we study an optimalcontrol problem for the 2D MHD equations with memory in bounded domains with Dirichlet boundary conditions, where the time needed to reach the desired state plays an essential role. ...
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In this paper, we study an optimalcontrol problem for the 2D MHD equations with memory in bounded domains with Dirichlet boundary conditions, where the time needed to reach the desired state plays an essential role. We first prove the existence of optimal solutions. Then we establish the first-order necessary and second-order sufficient optimality conditions. The second-order optimality ones obtained in the paper seem to be optimal in the sense that the gap between them is minimal.
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