46 Result(s)
within
English
Mathematics
Systems Theory, Control
Bopeng RAO
Chapter
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Chapter
Approximate Internal Controllability
In this chapter we show that the classic Kalman’s rank condition is not only necessary but also sufficient for the uniqueness of solution to the adjoint system
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Chapter
Approximate Internal Synchronization
The exact boundary synchronization has been studied for the coupled systems governed by PDEs since the year 2012 in [32, 33].
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Chapter
Stability of Exact Internal Synchronization
In this chapter, we will establish the equivalence between the non approximate controllability and the independence of exactly synchronizable state with respect to applied controls. The main idea consists of u...
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Chapter
Exact Internal Synchronization by Groups
In order to consider the situation that the number of internal controls is further reduced, in this chapter we investigate the exact internal synchronization by groups for system (I).
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Chapter
Approximate Internal Synchronization by Groups
In this chapter, we will clarify that the independence of approximately synchronizable state by groups with respect to applied controls the non extensibility to other approximate synchronization, the linear in...
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Chapter
Exact Internal Synchronization
In this chapter, based on the results given by Chap. 7, the exact internal synchronization and related topics will be discussed.
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Chapter
Stability of Exact Internal Synchronization by Groups
In this chapter, we will deepen the consideration in the previous chapter and show that the state variable can be divided into three groups: the first ...
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Chapter
Approximate Mixed Controllability
We will show that Kalman’s rank condition is still necessary and sufficient for the uniqueness of solution to the adjoint system associated with incomplete internal and boundary observations, therefore for the...
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Chapter
Exact Mixed Controllability
Under a suitable balanced distribution of observations, system \((I\!\!I^*)\) ( ...
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Chapter
Exact Internal Controllability
In this chapter, we show that system (I) possesses the exact controllability if and only if \({{\,\textrm{rank}\,}}(D)= N\) ...
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Chapter
Family of Exact Internal Synchronizations
The goal of this chapter is to extend the previous study from a specific grou** to the general grou**s. As a result we will examine the possibility to realize several exact internal synchronizations by gro...
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Chapter
Approximate Mixed Synchronization by Groups
In this chapter, we will study the approximate internal synchronization by groups under the internal and boundary controls such as the necessity of the condition of
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Chapter
Exact Mixed Synchronization by Groups
In this chapter we consider the exact synchronization by groups under mixed controls, and study the necessity of the condition of \(C_p\) ...
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Chapter
Indirect Internal Controls
The notion of the indirect dam** was introduced by Russell [1] in the early 1967s.
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Chapter
Exact Boundary Controllability and Non-exact Boundary Controllability
Since the exact synchronization on a finite time interval is closely linked with the exact boundary null controllability, we first consider the exact boundary controllability and the non-exact boundary nul...
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Chapter
Necessity of the Conditions of \(C_p\)-Compatibility
In this chapter, we will discuss the necessity of the conditions of \(C_p\)-compatibility for system (III) with coupled Robin boundary controls. This problem is closely related to the number of applied boundary c...
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Chapter
Exactly Synchronizable States
When system (I) possesses the exact boundary synchronization, the corresponding exactly synchronizable states will be studied in this chapter.
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Chapter
Some Algebraic Lemmas
In order to study the approximate boundary synchronization for system (III) with coupled Robin boundary controls, some algebraic lemmas are given in this chapter.
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Chapter
Approximate Boundary Synchronization by p-Groups
The boundary by p-groups is introduced and studied in this chapter for system (III) with coupled Robin controls.
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Chapter
Exactly Synchronizable States by p-Groups
When system (I) possesses the exact synchronization by p-groups, the corresponding exactly synchronizable states by p-groups will be studied in this chapter.
