http://control.disp.uniroma2.it/galeani/CO/materiale/automatica2000.pdf

Survey Constrained model predictive control: Stability and optimality

http://web.aeromech.usyd.edu.au/AMME4500/mpc_survey.pdf

A survey of industrial model predictive control technology

The explicit linear quadratic regulator for constrained systems

Robust constrained model predictive control using linear matrix inequalities

https://www.itk.ntnu.no/fag/fordypning/TK16-filer/Samling1_MorariLee.pdf

Model predictive control: past, present and future

An infinite horizon controller that allows incorporation of input and state constraints in a receding horizon feedback strategy is developed. For both stable and unstable linear plants, feasibility of the contraints guarantees nominal closed-loop stability for all choices of the tuning parameters in the control law. The constraints' feasibility can be checked efficiently with a linear program. It is always possible to remove state constraints in the early portion of the infinite horizon to make them feasible. The controller's implementation requires only the solution of finite-dimensional quadratic programs. >

/pdf/the-stability-of-constrained-receding-horizon-control-3tg17zur7n.pdf

The stability of constrained receding horizon control

This article discusses the existing linear model predictive control concepts in a unified theoretical framework based on a stabilizing, infinite horizon, linear quadratic regulator. In order to represent unstable as well as stable multivariable systems, the standard state-space formulation is used for the plant model. The incorporation of a nominally stabilizing constrained regulator eliminates the current requirement of tuning for nominal stability. Output feedback is addressed in the well-established framework of the linear quadratic state-estimation problem. This framework allows the flexibility to handle nonsquare systems, noisy inputs and outputs, and nonzero input, output, and state disturbances. This formulation subsumes the integral control schemes designed to remove steady-state offset currently in industrial use. The online implementation of the controller requires the solution of a standard quadratic program that is no more computationally intensive than existing algorithms.

Model predictive control with linear models

Nonlinear Model Predictive Control: A Tutorial and Survey

A discrete time, receding horizon, recursive state estimation scheme based on the batch state estimation least squares formulation is presented. It is shown that this procedure yields the same state estimate as the standard Kalman filter. Nominal stability of a constrained batch state estimation formulation is demonstrated and a constrained, receding horizon, recursive state estimation formulation is presented.

Receding Horizon Recursive State Estimation

MHE is an optimization based strategy for state estimation that explicitly allows for nonlinear models and inequality constraints. In this work we investigate strategies to guarantee the stability of moving horizon estimation (MHE). We begin our discussion by analyzing the stability of the abstract MHE problem. Sufficient conditions for asymptotic stability are established. Using forward dynamic programming to analyze MHE, we introduce the fundamental concept of arrival cost to bound the size of the estimation problem. The key result is if one can construct a global lower bound for the arrival cost, then asymptotic stability is guaranteed. In the second part of our discussion, we propose a strategy that circumvents the need for a global lower bound for the arrival cost. In particular, by including bounds to guarantee the existence of a decreasing nominal sequence, we circumvent the need for a global lower bound for the arrival cost. This result is significant, because, in general, we cannot calculate nor bound the arrival cost. Notable exceptions are linear systems, where the Kalman filter covariance generates a global lower bound for the arrival cost.

Kenneth R. Muske

Papers

The stability of constrained receding horizon control

Model predictive control with linear models

Nonlinear Model Predictive Control: A Tutorial and Survey

Receding Horizon Recursive State Estimation

Nonlinear Moving Horizon State Estimation