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Preuster, Till ; Worthmann, Karl ; Grüne, Lars ; Schaller, Manuel:
Cost controllability and predictive control of input-constrained monotone systems on Hilbert spaces.
Chemnitz ; Ilmenau ; Bayreuth
,
2026
. - 19 S.
DOI: https://doi.org/10.48550/arXiv.2611.14393
Abstract
Cost controllability, relating controllability and a performance measure like the stage cost in model predictive control (MPC), is a key tool in the stability and suboptimality analysis of closed-loop systems. We establish cost controllability for maximal monotone control systems subject to input constraints, a class encompassing finite- and infinite-dimensional port-Hamiltonian systems with colocated input and output. To this end, we employ a recently proposed saturated feedback to derive state-dependent bounds on the closed-loop cost. Our main result is that cost controllability holds globally with semiglobal exponential rate. We first establish this result in continuous time and then extend it to sampled-data systems. Whereas a qualitative detectability-like property is sufficient for asymptotic convergence of the controller, cost controllability requires quantitative rates. We provide two verifiable conditions ensuring cost controllability with explicit exponential rates: coercivity of the sum of system operator and output injection, and exponential detectability of the linear part. Moreover, under the coercivity condition, the resulting MPC scheme without terminal conditions renders the equilibrium globally asymptotically stable with semiglobal exponential rate already for prediction horizon two. We illustrate our results by a nonlinear finite-dimensional system, a semilinear heat equation and a nonlinearly damped wave equation.