Concurrent Learning Adaptive Model Predictive Control with Pseudospectral Implementation

This paper presents a control architecture in which a direct adaptive control technique is used within the model predictive control framework, using the concurrent learning based approach, to compensate for model uncertainties. At each time step, the control sequences and the parameter estimates are both used as the optimization arguments, thereby undermining the need for switching between the learning phase and the control phase, as is the case with hybrid-direct-indirect control architectures. The state derivatives are approximated using pseudospectral methods, which are vastly used for numerical optimal control problems. Theoretical results and numerical simulation examples are used to establish the effectiveness of the architecture.Comment: 21 pages, 13 figure

Nonlinear Receding-Horizon Control of Rigid Link Robot Manipulators

The approximate nonlinear receding-horizon control law is used to treat the trajectory tracking control problem of rigid link robot manipulators. The derived nonlinear predictive law uses a quadratic performance index of the predicted tracking error and the predicted control effort. A key feature of this control law is that, for their implementation, there is no need to perform an online optimization, and asymptotic tracking of smooth reference trajectories is guaranteed. It is shown that this controller achieves the positions tracking objectives via link position measurements. The stability convergence of the output tracking error to the origin is proved. To enhance the robustness of the closed loop system with respect to payload uncertainties and viscous friction, an integral action is introduced in the loop. A nonlinear observer is used to estimate velocity. Simulation results for a two-link rigid robot are performed to validate the performance of the proposed controller. Keywords: receding-horizon control, nonlinear observer, robot manipulators, integral action, robustness

Extremum Seeking-based Iterative Learning Linear MPC

In this work we study the problem of adaptive MPC for linear time-invariant uncertain models. We assume linear models with parametric uncertainties, and propose an iterative multi-variable extremum seeking (MES)-based learning MPC algorithm to learn on-line the uncertain parameters and update the MPC model. We show the effectiveness of this algorithm on a DC servo motor control example.Comment: To appear at the IEEE MSC 201

Robust Constrained Model Predictive Control using Linear Matrix Inequalities

The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a state-feedback control law which minimizes a "worst-case" infinite horizon objective function, subject to constraints on the control input and plant output. Using standard techniques, the problem of minimizing an upper bound on the "worst-case" objective function, subject to input and output constraints, is reduced to a convex optimization involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon state-feedback control design robustly stabilizes the set of uncertain plants under consideration. Several extensions, such as application to systems with time-delays and problems involving constant set-point tracking, trajectory tracking and disturbance rejection, which follow naturally from our formulation, are discussed. The controller design procedure is illustrated with two examples. Finally, conclusions are presented

Robust and Stable Predictive Control with Bounded Uncertainties

[EN] Min-Max optimization is often used for improving robustness in Model Predictive Control (MPC). An analogy to this optimization could be the BDU (Bounded Data Uncertainties) method, which is a regularization technique for least-squares problems that takes into account the uncertainty bounds. Stability of MPC can be achieved by using terminal constraints, such as in the CRHPC (Constrained Receding-Horizon Predictive Control) algorithm. By combining both BDU and CRHPC methods, a robust and stable MPC is obtained, which is the aim of this work. BDU also offers a guided method of tuning the empirically tuned penalization parameter for the control effort in MPC. (C) 2008 Elsevier Inc. All rights reserved.This work has been partially financed by DPI2005-07835 and DPI2004-08383-C03-02 MEC-FEDER.Ramos Fernández, C.; Martínez Iranzo, MA.; Sanchís Saez, J.; Herrero Durá, JM. (2008). Robust and Stable Predictive Control with Bounded Uncertainties. Journal of Mathematical Analysis and Applications. 342(2):1003-1014. https://doi.org/10.1016/j.jmaa.2007.12.073S10031014342

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