Feedback control problems involving autonomous polynomial systems are prevalent, yet there limited algorithms and software for approximating their solution. This paper represents a step forward by considering the special case of regulator problem where state equation has nonlinearity, costs quadratic, feedback is approximated low-degree polynomials. As this natural extension linear-quadratic (L...

This paper presents a decision procedure for a certain class of sentences of first order logic involving integral polynomials and a certain specific analytic transcendental function trans(x) in which the variables range over the real numbers. The list of transcendental functions to which our decision method directly applies includes exp(x), the exponential function with respect to base e, ln(x)...

We find polynomial-time solutions to the word problem for free-by-cyclic groups, the word problem for automorphism groups of free groups, and the membership problem for the handlebody subgroup of the mapping class group. All of these results follow from observing that automorphisms of the free group strongly resemble straight line programs, which are widely studied in the theory of compressed d...