Robust MPC for tracking changing setpoints in discrete‐time non‐linear systems with non‐additive unknown disturbance

Abstract

This paper develops a novel observer-based robust tracking predictive controller for discrete-time nonlinear affine systems capable of dealing with changing setpoints and nonadditive non-slowly varying unknown disturbance with bounded variations. The existence of disturbance and/or sudden changes in a setpoint may lead to feasibility and stability issues in the stabilizing terminal constraint-based MPC. Since robust tracking MPCs usually consider additive disturbance, the recursive feasibility of these methods may be lost in the presence of non-additive non-slowly varying disturbance. The robust tracking MPC presented here extends the artificial reference-based MPC to deal with both changing setpoints and non-additive non-slowly varying disturbance. The key idea is the addition of tightened input and state constraints as new system constraints. The authors also guarantee the boundedness of disturbance observation error and closed-loop tracking error. In this method, the optimal tracking error converges asymptotically to the terminal region, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. It is shown that the proposed controller can achieve offset-free tracking in the presence of constant disturbance. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.

A new less conservative design for nonlinear robust tracking predictive controller

“…The nominal tracking error converges to terminal region in one step using terminal control law as well as the state constraint (9h) is satisfied in this region. These results have been proved in Lemma 1 (condition I and II) of [46] and [45] that leads to ensuring of recursive feasibility of RTMPC optimization problem in the presence of non-additive disturbance.…”

“…− 𝑥 𝑠 are the sequences of control and state error, 𝑢(. ) is a sequence of control {𝑢(𝑘), 𝑢(𝑘 + 1), … , 𝑢(𝑘 + 𝑁 𝑐 − 1)} , 𝑘(𝑥(𝑘 + 𝑗), 𝑦 𝑠 ) = 𝐾 𝑡 (𝑦 𝑠 )𝑥(𝑘 + 𝑗) + 𝑔 𝑢 (𝑦 𝑠 ) is the appropriate terminal control law in which 𝐾 𝑡 (𝑦 𝑠 ) is obtained from solving the LMI problem [46], 𝑁 𝑝 and 𝑁 𝑐 are the prediction and control horizons, 𝑙(. ) = 𝑥 ̃(. )…”

“…Given Lemma 1 in [46], the disturbance observation error is bounded and its dynamic equation is given by 𝑒(𝑘 + 1) = (1 − 𝑇 𝑠 𝐿 𝑑 (𝑥)𝑔 2 (𝑥))𝑒(𝑘) + ∆𝑑(𝑘)…”

“…These methods include reference governor-based MPC (RGMPC) [26][27] and artificial reference-based MPC (ARMPC) [2,[28][29][30][31][32]. Using these tracking methods, several robust tracking MPCs have been presented to deal with both changing setpoints and additive disturbance [33][34][35][36][37][38][39][40][41][42][43][44] and non-additive disturbance [45][46]. To deal with additive disturbance the authors in [38][39][40][41][42] combined tube-based MPC with ARMPC for discrete-time linear [38][39][40][41] and nonlinear [42] systems.…”

Generalized Dynamic Predictive Control for Nonlinear Systems Subject to Mismatched Disturbances With Application to PMSM Drives

“…For example, the trajectory of the nonlinear tracking system subject to matched/mismatched disturbances and input constraints can be regulated by a reduced order disturbance-observer-based fuzzy MPC in [20]. The authors in [21] investigate an observer-based robust tracking predictive controller for discrete-time nonlinear affine systems to cope with changing setpoints and non-additive non-slowly varying unknown disturbance with bounded variations. A composite controller constituted by an explicit nonlinear MPC and a nonlinear disturbance observer (NDO) is proposed to tackle the autonomous flight of small-scale helicopters, which can be referred to [22].…”