Zhaoyang Wan

Brief An efficient off-line formulation of robust model predictive control using linear matrix inequalities

The practicality of model predictive control (MPC) is partially limited by its ability to solve optimization problems in real time. Moreover, on-line computational demand for synthesizing a robust MPC algorithm will likely grow significantly with the problem size. In this paper, we use the concept of an asymptotically stable invariant ellipsoid to develop a robust constrained MPC algorithm which gives a sequence of explicit control laws corresponding to a sequence of asymptotically stable invariant ellipsoids constructed off-line one within another in state space. This off-line approach can address a broad class of model uncertainty descriptions with guaranteed robust stability of the closed-loop system and substantial reduction of the on-line MPC computation. The controller design is illustrated with two examples.

Efficient robust constrained model predictive control with a time varying terminal constraint set

Abstract An efficient robust constrained model predictive control algorithm with a time varying terminal constraint set is developed for systems with model uncertainty and input constraints. The approach is novel in that it off-line constructs a continuum of terminal constraint sets and on-line achieves robust stability by using a relatively short control horizon (even N =0) with a time varying terminal constraint set. This algorithm not only dramatically reduces the on-line computation but also significantly enlarges the size of the allowable set of initial conditions. Moreover, this control scheme retains the unconstrained optimal performance in the neighborhood of the equilibrium. The controller design is illustrated through a benchmark problem.

Comments on: "Efficient robust constrained model predictive control with a time varying terminal constraint set" by Wan and Kothare

Abstract We present an algorithm that modifies the original formulation proposed in Wan and Kothare [Efficient robust constrained model predictive control with a time-varying terminal constraint set, Systems Control Lett. 48 (2003) 375–383]. The modified algorithm can be proved to be robustly stabilizing and preserves all the advantages of the original algorithm, thereby overcoming the limitation pointed out recently by Pluymers et al. [Min–max feedback MPC using a time-varying terminal constraint set and comments on “Efficient robust constrained model predictive control with a time-varying terminal constraint set”, Systems Control Lett. 54 (2005) 1143–1148].

Efficient scheduled stabilizing output feedback model predictive control for constrained nonlinear systems

In this paper, we present a computationally efficient scheduled output feedback model predictive control (MPC) algorithm for constrained nonlinear systems with large operating regions. We design a set of local output feedback predictive controllers with their estimated regions of stability covering the desired operating region, and implement them as a single scheduled output feedback MPC which online switches between the set of local controllers and achieves nonlinear transitions with guaranteed stability. The algorithm is illustrated with a highly nonlinear continuously stirred tank reactor (CSTR) process.

Computationally efficient scheduled model predictive control for constrained nonlinear systems with stability guarantees

We present a computationally efficient scheduled formulation of model predictive control (MPC) for constrained nonlinear systems with large operating regions. We design a set of local predictive controllers with their explicit regions of stability covering the desired operating region, and implement them as a single scheduled MPC which switches between the set of local controllers and achieves nonlinear transitions with guaranteed stability. This algorithm is computationally efficient and provides a general framework for scheduled MPC design.

A Computationally Efficient Scheduled Model Predictive Control Algorithm for Control of a Class of Constrained Nonlinear Systems

We present an overview of our results on stabilizing scheduled output feedback Model Predictive Control (MPC) algorithm for constrained nonlinear systems based on our previous publications [19, 20]. Scheduled MPC provides an important alternative to conventional nonlinear MPC formulations and this paper addresses the issues involved in its implementation and analysis, within the context of the NMPC05 workshop. The basic formulation involves the design of a set of local output feedback predictive controllers with their estimated regions of stability covering the desired operating region, and implement them as a single scheduled output feedback MPC which on-line switches between the set of local controllers and achieves nonlinear transitions with guaranteed stability. This algorithm provides a general framework for scheduled output feedback MPC design.

A two-level model predictive control formulation for stabilization and optimization

In this paper, we present a novel MPC algorithm, which has a two-level hierarchical structure. For the lower level control objective of stabilization, no optimization is involved, making it computationally efficient. For the higher-level control objective of achieving an economic target, on-line optimization is performed with any desired objective function and control horizon without affecting the stability of the closed-loop system. This higher-level optimization problem does not have to be solved within one sampling period, making the overall algorithm computationally attractive. The proposed two-level algorithm is illustrated with a benchmark problem.

Robust output feedback model predictive control using off-line linear matrix inequalities

We present a robust constrained output feedback model predictive control (MPC) algorithm which provides an explicit control law. With the off-line MPC law, we are able to analyze robust stabilizability of the combined control law and estimator and thus guarantee robust stability of the closed-loop system in the presence of constraints.

A Framework for Design of Scheduled Output Feedback Model Predictive Control

Abstract We present a stabilizing scheduled output feedback Model Predictive Control (MPC) algorithm for constrained nonlinear systems with large operating regions. We design a set of local output feedback predictive controllers with their estimated regions of stability covering the desired operating region, and implement them as a single scheduled output feedback MPC which on-line switches between the set of local controllers and achieves nonliilear transitions with guaranteed stability. This algorithm provides a general framework for scheduled output feedback MPC design.