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Projected dynamical systems in a complementarity formalism. (English) Zbl 0980.93031
The authors consider the so-called gradient complementarity systems of differential equations $\dot x(t)=- F(x(t))+ [H(x(t))]^T u(t),$ where $$H$$ is the Jacobian of $$h$$, $$h(x,t): \mathbb{R}^n\to \mathbb{R}^p$$, $$0\leq y(t)\perp u(t)\geq 0$$. The authors state that such equations belong to the class of projected dynamical equations of the form $\dot x(t)= \Pi_K(x(t)- F(x(t))),$ where $$F$$ is a vector field, $$K$$ is a closed convex set, and $$\Pi_K$$ is a projection operator, that prevents the solution from moving outside the constrained set $$K$$. The establishment of a connection between the areas of projected dynamical systems and complementarity systems facilitates the transfer of techniques from one domain to the other.

##### MSC:
 93C15 Control/observation systems governed by ordinary differential equations
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