Model mismatch often presents significant challenges in model-based controller design. This paper investigates model predictive control (MPC) for uncertain linear systems with input constraints, where the uncertainty is characterized by a parametric mismatch between the true system and its estimated model. The main contributions of this work are twofold. First, a theoretical performance bound is derived using relaxed dynamic programming. This bound provides a novel insight into how the prediction horizon and modeling errors affect the suboptimality of the MPC controller to the oracle infinite-horizon optimal controller, which has complete knowledge of the true system. Second, sufficient conditions are established under which the nominal MPC controller, which relies solely on the estimated system model, can stabilize the true system despite model mismatch. Numerical simulations are presented to validate these theoretical results, demonstrating the practical applicability of the derived conditions and bounds. These findings offer practical guidelines for achieving desired modeling accuracy and selecting an appropriate prediction horizon in designing certainty-equivalence MPC controllers for uncertain linear systems.@en

Nonlinear Programs (NLPs) are prevalent in optimization-based control of nonlinear systems. Solving general NLPs is computationally expensive, necessitating the development of fast hardware or tractable suboptimal approximations. This paper investigates the sensitivity of the solutions of NLPs with polytopic constraints when the nonlinear continuous objective function is approximated by a PieceWise-Affine (PWA) counterpart. By leveraging perturbation analysis using a convex modulus, we derive guaranteed bounds on the distance between the optimal solution of the original polytopically-constrained NLP and that of its approximated formulation. Our approach aids in determining criteria for achieving desired solution bounds. Two case studies on the Eggholder function and nonlinear model predictive control of an inverted pendulum demonstrate the theoretical results.

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This letter proposes a passive-active model identification algorithm for affine discrete-time systems that integrates active model discrimination (AMD) and model invalidation (MI). A look-up tree consisting of control inputs is constructed offline for this integrated model identification (IMI) technique to discriminate among models in a time-varying model set, which is only known at run time when repeatedly applying MI online. Furthermore, a novel tunable AMD (TAMD), with its mixed-integer linear programming (MILP) formulation, is proposed and combined with the IMI algorithm, which can improve model discrimination performance. The effectiveness of the proposed IMI algorithm is demonstrated through simulations for identifying intention models of human-driven vehicles in a lane changing scenario.

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