Dynamic Output Feedback Robust Model Predictive Control via Zonotopic Set-Membership Estimation for Constrained Quasi-LPV Systems

Abstract

For the quasi-linear parameter varying (quasi-LPV) system with bounded disturbance, a synthesis approach of dynamic output feedback robust model predictive control (OFRMPC) is investigated. The estimation error set is represented by a zonotope and refreshed by the zonotopic set-membership estimation method. By properly refreshing the estimation error set online, the bounds of true state at the next sampling time can be obtained. Furthermore, the feasibility of the main optimization problem at the next sampling time can be determined at the current time. A numerical example is given to illustrate the effectiveness of the approach.

Dynamic Output Feedback Robust MPC with Input Saturation Based on Zonotopic Set-Membership Estimation

“…An approach to deal with input saturation is to penalize the control input such that input constraint is never violated. This approach is common in the synthesis approach of MPC; for example, see [3][4][5][6][7][8][9]. In the synthesis approach of MPC, at each sampling time, the on-line optimization problem is solved to obtain an optimal controller, which considers physical constraints (e.g., input constraint and output constraint) and stability condition.…”

“…By applying plenty of methods and techniques developed for linear systems, LPV models provide efficient ways to deal with some complex nonlinear systems [12][13][14]. When the scheduling parameters of LPV systems are exactly known at the current time but unknown in future, it is quasi-LPV system [7][8][9]. In robust MPC (RMPC) studies, a real nonlinear system is often approximated or included by polytopic uncertainty and then represented by LPV description.…”

“…In robust MPC (RMPC) studies, a real nonlinear system is often approximated or included by polytopic uncertainty and then represented by LPV description. The synthesis approach of RMPC is often solved by on-line min-max optimization, which considers all the possible realizations of polytopic model parametric uncertainty, constraints, and/or not bounded disturbance; for example, see [3,5,[7][8][9]. For the control of nonlinear systems subject to uncertainty, constraints, and faults in the control actuators, the authors in [15,16] investigate a RMPC design for fault-tolerant control.…”

“…In [7][8][9], the dynamic OFRMPC approach considers quasi-LPV systems with bounded disturbance. By taking controller parameters with a parameter-dependent form, the main optimization problem is solved as convex optimization.…”

Zonotope-based set-membership parameter identification of linear systems with additive and multiplicative uncertainties: A new algorithm

“…build a zonotope AFSS k,i =Z * k,i = p * k,i ⊕H * k,i B r that overbounds AFSS k,i−1 ∩ P k,i with minimal P-radius; 14: set i=i+1; 15: end while 16:…”