Algorithm for Bernstein Polynomial Control Design

Abstract This paper considers control synthesis for polynomial control systems. The developed method leans upon Lyapunov stability and Bernstein certificates of positivity. We strive to develop an algorithm that computes a polynomial control and a polynomial Lyaponov function in the simplicial Bernstein form. Subsequently, we reduce the control synthesis problem to a finite number of evaluations of a polynomial within Bernstein coefficient bounds representing controls and Lyapunov functions. As a consequence, the equilibrium is asymptotically stable with this control.

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