Projected dynamical system

Projected dynamical systems is a <a href="/facts/Mathematics/pxTouaz4">mathematical</a> theory investigating the behaviour of <a href="/facts/Dynamical_system/782gREl5">dynamical systems</a> where solutions are restricted to a constraint set. The discipline shares connections to and applications with both the static world of <a href="/facts/Optimization_(mathematics)/oRn8Iv5I">optimization</a> and <a href="/facts/Equilibrium_point/DgbGMPkg">equilibrium</a> problems and the dynamical world of <a href="/facts/Ordinary_differential_equations/ygKGQ8kD">ordinary differential equations</a>. A projected dynamical system is given by the <a href="/facts/Flow_(mathematics)/CrmJPfeV">flow</a> to the projected differential equation

d
              x
              (
              t
              )
            
            
              d
              t
            
          
        
        =
        
          Π
          
            K
          
        
        (
        x
        (
        t
        )
        ,
        −
        F
        (
        x
        (
        t
        )
        )
        )
      
    
    {\displaystyle {\frac {dx(t)}{dt}}=\Pi _{K}(x(t),-F(x(t)))}

where K is our constraint set. Differential equations of this form are notable for having a discontinuous vector field.

Projected dynamical system open-in-new

Projected dynamical system