Further results and properties of indirect adaptive model predictive control for linear systems with polytopic uncertainty

Stabilizing predictive control with persistence of excitation for constrained linear systems

“…This may appear as a shortcoming when compared to the seamless model update allowed by other approaches such as [5,6,10], but it rather owes to the expected trade-off between complexity and performance. Indeed, the design and implementation complexity of proposals such as [5,6,10] is higher when compared to the approach proposed here, demanding for example the online re-computation of various MPC elements at each time instant, or the implementation of min-max optimizations. The adaptive controller proposed in this paper is simpler in formulation and design, but at the price of not necessarily being able to update the prediction model with the true plant parameters.…”

“…Albeit several approaches have been proposed, e.g. [5][6][7][8][9][10][11][12][13][14], AMPC remains to a large extent an open problem [15,Section 3.1]. One of the reasons for this is the duality [16] of the optimal control problem, in which the objectives of achieving sufficient excitation of the system for a successful (closed-loop) identification and satisfactory regulation are competing.…”

“…Different AMPC approaches place different emphasis on these competing objectives. In [5][6][7][8][9][10], the main concern is the control objective, and different robust approaches (such as min-max optimization [6] and constraint tightening [8][9][10]) are employed in order to ensure robust constraint satisfaction and stability. The main assumption common to these approaches is that a bound on the initial modelling error is known, and that it does not increase over time; the latter is achieved by allowing parameter estimates to be updated only when the closed-loop output data is informative enough [17], but there are no guarantees that this will occur.…”

Design of adaptive model predictive control for a class of uncertain non‐linear dynamic systems: stability, convergence, and robustness analysis

“…The stability and feasibility with handling constraints are the advantages of the method of [15], however, there exists a greedy constraint on the state‐space representation that is the limitation of the algorithm. The control algorithms of [16, 17] are in fact an extension for [18]. In [18], the authors represent the uncertain dynamic model using different state‐space representation with individual coefficients that the authors of [16, 17] present a methodology to estimate the unknown coefficients.…”

“…The control algorithms of [16, 17] are in fact an extension for [18]. In [18], the authors represent the uncertain dynamic model using different state‐space representation with individual coefficients that the authors of [16, 17] present a methodology to estimate the unknown coefficients. A simple structure AMPC is given in [19, 20] for a class of non‐linear dynamic systems.…”