Computational burden reduction in Min-Max MPC

Min–max model predictive control (MMMPC) is one of the strategies used to control plants subject to bounded uncertainties. The implementation of MMMPC suffers a large computational burden due to the complex numerical optimization problem that has to be solved at every sampling time. This paper shows how to overcome this by transforming the original problem into a reduced min–max problem whose solution is much simpler. In this way, the range of processes to which MMMPC can be applied is considerably broadened. Proofs based on the properties of the cost function and simulation examples are given in the paper

Robust predictive feedback control for constrained systems

A new method for the design of predictive controllers for SISO systems is presented. The proposed technique allows uncertainties and constraints to be concluded in the design of the control law. The goal is to design, at each sample instant, a predictive feedback control law that minimizes a performance measure and guarantees of constraints are satisfied for a set of models that describes the system to be controlled. The predictive controller consists of a finite horizon parametric-optimization problem with an additional constraint over the manipulated variable behavior. This is an end-constraint based approach that ensures the exponential stability of the closed-loop system. The inclusion of this additional constraint, in the on-line optimization algorithm, enables robust stability properties to be demonstrated for the closed-loop system. This is the case even though constraints and disturbances are present. Finally, simulation results are presented using a nonlinear continuous stirred tank reactor model

Min-Max MPC based on a computationally efficient upper bound of the worst case cost

Min-Max MPC (MMMPC) controllers [P.J. Campo, M. Morari, Robust model predictive control, in: Proc. American Control Conference, June 10–12, 1987, pp. 1021–1026] suffer from a great computational burden which limits their applicability in the industry. Sometimes upper bounds of the worst possible case of a performance index have been used to reduce the computational burden. This paper proposes a computationally efficient MMMPC control strategy in which the worst case cost is approximated by an upper bound based on a diagonalization scheme. The upper bound can be computed with O(n3) operations and using only simple matrix operations. This implies that the algorithm can be coded easily even in non-mathematical oriented programming languages such as those found in industrial embedded control hardware. A simulation example is given in the paper

Predictive feedback control using a multiple model approach

A new method of designing predictive controllers for SISO systems is presented. The controller selects the model used in the design of the control law from a given set of models according to a switching rule based on output prediction errors. The goal is to design, at each sample instant, a feedback control law that ensures robust stability of the closed–loop system and gives better performance for the current operating point. The overall multiple model predictive control scheme quickly identifies the closest linear model to the dynamics of the current operating point, and carries out an automatic reconfiguration of the control system to achieve a better performance. The results are illustrated with simulations of a continuous stirred tank reactor