# What does the term “attainable set” mean?

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What does the term “attainable set” mean? |

Explanation

Reference:

Ancona, F., & Marson, A. (1998). On the attainable set for scalar nonlinear conservation laws with boundary control. SIAM Journal on Control and Optimization, 36(1), 290-312.

Guseinov, K. G., & Nazlipinar, A. S. (2010). Attainable sets of the control system with limited resources. Труды Института математики и механики УрО РАН, 16(5), 261-268.

Grigorieva, E. V., & Khailov, E. N. (2005). Attainable set of a nonlinear controlled microeconomic model. Journal of dynamical and control systems, 11(2), 157-176.

Benzerrouk, A., Adouane, L., & Martinet, P. (2013, June). Obstacle avoidance controller generating attainable set-points for the navigation of multi-robot system. In 2013 IEEE Intelligent Vehicles Symposium (IV) (pp. 487-492). IEEE.

Answer

Attainable set

attainable set addresses all portfolios that can be developed from a given set of stocks; otherwise called the feasible set.

The set of portions fulfils all the imperatives in a monetary model. For a customer, for instance, the possible set is all utilization designs that fulfil the spending requirement. For a trade economy.

Deciding the Attainable set

There are three different ways to decide the practical set for an arrangement of disparities. All techniques start by drawing the imperative lines.

1. For every imperative disparity, choose which side of the limitation line fulfils the imbalance. Take the crossing point of every one of the sets.

2. Pick a point in a district and check whether it fulfils the imbalance. If it does, the area containing this point is the achievable set. If not, pick a point in an alternate district. Proceed until you locate the achievable set. If you check all the locales and none work, the practical set is unfilled. Deciding the attainable set

3. This strategy is a mix of the initial two.

Stage 1. Name every locale.

Stage 2. Pick a requirement line. Gap the set of districts into those which fulfils the line's > disparity and those which fulfil its < imbalance. Those which fulfil the right disparity structure the "conceivable set", P1. The rest can be overlooked.

Stage 3. Pick another limitation line and gap P1 into those areas which fulfil the > imbalance and those which fulfils the < disparity. The new "conceivable set" P2 is the subset of the past "conceivable set" which fulfil the right second imbalance.

Stage 4 Repeat stage 3 until you have utilized all the requirement lines, getting P3, . . . , Pn. If whenever Pr is vacant you are done and the plausible set is unfilled. After you have utilized all the limitation lines, the Pn will have one locale left in it and this district is the attainable set.

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