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arXiv · 2608.17652

On the behavior assignment problem

Francesca Mazzolani·Michelangelo Bin·Lorenzo Marconi
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Abstract

This paper introduces the asymptotic behavior assignment problem for nonlinear systems. Given a controlled system and a reference system with an ``open'' input, the goal is to design a regulator such that, for every admissible input, the asymptotic input-output behavior of the closed-loop system reproduces that of the reference. This formulation captures, as special cases, classical model matching, disturbance rejection, and master-slave synchronization, but does not assume that an explicit tracking or regulation error is available for feedback. Motivated by nonlinear output regulation, we discuss how steady-state concepts for autonomous systems must be adapted when the closed-loop dynamics is not autonomous. In a SISO normal-form setting we devise sufficient conditions for the solution of the behavior assignment problem by introducing a synchrony-detection signal whose convergence to zero is equivalent to successful behavior assignment, thereby reducing the problem to a standard stabilization one. Two examples, a tunnel-diode circuit with multiple input-dependent equilibria, and a pendulum frequency-matching problem, illustrate how the proposed framework avoids artificially selecting a specific steady state.

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Francesca Mazzolani, Michelangelo Bin, Lorenzo Marconi. 2026-08-18. On the behavior assignment problem. https://arxiv.org/abs/2608.17652

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