Off-line Robust Model Predictive Control Research Articles

Design and Verification of Offline Robust Model Predictive Controller for Wheel Slip Control in ABS Brakes

Wheel slip control is a critical aspect of vehicle safety systems, notably the antilock braking system (ABS). Designing a robust controller for the ABS faces the challenge of accommodating its strong nonlinear behavior across varying road conditions and parameters. To ensure optimal performance during braking and prevent skidding or lock-up, the ideal wheel slip value can be determined from the peak of the tire–road friction curve and maintained throughout the braking process. Among various control approaches, model predictive control (MPC) demonstrates superior performance and robustness. However, online MPC implementation encounters significant computational burdens and real-time limitations, particularly when dealing with larger problem sizes. To address these issues, this study introduces an offline robust model predictive control (RMPC) methodology. The proposed approach is based on the robust asymptotically stable invariant ellipsoid methodology, which employs linear matrix inequalities (LMIs) to calculate a collection of invariant state feedback laws associated with a sequence of nested invariant stable ellipsoids. Simulation results indicate a significant reduction in computational burden with the offline RMPC approach compared to online implementation, while effectively tracking the desired wheel slip reference values and system constraints. Moreover, the offline RMPC design aligns well with the online MPC design and verifies its effectiveness in practice.

A New Approach to Off-Line Robust Model Predictive Control for Polytopic Uncertain Models

Concerning the robust model predictive control (MPC) for constrained systems with polytopic model characterization, some approaches have already been given in the literature. One famous approach is an off-line MPC, which off-line finds a state-feedback law sequence with corresponding ellipsoidal domains of attraction. Originally, each law in the sequence was calculated by fixing the infinite horizon control moves as a single state feedback law. This paper optimizes the feedback law in the larger ellipsoid, foreseeing that, if it is applied at the current instant, then better feedback laws in the smaller ellipsoids will be applied at the following time. In this way, the new approach achieves a larger domain of attraction and better control performance. A simulation example shows the effectiveness of the new technique.

An Off-line RMPC Algorithm for Uncertain Systems Using Polyhedral Invariant Sets

Based on the polyhedral invariant sets, an off-line robust model predictive control algorithm is developed for an input-constrained and output-constrained uncertain linear discrete system. First, a sequence of discrete states is chosen to compute the corresponding state feedback control laws, and also construct each polyhedral invariant set. At each sampling time, the smallest polyhedral invariant set that the current measured state can be embedded is determined. Implementing the continuous state feedback control laws based on the position of the current measured state between the adjacent polyhedral invariant sets. Simulation results show that, compared to the ellipsoidal off-line RMPC algorithm, the proposed algorithm yields a substantial expansion of the region can be stabilized, achieve a less conservative result.

A Polyhedral Off-Line Robust MPC Strategy for Uncertain Polytopic Discrete-Time Systems

In this paper, an off-line synthesis approach to robust constrained model predictive control for uncertain polytopic discrete-time systems is presented. Most of the computational burdens are moved off-line by pre-computing a sequence of state feedback control laws that corresponds to a sequence of polyhedral invariant sets. The state feedback control laws computed are derived by minimizing the nominal performance cost in order to improve control performance. At each sampling instant, the smallest polyhedral invariant set containing the currently measured state is determined. The corresponding state feedback control law is then implemented to the process. The controller design is illustrated with two examples in chemical processes. The proposed algorithm is compared with an ellipsoidal off-line robust model predictive control algorithm derived by minimizing the worst-case performance cost and an ellipsoidal off- line robust model predictive control algorithm derived by minimizing the nominal performance cost. The results show that the proposed algorithm can achieve better control performance. Moreover, a significantly larger stabilizable region is obtained.

An off-line robust MPC algorithm for uncertain polytopic discrete-time systems using polyhedral invariant sets

In this paper, an off-line synthesis approach to robust model predictive control (MPC) using polyhedral invariant sets is presented. Most of the computational burdens are moved off-line by computing a sequence of state feedback control laws corresponding to a sequence of polyhedral invariant sets. At each sampling time, the smallest polyhedral invariant set that the currently measured state can be embedded is determined. The corresponding state feedback control law is then implemented to the process. The controller design is illustrated with two examples. Comparisons between the proposed algorithm and an ellipsoidal off-line robust MPC algorithm have been undertaken. The proposed algorithm yields a substantial expansion of the stabilizable region. Therefore, it can achieve less conservative result as compared to an ellipsoidal off-line robust MPC algorithm.

An ellipsoidal off-line robust model predictive control strategy for uncertain polytopic discrete-time systems

In this paper, an off-line robust model predictive control strategy for uncertain polytopic discrete-time systems is presented. The on-line computational burdens are reduced by precomputing off-line the sequence of state feedback gains corresponding to the sequences of nested ellipsoids. The number of sequences of nested ellipsoids constructed is equal to the number of vertices of polytope. At each sampling instant, the smallest ellipsoid containing the currently measured state is determined in each sequence of ellipsoids. The real-time state feedback gain is then calculated by solving a numerically low-demanding optimization problem. The nominal model of the plant is included in the controller design in order to improve control performance. An overall algorithm is proved to guarantee robust stability.

The Polyhedral Off-line Robust Model Predictive Control Strategy for Uncertain Polytopic Discrete-time Systems

In this paper, an off-line synthesis approach to robust constrained model predictive control is presented. Most of the computational burdens are reduced by computing off-line a sequence of state feedback control laws that corresponds to a sequence of polyhedral invariant sets. At each sampling time, the smallest polyhedral invariant set containing the currently measured state is determined and the corresponding state feedback control law is implemented to the process. The proposed algorithm is compared with an ellipsoidal off-line robust model predictive control algorithm. The results show that the proposed algorithm can achieve better control performance. Moreover, a significantly larger feasible region is obtained. The controller design is illustrated with an example of continuous stirred-tank reactor.

New formulation of robust MPC by incorporating off-line approach with on-line optimization

This article addresses robust model predictive control (MPC) for systems with polytopic description. An existing off-line robust MPC enables the on-line computation as simple as searching a state feedback gain among the look-up table. We consider enlarging the region of attraction of the off-line MPC by incorporating free perturbation items. First, a larger ellipsoidal region of attraction is off-line constructed, in which a simple optimization problem is solved on-line. Then, outside of this larger ellipsoid, a standard robust MPC is solved on-line such that the overall region of attraction can be rendered as a much larger nonellipsoidal one. The proposed approach possesses all the merits of the off-line MPC and greatly enlarges the region of attraction. A simulation example is given to demonstrate the effectiveness.