On the dynamic programming approach to Pontriagin's maximum principle

1968 ◽  
Vol 5 (3) ◽  
pp. 679-692 ◽  
Author(s):  
Richard Morton
Keyword(s):  
Dynamic Programming ◽  
Maximum Principle ◽  
The State ◽  
Dynamic Programming Principle ◽  
Programming Approach ◽  
Bellman Function ◽  
State Variables ◽  
Dynamic Programming Approach ◽  
Minimum Value ◽  
Image Position

Suppose that the state variables x = (x1,…,xn)′ where the dot refers to derivatives with respect to time t, and u ∊ U is a vector of controls. The object is to transfer x to x1 by choosing the controls so that the functional takes on its minimum value J(x) called the Bellman function (although we shall define it in a different way). The Dynamic Programming Principle leads to the maximisation with respect to u of and equality is obtained upon maximisation.

On the dynamic programming approach to Pontriagin's maximum principle

1968 ◽  
Vol 5 (03) ◽  
pp. 679-692
Author(s):  
Richard Morton
Keyword(s):  
Dynamic Programming ◽  
Maximum Principle ◽  
The State ◽  
Dynamic Programming Principle ◽  
Programming Approach ◽  
Bellman Function ◽  
State Variables ◽  
Dynamic Programming Approach ◽  
Minimum Value ◽  
Image Position

Suppose that the state variables x = (x 1,…,x n )′ where the dot refers to derivatives with respect to time t, and u ∊ U is a vector of controls. The object is to transfer x to x 1 by choosing the controls so that the functional takes on its minimum value J(x) called the Bellman function (although we shall define it in a different way). The Dynamic Programming Principle leads to the maximisation with respect to u of and equality is obtained upon maximisation.

A dynamic programming approach to evolutionarily stable strategy theory

1980 ◽  
Vol 12 (1) ◽  
pp. 3-5 ◽  
Author(s):  
C. Cannings ◽  
D. Gardiner
Keyword(s):  
Dynamic Programming ◽  
Density Function ◽  
Evolutionarily Stable Strategy ◽  
Programming Approach ◽  
Stable Strategy ◽  
War Of Attrition ◽  
Dynamic Programming Approach ◽  
The Individual ◽  
Image Position ◽  
Evolutionarily Stable

In the war of attrition (wa), introduced by Maynard Smith (1974), two contestants play values from [0, ∞), the individual playing the longer value winning a fixed prize V, and both incurring a loss equal to the lesser of the two values. Thus the payoff, E(x, y) to an animal playing x against one playing y, is A more general form (Bishop and Cannings (1978)) has and it was demonstrated that with and there exists a unique evolutionarily stable strategy (ess), which is to choose a random value from a specified density function on [0, ∞). Results were also obtained for strategy spaces [0, s] and [0, s).

Dynamic Programming and a Distributed Parameter Maximum Principle

1968 ◽  
Vol 90 (2) ◽  
pp. 152-156 ◽  
Author(s):  
W. L. Brogan
Keyword(s):  
Dynamic Programming ◽  
Maximum Principle ◽  
Programming Approach ◽  
Distributed Parameter ◽  
Programming Technique ◽  
Nonhomogeneous Boundary Condition ◽  
The Maximum Principle ◽  
Dynamic Programming Approach ◽  
Nonhomogeneous Boundary ◽  
Definition Of

A proof of a distributed parameter maximum principle is given by using dynamic programming. An example problem involving a nonhomogeneous boundary condition is also treated by using the dynamic programming technique and by extending the definition of the differential operator. It is thus demonstrated that for linear systems the dynamic programming approach is just as powerful as the variational approach originally used to derive the maximum principle.

NUMERICAL METHODS FOR DIFFERENTIAL GAMES BASED ON PARTIAL DIFFERENTIAL EQUATIONS

2006 ◽  
Vol 08 (02) ◽  
pp. 231-272 ◽  
Author(s):  
M. FALCONE
Keyword(s):  
Dynamic Programming ◽  
Numerical Methods ◽  
Differential Games ◽  
Value Function ◽  
Approximation Schemes ◽  
Dynamic Programming Principle ◽  
Programming Approach ◽  
Feedback Controls ◽  
Dynamic Programming Approach ◽  
Discrete Time Dynamical System

In this paper we present some numerical methods for the solution of two-persons zero-sum deterministic differential games. The methods are based on the dynamic programming approach. We first solve the Isaacs equation associated to the game to get an approximate value function and then we use it to reconstruct approximate optimal feedback controls and optimal trajectories. The approximation schemes also have an interesting control interpretation since the time-discrete scheme stems from a dynamic programming principle for the associated discrete time dynamical system. The general framework for convergence results to the value function is the theory of viscosity solutions. Numerical experiments are presented solving some classical pursuit-evasion games.

scholarly journals Optimal Talent Management of the Acquisition Workforce in Response to COVID-19: Dynamic Programming Approach

2022 ◽  
Vol 29 (99) ◽  
pp. 50-77
Author(s):  
Tom Ahn ◽  
Amilcar Menichini
Keyword(s):  
Dynamic Programming ◽  
Labor Market ◽  
The State ◽  
Retention Rates ◽  
Programming Approach ◽  
High Quality ◽  
Dynamic Programming Approach ◽  
Long Run ◽  
Short Run ◽  
The Impact

As the economic impact of the COVID-19 pandemic lingers, with the speed of recovery still uncertain, the state of the civilian labor market will impact the public sector. Specifically, the relatively stable and insulated jobs in the Department of Defense (DoD) are expected to be perceived as more attractive for the near future. This implies changes in DoD worker quit behavior that present both a challenge and an opportunity for the DoD leadership in retaining high-quality, experienced talent. The authors use a unique panel dataset of DoD civilian acquisition workers and a dynamic programming approach to simulate the impact of the pandemic on employee retention rates under a variety of recovery scenarios. Their findings posit that workers will choose not to leave the DoD while the civilian sector suffers from the impact of the pandemic. This allows leadership to more easily retain experienced workers. However, once the civilian sector has recovered enough, these same workers quit at an accelerated rate, making gains in talent only temporary. These results imply that while the DoD can take short-run advantage of negative shocks to the civilian sector to retain and attract high-quality employees, long-run retention will be achieved through more fundamental reforms to personnel policy that make DoD jobs more attractive, no matter the state of the civilian labor market.

Scheduling and control of linear projects

1994 ◽  
Vol 21 (2) ◽  
pp. 219-230 ◽  
Author(s):  
Neil N. Eldin ◽  
Ahmed B. Senouci
Keyword(s):  
Dynamic Programming ◽  
Programming Approach ◽  
State Variables ◽  
Project Schedule ◽  
Numerical Illustration ◽  
Total Cost ◽  
Dynamic Programming Approach ◽  
Completion Date ◽  
And Control ◽  
Linear Projects

A two-state-variable, N-stage dynamic programming approach to scheduling and control of linear projects is presented. This approach accounts for practical considerations related to work continuity, interruptions, and lags between successive activities. In the dynamic programming formulation, stages represent project activities and state variables represent possible activity resources and interruptions at each location. The objective of the dynamic programming solution is to provide for the selection of resources, interruptions, and lags for production activities that lead to the minimum project total cost. In addition, the presented system produces a graphical presentation of the optimum project schedule and updates the original schedule based on update information input by the user. The updated schedule determines the new completion date, and forecasts the project new total cost based on the current project performance. A small linear project is provided as a numerical illustration of the system. Key words: dynamic programming, linear projects, scheduling systems, optimization of cost and scheduling durations.

A dynamic programming approach to evolutionarily stable strategy theory

1980 ◽  
Vol 12 (01) ◽  
pp. 3-5
Author(s):  
C. Cannings ◽  
D. Gardiner
Keyword(s):  
Dynamic Programming ◽  
Density Function ◽  
Evolutionarily Stable Strategy ◽  
Programming Approach ◽  
Stable Strategy ◽  
War Of Attrition ◽  
Dynamic Programming Approach ◽  
The Individual ◽  
Image Position ◽  
Evolutionarily Stable

In the war of attrition (wa), introduced by Maynard Smith (1974), two contestants play values from [0, ∞), the individual playing the longer value winning a fixed prize V, and both incurring a loss equal to the lesser of the two values. Thus the payoff, E(x, y) to an animal playing x against one playing y, is A more general form (Bishop and Cannings (1978)) has and it was demonstrated that with and there exists a unique evolutionarily stable strategy (ess), which is to choose a random value from a specified density function on [0, ∞). Results were also obtained for strategy spaces [0, s] and [0, s).

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