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The principle of optimality :
- a)The optimal control sequence is function of initial state
- b)The optimal control sequence is function of number of stages N
- c)The principle maintains the N-stage decision process
- d)Find one control value at a time until optimal policy is determined
Correct answer is option 'A'. Can you explain this answer?
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The principle of optimality :a)The optimal control sequence is functio...
The principle of optimality reduces the N-stage decision process into N-stage single state process, which state that an optimal control policy has the property that whatever the initial state and conditions are final state must follow the optimal policy.
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The principle of optimality :a)The optimal control sequence is functio...
The Principle of Optimality Explained
The principle of optimality is a fundamental concept in dynamic programming and control theory. It essentially states that an optimal policy has the property that whatever the initial state and decision are, the remaining decisions must constitute an optimal policy for the resulting state. Here’s a deeper dive into why option 'A' is the correct answer.
Optimal Control Sequence and Initial State
- The optimal control sequence is indeed a function of the initial state. This means that the first decision (or control action) taken depends on where the system starts. Each control action has implications for future states, and hence, optimal decisions are contingent upon the initial conditions.
Influence of Stages on Control Sequence
- While the number of stages (option B) does play a role in dynamic programming, the essence of the principle of optimality emphasizes the relationship between the current state and future states rather than the number of stages involved.
Maintaining the N-Stage Decision Process
- Option C suggests that the principle maintains the N-stage decision process, which is true in a broader sense, but it does not capture the essence of how decisions are made based on the initial state.
Sequential Control Value Selection
- Option D implies a method of finding one control value at a time. This might describe a sequential approach, but it overlooks the crucial dependency on the initial state, which is central to the principle of optimality.
Conclusion
In summary, the principle of optimality asserts that the optimal control sequence is fundamentally linked to the initial state, making option 'A' the most accurate representation of this concept. Understanding this relationship is crucial for effective decision-making in control systems and dynamic programming.
The principle of optimality is a fundamental concept in dynamic programming and control theory. It essentially states that an optimal policy has the property that whatever the initial state and decision are, the remaining decisions must constitute an optimal policy for the resulting state. Here’s a deeper dive into why option 'A' is the correct answer.
Optimal Control Sequence and Initial State
- The optimal control sequence is indeed a function of the initial state. This means that the first decision (or control action) taken depends on where the system starts. Each control action has implications for future states, and hence, optimal decisions are contingent upon the initial conditions.
Influence of Stages on Control Sequence
- While the number of stages (option B) does play a role in dynamic programming, the essence of the principle of optimality emphasizes the relationship between the current state and future states rather than the number of stages involved.
Maintaining the N-Stage Decision Process
- Option C suggests that the principle maintains the N-stage decision process, which is true in a broader sense, but it does not capture the essence of how decisions are made based on the initial state.
Sequential Control Value Selection
- Option D implies a method of finding one control value at a time. This might describe a sequential approach, but it overlooks the crucial dependency on the initial state, which is central to the principle of optimality.
Conclusion
In summary, the principle of optimality asserts that the optimal control sequence is fundamentally linked to the initial state, making option 'A' the most accurate representation of this concept. Understanding this relationship is crucial for effective decision-making in control systems and dynamic programming.
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The principle of optimality :a)The optimal control sequence is function of initial stateb)The optimal control sequence is function of number of stages Nc)The principle maintains the N-stage decision processd)Find one control value at a time until optimal policy is determinedCorrect answer is option 'A'. Can you explain this answer?
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