Sufficient conditions for asymptotic optimal control

1980 ◽  
Vol 32 (3) ◽  
pp. 307-325
Author(s):  
G. M. Ewing
Keyword(s):  
Optimal Control ◽  
Sufficient Conditions ◽  
Asymptotic Optimal Control

Some Sufficiency Conditions for Pareto-Optimal Control

1973 ◽  
Vol 95 (4) ◽  
pp. 356-361 ◽  
Author(s):  
G. Leitmann ◽  
W. Schmitendorf
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Pareto Optimality ◽  
Optimal Control Theory ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Pareto Optimal ◽  
Vector Valued ◽  
Sufficiency Conditions

We consider the optimal control problem with vector-valued criterion (including cooperative games) and seek Pareto-optimal (noninferior) solutions. Scalarization results, together with modified sufficiency theorems from optimal control theory, are used to deduce sufficient conditions for Pareto-optimality. The utilization of these conditions is illustrated by various examples.

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.

Optimal control of production with improvement

2018 ◽  
Vol 232 (6) ◽  
pp. 777-785
Author(s):  
Nobuyuki Tamura
Keyword(s):  
Optimal Control ◽  
State Space Model ◽  
Sufficient Conditions ◽  
Control Policy ◽  
Quality Characteristic ◽  
Process Mean ◽  
Initial Value ◽  
Target Value ◽  
The Relationship ◽  
Asymmetric Function

This article considers a process that produces items and in which the process mean is observed periodically. We use a state-space model to describe the relationship between the process mean and the quality characteristic of the items. At each observation, one of the following actions can be taken: production, repair, replacement, or improvement. When production is chosen, some number of items are produced. The quality characteristic of the items has a target value, and the quality loss is expressed by an asymmetric function of the deviation of the quality characteristic from the target value. Replacement resets the process mean to an initial value. When improvement is selected, the process mean is returned to the same initial value as in replacement. When improvement is repeated, it becomes less likely that the process mean will increase. There are several kinds of repairs, and each repair returns the process mean to some value greater than the initial value. For this model, we obtain a total expected discount cost for an unbounded horizon, and we show that under several reasonable assumptions, a control-limit policy is optimal. Furthermore, we derive the sufficient conditions to ensure that the optimal control policy has monotonic structures.

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