Adaptive receding horizon predictive control for constrained discrete-time linear systems with parameter uncertainties

Abstract

This paper proposes a discrete-time model predictive control (MPC) scheme combined with an adaptive mechanism. To this end, first, an adaptive parameter estimation algorithm suitable for MPC is proposed, which uses the available input and output signals to estimate the unknown system parameters. It enables the prediction of a monotonically decreasing worst-case estimation error bound over the prediction horizon of MPC. These distinctive features allow for future model improvement to be explicitly considered in MPC. Thus, a less conservative adaptive-type MPC controller can be developed based on the proposed estimation method. Second, we show how the discrete-time adaptive-type state-feedback MPC controller is constructed by combining the on-line parameter estimation scheme with a modified robust MPC method based on the comparison model. The developed MPC controller guarantees feasibility and stability of the closed-loop system theoretically in the presence of input and state constraints. A numerical example is given to demonstrate its effectiveness.

Adaptive receding horizon control for constrained MIMO systems

“…The required initial information on the system is given by some (eventually very loose) bounds on its impulse response coefficients and by bounds on the magnitudes of the output disturbance and measurement noise. Unlike the methods in Aswani et al (2013) and Kim and Sugie (2008), the proposed approach cannot be used to control open-loop unstable systems but, on the other hand, it can handle systems with multiple inputs and measurement noise and requires a smaller amount of initial knowledge on the plant. It has to be noted that the requirement for open-loop stability is quite common in the context of system identification and adaptive control.…”

“…adaptive control approaches cannot deal with hard output constraints. In Kim and Sugie (2008), an adaptive MPC algorithm for a class of single input multiple output linear systems, based on modified recursive least squares identification and tube-like robust MPC, was proposed. The algorithm is capable of handling both input and output constraints and it guarantees stability and recursive feasibility, but the state space structure of the plant needs to be known and noise free measurements of the plant states are required.…”

Experimental testing of an adaptive model predictive controller on a quad-tank system

“…When the system to be controlled is uncertain, an attractive idea is to combine MPC with an on-line identification procedure, in order to gradually improve performance over time, as more data is collected from the system, while at the same time still satisfying the input and output constraints. This idea has been explored by several researchers ( [1], [2], [3], [4]). …”

Towards dual robust nonlinear model predictive control: A multi-stage approach

“…Recently, [10] presented a dual control approach to linear MPC using expected cost and uncertainty reduction via iterative learning using recursive least squares method and [11] presented a method that takes into account in the prediction the expected reduction of the uncertainty.…”

“…On the one hand, the use of multistage NMPC and the representation of the uncertainty as a scenario tree makes it possible to take into account that the future control inputs can be adapted to the observations. This means that the future control actions act as recourse variables without a fixed feedback structure (in contrast to [11]), which can improve significantly the performance as shown in [12]. On the other hand, the branches of the scenario tree can be adapted along the prediction horizon according to the expected reduction of the uncertainty.…”