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This paper proposes a scheme for the coordination of planar mobile robots based on Zero-Sum differential game model. The robots' dynamic are given in the polynomial approximation of the nonlinear model, we explore the so-called state-dependent Riccati equations to find a set of strategies that guarantee the effectively drive the robots to a particular formation. One of the robots acts as the leader following a free designed trayectory meanwhile the rest of the robots just follow him. The proposed solution is given as a polynomial Riccati-like state-dependent differential equation which utilizes a p-linear form tensor representation for its polynomial part. A numerical example is presented to illustrate effectiveness of the approach.

This paper studies the control of a nonlinear electrical circuit exemplified by a Duffing equation, which contains parameter uncertainties in the right hand side of this nonlinear differential equation. Even though this type of circuit has been object of a variety of control strategies in the past, very few papers have been devoted to the design of an optimal control law with a quadratic performance index and subject to that type of uncertainties. We develop simulation examples that show that not only an optimal control strategy can be applied to such a system, in case of an optimal control strategy without uncertainties, but an optimal control of the mini-max type can also be implemented in case of the uncertainty in the model.