Patent ID: 11923969
Assignee: THE REGENTS OF THE UNIVERSITY OF CALIFORNIA
Field: Computer technology (Electrical engineering)
Classification: CPC G  H | IPC G  H

Claim 9:
10. The system of claim 8, wherein:
determining the time rate of change of the system state between communication event times comprises setting:, u
                      .
                    
                    i
                  
                  =
                  
                    
                      
                        h
                        i
                      
                      ⁢
                      
                        η
                        i
                      
                    
                    -
                    
                      
                        μ
                        i
                      
                      ⁡
                      
                        (
                        
                          
                            
                              τ
                              ^
                            
                            i
                          
                          -
                          
                            τ
                            i
                            *
                          
                        
                        )
                      
                    
                  
                
                ,
                
                  
                    
                      η
                      .
                    
                    i
                  
                  =
                  
                    
                      h
                      i
                    
                    ⁢
                    
                      η
                      i
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      a
                      
                        .
                        ^
                      
                    
                    i
                  
                  =
                  
                    -
                    
                      
                        μ
                        i
                      
                      ⁡
                      
                        (
                        
                          
                            
                              τ
                              ^
                            
                            1
                          
                          -
                          
                            τ
                            i
                            *
                          
                        
                        )
                      
                    
                  
                
                ,
                
                  
                    
                      τ
                      
                        .
                        ^
                      
                    
                    i
                  
                  =
                  
                    
                      
                        a
                        ^
                      
                      i
                    
                    -
                    
                      (
                      
                        
                          
                            τ
                            ^
                          
                          i
                        
                        -
                        
                          τ
                          i
                          *
                        
                      
                      )
                    
                  
                
              
            
          
        
        }
      
      ⁢
      τ
    
    ∈
    
      [
      
        0
        ,
        
          T
          2
        
      
      ]
    
  
  ;, and, updating the system state at the communication event times comprises setting:, u
                  i
                  +
                
                =
                
                  
                    
                      -
                      
                        γ
                        i
                      
                    
                    ⁢
                    
                      
                        ∑
                        
                          k
                          ⁢
                          
                            
                          
                          ⁢
                          
                            ϵ𝒩
                            ⁡
                            
                              (
                              i
                              )
                            
                          
                        
                      
                      ⁢
                      
                        (
                        
                          
                            
                              τ
                              ~
                            
                            i
                          
                          -
                          
                            
                              τ
                              ~
                            
                            k
                          
                        
                        )
                      
                    
                  
                  -
                  
                    
                      a
                      ^
                    
                    i
                  
                  +
                  
                    σ
                    *
                  
                
              
              ,
              
                
                  
                    a
                    ^
                  
                  i
                  +
                
                =
                
                  
                    a
                    ^
                  
                  i
                
              
            
          
        
        
          
            
              
                
                  η
                  i
                  +
                
                =
                
                  
                    -
                    
                      γ
                      i
                    
                  
                  ⁢
                  
                    
                      ∑
                      
                        k
                        ⁢
                        
                          
                        
                        ⁢
                        
                          ϵ𝒩
                          ⁡
                          
                            (
                            i
                            )
                          
                        
                      
                    
                    ⁢
                    
                      (
                      
                        
                          
                            τ
                            ~
                          
                          i
                        
                        -
                        
                          
                            τ
                            ~
                          
                          k
                        
                      
                      )
                    
                  
                
              
              ,
              
                
                  
                    τ
                    ^
                  
                  i
                  +
                
                =
                
                  
                    τ
                    ^
                  
                  i
                
              
            
          
        
      
      }
    
    ⁢
    τ
  
  =
  0

where h, μ and y are parameters set to aid convergence of the clock rate τi to the common clock rate σ*,

ei−ek={tilde over (τ)}i−{tilde over (τ)}k, and

ui, τi, τi, âi, and {circumflex over (τ)}i, are variables representing the system state.