scholarly journals A closed-loop strategy in an optimal guaranteed control problem for a linear system

2020 ◽  
Vol 64 (5) ◽  
pp. 519-525
Author(s):  
Dz. A. Kastsiukevich ◽  
N. M. Dmitruk
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Time Instant ◽  
Optimal Control Strategy ◽  
Guaranteed Control ◽  
Linear Discrete System ◽  
Control Goal ◽  
Bounded Disturbances ◽  
Target Set ◽  
Account Information

This paper deals with an optimal control problem for a linear discrete system subject to unknown bounded disturbances with the control goal being to steer the system with guarantees to a given target set while minimizing a given cost function. We define an optimal control strategy with one correction time instant, meaning taking into account information about one future state of the object, and propose an efficient numerical method for constructing it.

scholarly journals A method for constructing an optimal control strategy in a linear terminal problem

2021 ◽  
pp. 38-50
Author(s):  
Dzmitry A. Kastsiukevich ◽  
Natalia M. Dmitruk
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Time Instant ◽  
Open Loop ◽  
Optimal Control Strategy ◽  
Worst Case ◽  
Terminal Set ◽  
Linear Discrete System ◽  
Control Goal ◽  
Bounded Disturbances

This paper deals with an optimal control problem for a linear discrete system subject to unknown bounded disturbances, where the control goal is to steer the system with guarantees into a given terminal set while minimising the terminal cost function. We define an optimal control strategy which takes into account the state of the system at one future time instant and propose an efficient numerical method for its construction. The results of numerical experiments show an improvement in performance under the optimal control strategy in comparison to the optimal open-loop worst-case control while maintaining comparable computation times.

scholarly journals Impulsive Control for Continuous-Time Markov Decision Processes

2015 ◽  
Vol 47 (1) ◽  
pp. 106-127 ◽  
Author(s):  
François Dufour ◽  
Alexei B. Piunovskiy
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Markov Decision Processes ◽  
Control Strategy ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
Optimal Control Strategy ◽  
Optimality Equation ◽  
Markov Decision

In this paper our objective is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite time horizon discounted cost. The continuous-time controlled process is shown to be nonexplosive under appropriate hypotheses. The so-called Bellman equation associated to this control problem is studied. Sufficient conditions ensuring the existence and the uniqueness of a bounded measurable solution to this optimality equation are provided. Moreover, it is shown that the value function of the optimization problem under consideration satisfies this optimality equation. Sufficient conditions are also presented to ensure on the one hand the existence of an optimal control strategy, and on the other hand the existence of a ε-optimal control strategy. The decomposition of the state space into two disjoint subsets is exhibited where, roughly speaking, one should apply a gradual action or an impulsive action correspondingly to obtain an optimal or ε-optimal strategy. An interesting consequence of our previous results is as follows: the set of strategies that allow interventions at time t = 0 and only immediately after natural jumps is a sufficient set for the control problem under consideration.

A Comfort Oriented Control Strategy for Semi-Active Suspensions Based on Half Car Model

2010 ◽  
Author(s):  
Cristiano Spelta ◽  
Diego Delvecchio ◽  
Sergio M. Savaresi
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Optimal Performance ◽  
Optimal Control Strategy ◽  
Active Suspensions ◽  
Quarter Car Model ◽  
Car Model ◽  
Control Goal ◽  
Quarter Car ◽  
Effective Description

This paper is devoted to the design of a novel semi-active comfort-oriented control strategy based on the “half-car” modeling of the vehicle. The half car model is an effective description of the vertical behaviors in a vehicle like a motorcycle, since it is able to represent both the heave and pitch dynamics. A recent control strategy (the “Mix-1-Sensor”) have been proven to be the quasi-optimal control strategy when the system is described with a quarter car model and the comfort objective is the control goal. This paper presents an analysis of the performances of the Mix-1-Sensor implemented in a half car: this strategy is able to guarantee a quasi optimal performance in terms of heave dynamics but it is not able to manage the pitch dynamics efficiently. A pitch-oriented extension of this strategy is proposed in order to guarantee a better filtering of the pitch dynamics.

scholarly journals Impulsive Control for Continuous-Time Markov Decision Processes

2015 ◽  
Vol 47 (01) ◽  
pp. 106-127 ◽  
Author(s):  
François Dufour ◽  
Alexei B. Piunovskiy
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Markov Decision Processes ◽  
Control Strategy ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
Optimal Control Strategy ◽  
Optimality Equation ◽  
Markov Decision

In this paper our objective is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite time horizon discounted cost. The continuous-time controlled process is shown to be nonexplosive under appropriate hypotheses. The so-called Bellman equation associated to this control problem is studied. Sufficient conditions ensuring the existence and the uniqueness of a bounded measurable solution to this optimality equation are provided. Moreover, it is shown that the value function of the optimization problem under consideration satisfies this optimality equation. Sufficient conditions are also presented to ensure on the one hand the existence of an optimal control strategy, and on the other hand the existence of a ε-optimal control strategy. The decomposition of the state space into two disjoint subsets is exhibited where, roughly speaking, one should apply a gradual action or an impulsive action correspondingly to obtain an optimal or ε-optimal strategy. An interesting consequence of our previous results is as follows: the set of strategies that allow interventions at time t = 0 and only immediately after natural jumps is a sufficient set for the control problem under consideration.

scholarly journals Construction of scattering curves in one class of time-optimal control problems with leaps of a target set boundary curvature

2020 ◽  
Vol 55 ◽  
pp. 93-112
Author(s):  
P.D. Lebedev ◽  
A.A. Uspenskii
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Time Optimal Control ◽  
Dimensional Manifold ◽  
Singular Set ◽  
Time Optimal ◽  
Characteristic Points ◽  
Target Set ◽  
The Right ◽  
Points Of Discontinuity

We consider a time-optimal control problem on the plane with a circular vectogram of velocities and a non-convex target set with a boundary having a finite number of points of discontinuity of curvature. We study the problem of identifying and constructing scattering curves that form a singular set of the optimal result function in the case when the points of discontinuity of curvature have one-sided curvatures of different signs. It is shown that these points belong to pseudo-vertices that are characteristic points of the boundary of the target set, which are responsible for the generation of branches of a singular set. The structure of scattering curves and the optimal trajectories starting from them, which fall in the neighborhood of the pseudo-vertex, is investigated. A characteristic feature of the case under study is revealed, consisting in the fact that one pseudo-vertex can generate two different branches of a singular set. The equation of the tangent to the smoothness points of the scattering curve is derived. A scheme is proposed for constructing a singular set, based on the construction of integral curves for first-order differential equations in normal form, the right-hand sides of which are determined by the geometry of the boundary of the target in neighborhoods of the pseudo-vertices. The results obtained are illustrated by the example of solving the control problem when the target set is a one-dimensional manifold.

scholarly journals OPTIMAL CONTROL OF SWITCHED IMPULSIVE SYSTEMS WITH TIME DELAY

2012 ◽  
Vol 53 (4) ◽  
pp. 292-307 ◽  
Author(s):  
K. H. WONG ◽  
W. M. TANG
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Time Instant ◽  
Computational Method ◽  
Impulsive Systems ◽  
Delay Differential ◽  
The Cost ◽  
System With Time Delay

AbstractWe develop a computational method for solving an optimal control problem governed by a switched impulsive dynamical system with time delay. At each time instant, only one subsystem is active. We propose a computational method for solving this optimal control problem where the time spent by the state in each subsystem is treated as a new parameter. These parameters and the jump strengths of the impulses are decision parameters to be optimized. The gradient formula of the cost function is derived in terms of solving a number of delay differential equations forward in time. Based on this, the optimal control problem can be solved as an optimization problem.

scholarly journals Maximize Expected Profits by Dynamic After-Sales Service Investment Strategy Based on Word-of-Mouth Marketing in Social Network Shopping

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Ying Yu ◽  
Jiaomin Liu ◽  
Jiadong Ren ◽  
Qian Wang ◽  
Cuiyi Xiao
Keyword(s):  
Optimal Control ◽  
Social Network ◽  
Control Problem ◽  
Control Strategy ◽  
Word Of Mouth ◽  
Investment Strategy ◽  
Negative Evaluation ◽  
Communication Model ◽  
Data Simulation ◽  
Optimal Control Strategy

This paper discusses how word-of-mouth marketing affects the profits of product sales in social network-based shopping under good after-sales service. First, a new word-of-mouth communication model based on silent evaluation, positive evaluation, and negative evaluation is proposed. Second, we use the way of increasing after-sales service to achieve high praise and thereby maximize the expected profits. Thus, the proportion control problem of after-sales service investment is modeled as an optimal control problem. Third, the existence of optimal control is proved, and an optimal control strategy for dynamic proportion of after-sales service investment is proposed. Fourth, through data simulation of different real-world networks, it is verified that the expected profits under the dynamic after-sales service strategy is higher than that under any uniform control strategy. Finally, sensitivity analysis is performed to explore how different parameters affect the expected profits.

Elements of analytical solutions constructor in a class of time-optimal control problems with the break of curvature of a target set

2020 ◽  
pp. 370-386
Author(s):  
Pavel D. Lebedev ◽  
Alexander A. Uspenskii
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Control Function ◽  
Extreme Points ◽  
Transversality Condition ◽  
Analytical Form ◽  
Singular Set ◽  
Entire Area ◽  
Target Set ◽  
Special Points

A planar velocity control problem with a disc indicatrix and a target set with a smooth boundary having finite discontinuities of second-order derivatives of coordinate functions is considered. We have studied pseudo-vertices-special points of the goal boundary that generate a singularity for the optimal control function. For non-stationary pseudo-vertices with discontinuous curvature, one-way markers are found, the values of which are necessary for analytical and numerical construction of branches of a singular set. It is proved that the markers lie on the border of the spectrum-the region of possible values. One of them is equal to zero, the other takes an invalid value -∞. In their calculation, asymptotic expansions of a nonlinear equation expressing the transversality condition are applied. Exact formulas for the extreme points of branches of a singular set are also obtained based on markers. An example of a control problem is presented, in which the constructive elements are obtained using the developed methods (pseudo-vertex, its markers, and the extreme point of a singular set), are sufficient to construct a singular set and an optimal result function in an explicit analytical form over the entire area of consideration.

scholarly journals Effects of Isoperimetric Constraint for Reducing HSV-2 Infection Using Optimal Control Strategy

2021 ◽  
pp. 62-68
Author(s):  
Samiha Islam Tanni ◽  
Jakia Sultana ◽  
Shamima Islam ◽  
Farzana Afroz ◽  
Md Robiul Islam
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Vaccination Schedule ◽  
State Variables ◽  
Optimal Control Strategy ◽  
Sexually Transmitted ◽  
Isoperimetric Constraint ◽  
Fourth Order Method ◽  
The Cost

Optimal control is helpful for testing and comparing different vaccination strategies of a certain disease. Genital herpes is one of the most prevalent sexually-transmitted diseases globally. In this paper, we have proposed an optimal control problem applied to HSV-2 model after introducing the constraint and state variables. Optimal control problem is formulated based on ordinary differential equation and isoperimetric constraint in the vaccine supply is also included. Mathematical analysis such as the characterization of optimal control using Pontryagin’s maximum principle is studied. Generally optimal control theory is used for finding the optimal way for implementing the strategies, minimizing the number of infectious and latent individuals and keeping the cost of implementation as low as possible. Here the optimality system is derived and solved numerically using a Runge-Kutta fourth order method and this is an iterative method. Using numerical simulation we observe that how the optimal vaccination schedule is altered by imposing isoperimetric constraint. Finally, on applying the isoperimetric constraint on the optimal control problem of HSV-2 epidemic model, we observe that optimal vaccination schedule with isoperimetric constraint indicates successful short-term control of the disease. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 7, Dec 2020 P 62-68

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