Robustness analysis for MPC and infinite-horizon optimal control under plant-model mismatch with quadratic costs. Covers discounted and undiscounted scenarios, stability guarantees, and suboptimality bounds. Use when: (1) MPC robustness analysis, (2) plant-model mismatch effects, (3) discounted infinite-horizon control, (4) model uncertainty in optimal control, (5) stability under model errors, (6) data-driven surrogate models.
Comprehensive framework for analyzing stability and suboptimality of MPC and infinite-horizon optimal control under plant-model mismatch.
Design optimal controls using surrogate model f instead of true plant dynamics g. Characterize:
True plant dynamics:
x+ = g(x, u), g(0,0) = 0
Surrogate model (used for control design):
x+ = f(x, u), f continuous, f(0,0) = 0
Key measure: Proportional plant-model mismatch
|f - g|_S := inf{p ≥ 0 : |f(x,u) - g(x,u)| ≤ p(|x| + |u|) ∀x ∈ S, u ∈ U}
Properties:
f(0,0) = g(0,0) = 0S (model assumptions hold / data available)L-Lipschitz continuity:
|f(x,u) - f(y,u)| ≤ L|x - y| ∀x,y ∈ R^n, ∀u ∈ U
Control set:
U closed, contains 0General form (finite/infinite horizon, discounted/undiscounted):
J_{γ,N}^f(x, u_N) = ∑_{k=0}^{N-1} γ^k ℓ(φ_f(k,x,u_k), u_k)