4.6 Example: The Arms Race A simple model of the arms race between two nations has been obtained by Richardson (1960). This can be written in state space notation as X₁ X₁ + X₂ + bu (4.39a) X₂X₁ + X₂ + b₂u₂ (4.39b) where the state variables x, and x, and coefficients a, are defined as follows: • x, and x₂: the arms expenditures of each of the two adversarial (groups of) nations. • az and an: threat coefficients which cause the (groups of) nations to increase their arms expenditure. an and agg: fatigue and expense coefficients, resulting from the burden of continuing the arms race. . u, and us: grievances and other factors which lead to nations arming at a constant rate.
4.6 Example: The Arms Race A simple model of the arms race between two nations has been obtained by Richardson (1960). This can be written in state space notation as X₁ X₁ + X₂ + bu (4.39a) X₂X₁ + X₂ + b₂u₂ (4.39b) where the state variables x, and x, and coefficients a, are defined as follows: • x, and x₂: the arms expenditures of each of the two adversarial (groups of) nations. • az and an: threat coefficients which cause the (groups of) nations to increase their arms expenditure. an and agg: fatigue and expense coefficients, resulting from the burden of continuing the arms race. . u, and us: grievances and other factors which lead to nations arming at a constant rate.
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which techniques of control theory can be used in the example and also elaborate on how control theory can contribute to sustainable development.
Transcribed Image Text:4.6 Example: The Arms Race
A simple model of the arms race between two nations has been obtained
by Richardson (1960). This can be written in state space notation as
X1 = - Xị + a2 Xạ + bịu,
(4.39a)
X2= a1 X + -a2 X2 + byu;
(4.39b)
where the state variables x, and x2 and coefficients ag are defined as
follows:
• x, and x;: the arms expenditures of each of the two adversarial (groups
of) nations.
• a1z and an: threat coefficients which cause the (groups of) nations to
increase their arms expenditure.
• a and az: fatigue and expense coefficients, resulting from the burden
of continuing the arms race.
• uj and uz: grievances and other factors which lead to nations arming at a
constant rate.
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