Model Predictive Control For Linear Systems Research Articles

Event‐triggered MPC for linear systems with bounded disturbances: An accumulated error based approach

A novel accumulated error based event-triggered model predictive control (MPC) algorithm is put forward on the basis of the dual-mode control strategy and state-feedback control for constrained continuous-time linear time-invariant (LTI) systems with constraints and bounded disturbances. First, a new event-triggered mechanism (ETM) is constructed based on the accumulated error (AE) between the optimal state trajectory and the real state trajectory. Next, in order to stabilize the system, the dual-mode event-triggered MPC strategy is established. Then, sufficient conditions are established to guarantee the algorithm feasibility, system stability, and to avoid the Zeno behavior. Finally, the numerical simulation shows the validity of the algorithm.

Robust Learning Model-Predictive Control for Linear Systems Performing Iterative Tasks

In this article, a robust learning model-predictive controller (LMPC) for uncertain systems performing iterative tasks is presented. At each iteration of the control task, the closed-loop state, input, and cost are stored and used in the controller design. This article first illustrates how to construct robust control invariant sets and safe control policies exploiting historical data. Then, we propose an iterative LMPC design procedure, where data generated by a robust controller at iteration <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$j$</tex-math></inline-formula> are used to design a robust LMPC at the next iteration <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$j+1$</tex-math></inline-formula> . We show that this procedure allows us to iteratively enlarge the domain of the control policy, and it guarantees recursive constraints satisfaction, input-to-state stability, and performance bounds for the certainty equivalent closed-loop system. The use of different feedback policies along the horizon is the key element of the proposed design. The effectiveness of the proposed control scheme is illustrated on a linear system subject to bounded additive disturbances.

On linear programming and robust model-predictive control using impulse-responses

Campo and Morari have derived a linear programming problem, with a potentially large number of constraints, which is equivalent to a min-max formulation for robust model-predictive control of linear systems. That formulation involves minimization, with respect to the controls, of the maximum, with respect to the system's impulse response (from a set of possible impulse responses), of the infinity norm of the error between the predicted and required system output sequences. Here an alternative linear programming problem is derived which has a smaller number of constraints and is therefore potentially more convenient for on-line control.