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maximum principle for optimal control of neutral stochastic functional differential systems

Science China Mathematics 2015年第6期58卷 1265-1284页

作者： WEI WenNing School of Mathematical Sciences Fudan University

This paper is concerned with optimal control of neutral stochastic functional differential equations(NSFDEs). The pontryagin maximum principle is proved for optimal control, where the adjoint equation is a linear neutral backward stochastic functional equation of Volterra type(VNBSFE). The existence and uniqueness of the solution are proved for the general nonlinear VNBSFEs. Under the convexity assumption of the Hamiltonian function, a sufficient condition for the optimality is addressed as well.

关键词： neutral stochastic functional differential equation neutral backward stochastic functional equationof Volterra type stochastic optimal control pontryagin maximum principle

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Truly optimal semi-active damping to control free vibration of a single degree of freedom system

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Theoretical & Applied Mechanics Letters 2024年第2期14卷 142-145页

作者： Viet Duc La Ngoc Tuan Nguyen Institute of Mechanics Vietnam Academy of Science and TechnologyHanoi 10000Vietnam Graduate University of Science and Technology Vietnam Academy of Science and TechnologyHanoi 10000Vietnam

This paper studies a single degree of freedom system under free vibration and controlled by a general semiactive damping.A general integral of squared error is considered as the performance index.A one-time switching damping controller is proposed and *** pontryagin maximum principle is used to prove that no other form of semi-active damping can provide the better performance than the proposed one-time switching damping.

关键词： Analytical optimization Quadratic integral Lyapunov equation pontryagin maximum principle

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Nearly time-optimal paths for a ground vehicle

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控制理论与应用（英文版） 2003年第1期1卷 2-8页

作者： David A.ANISI Johan HAMBERG Department of Autonomous Systems Swedish Defence Research Agency SE-172 90 Stockholm Sweden

It is well known that the sufficient family of time-optimal paths for both Dubins' as well as Reeds-Shepp' s car models consist of the concatenation of circular arcs with maximum curvature and straight line segments, all tangentially connected. These time-optimal solutions suffer from some drawbacks. Their discontinuous curvature profile, together with the wear and impairment on the control equipment that the bang-bang solutions induce, calls for ' smoother' and more supple reference paths to follow. Avoiding the bang-bang solutions also raises the robustness with respect to any possible uncertainties. In this paper, our main tool for generating these “nearly time-optimal” , but nevertheless continuous-curvature paths, is to use the pontryagin maximum principle (PMP) and make an appropriate and cunning choice of the Lagrangian function. Despite some rewarding simulation results, this concept turns out to be numerically divergent at some instances. Upon a more careful investigation, it can be concluded that the problem at hand is nearly singular. This is seen by applying the PMP to Dubins car and studying the corresponding two point boundary value problem, which turn out to be singular. Realizing this, one is able to contradict the widespread belief that all the information about the motion of a mobile platform lies in the initial values of the auxiliary variables associated with the PMP. Keywords Time-optimal paths - Motion planning - Optimal control - pontryagin maximum principle - UGV

关键词： Time-optimal paths Motion planning Optimal control pontryagin maximum principle UGV

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