Linear Tracking MPC for Nonlinear Systems-Part I: The Model-Based Case
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2022-09
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Journal Article
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Abstract
In this article, we develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed MPC scheme exponentially stabilizes the optimal reachable equilibrium w.r.t. a desired target setpoint. Our theoretical results rely on the fact that, close to the steady-state manifold, the prediction error of the linearization is small, and hence, we can slide along the steady-state manifold toward the optimal reachable equilibrium. The closed-loop stability properties mainly depend on a cost matrix, which allows us to trade off performance, robustness, and the size of the region of attraction. In an application to a nonlinear continuous stirred tank reactor, we show that the scheme, which only requires solving a convex quadratic program online, has comparable performance to a nonlinear MPC scheme while being computationally significantly more efficient. Furthermore, our results provide the basis for controlling nonlinear systems based on data-dependent linear prediction models, which we explore in our companion paper.
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67 (9)
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4390 - 4405
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IEEE
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