Abstract
SummaryFor systems with uncertain linear models, bounded additive disturbances and state and control constraints, a robust model predictive control (MPC) algorithm incorporating online model adaptation is proposed. Sets of model parameters are identified online and employed in a robust tube MPC strategy with a nominal cost. The algorithm is shown to be recursively feasible and input‐to‐state stable. Computational tractability is ensured by using polytopic sets of fixed complexity to bound parameter sets and predicted states. Convex conditions for persistence of excitation are derived and are related to probabilistic rates of convergence and asymptotic bounds on parameter set estimates. We discuss how to balance conflicting requirements on control signals for achieving good tracking performance and parameter set estimate accuracy. Conditions for convergence of the estimated parameter set are discussed for the case of fixed complexity parameter set estimates, inexact disturbance bounds, and noisy measurements.
Highlights
Model predictive control (MPC) repeatedly solves a finite-horizon optimal control problem subject to input and state constraints
Tanaskovic et al[9] consider a linear finite impulse response (FIR) model with measurement noise and constraints. This approach updates a model parameter set using online set membership identification; constraints are enforced for the entire parameter set and performance is optimized for a nominal prediction model
We propose an adaptive robust MPC algorithm that combines robust tube MPC and set membership identification
Summary
Model predictive control (MPC) repeatedly solves a finite-horizon optimal control problem subject to input and state constraints. Tanaskovic et al[9] consider a linear finite impulse response (FIR) model with measurement noise and constraints This approach updates a model parameter set using online set membership identification; constraints are enforced for the entire parameter set and performance is optimized for a nominal prediction model. The approach suffers from a lack of flexibility in its robust MPC formulation, which is based on homothetic tubes,[14] allowing only the centers and scalings of tube cross-sections to be optimized online, and it does not provide convex and recursively feasible conditions to ensure PE control inputs. We consider linear systems with parameter uncertainty, additive disturbances, and constraints on system states and control inputs.
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