Model Predictive Controllers

Abstract

This chapter describes the elements that are common to all Model Predictive controllers, showing the various alternatives used in the different implementations. Some of the most popular methods will later be reviewed to demonstrate their most outstanding characteristics. MPC ElementsAll the MPC algorithms possess common elements, and different options can be chosen for each element giving rise to different algorithms. These elements are:• prediction model, • objective function and • obtaining the control law. Prediction ModelThe model is the cornerstone of MPC; a complete design should include the necessary mechanisms for obtaining the best possible model, which should be complete enough to fully capture the process dynamics and allow the predictions to be calculated, and at the same time to be intuitive and permit theoretic analysis. The use of the process model is determined by the necessity to calculate the predicted output at future instantsŷ(t + k | t). The different strategies of MPC can use various models to represent the relationship between the outputs and the measurable inputs, some of which are manipulated variables and others can be considered to be measurable disturbances which can be compensated for by feedforward action. A disturbance model can also be taken into account to describe the behaviour not reflected by the process model, including the effect of nonmeasurable inputs, E. F. Camacho et al., Model Predictive Control

Recent Advances in Opinion Modeling: Control and Social Influence

“…We refer to [3,6,36,60] for further discussion on the analytical and numerical studies on this class of problems. The additional constraints on the pointwise values of u(t) given by uL and uR, are necessary in order to preserve the bounds of wi ∈ I (see [35,82]). …”

“…In what follows we sketch an approximation method for the solution of (2.1)-(2.2), based on model predictive control (MPC), which furnishes a suboptimal control by an iterative solution over a sequence of finite time steps, but, nonetheless, it allows an explicit representation of the control strategy [6,35,81,80].…”

“…Then the average opinion m(t) evolves according to 35) which is obtained from the scaled equation (2.26) through the quasi-invariant opinion limit (cf. also equation (2.24) for a comparison).…”

Model predictive control application to spacecraft rendezvous in mars sample return scenario

“…constraints to express the 1-norm in (3), plus as many constraints as the ones that are optionally de¦ned in (2). The user can exploit the maximum §exibility o¨ered by the EML language to de¦ne the prediction model (1) and all the parameters appearing in the MPC optimization problem (2) in an EML module, which is then used by the LTV-MPC Simulink block to construct and solve problem (3).…”

Model Predictive Control for Nonlinear Parabolic Differential Equations Based on a Linear Quadratic Gaussian Design

“…We refer for instance to [6] for a detailed study of the LQG design, to [1] for the MPC strategy and to [2] for Riccati equations.…”