Modeling method of complex dynamic network and design method of model controller
A technology of complex dynamic network and modeling method, which is applied in the design field of random pinning controller, and can solve the problem that the design of random pinning controller is not very good.
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Embodiment 1
[0047] S1. Consider a complex dynamic network with non-time-delay and time-delay coupling. It is composed of N nodes, and each node is an n-dimensional dynamic system. The specific description is:
[0048]
[0049]
[0050] S2, take A=(a ij )∈R N×N And B=(b ij )∈R N×N Respectively represent the non-delay and time-delay coupling matrices of the complex dynamic network; matrices A and B are symmetric and satisfy
[0051]
[0052] Among them, i≠j, if there is non-delay and time-delay coupling between nodes i and j, then a ij >0 and b ij >0; otherwise, a ij = 0 and b ij =0;
[0053] Consider the random exchange of related coupling matrices, that is, matrices A and B can be interchanged, and the following complex dynamic network is obtained:
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[0055] Among them, the switching between systems (1) and (2) is independent and random;
[0056] S3. Use a robust method to describe the random switching between the coupling matrix A and B, namely
[0057]
[0058] Among them, ΔA=(Δa ij )∈R ...
Embodiment 2
[0060] Design a partial delay-dependent stochastic containment controller for the above system model,
[0061] Select the first l nodes to join the partial delay-dependent stochastic pin controller u i (t), the specific description is as follows:
[0062]
[0063] Here k i And k di Respectively represent the non-time delay and time delay state feedback control gain. α(t) is a Bernoulli random variable and is described as follows:
[0064]
[0065] The corresponding probability is expressed as:
[0066] Pr{α(t)=1}=ε{α(t)}=α * , Pr{α(t)=0}=1-α *
[0067] Here α * ∈[0,1] and ε{α(t)-α * } = 0; the first form of the controller is suitable for α * There are two cases of precise known and uncertain. Its characteristic is that during the establishment process, the controller includes two parts, non-time-delay and time-delay, and these two parts appear based on certain probability conditions. The controller can stabilize the complex network system by solving the appropriate control gain....
Embodiment 3
[0069] Construct an adaptive stochastic containment controller, suitable for the following two situations
[0070] α * Unknown, δ * Known and α * Known, δ * unknown;
[0071] For the former, it has the following forms during the establishment process:
[0072]
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