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- Paul J. Goulart, Eric C. Kerrigan, Jan M. Maciejowski
- Automatica
- 2006

This paper is concerned with the optimal control of linear discrete-time systems, which are subject to unknown but bounded state disturbances and mixed constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with memory of prior states is equivalent to the class of admissible feedback policies that… (More)

- Eric C. Kerrigan
- 2000

Set invariance plays a fundamental role in the design of control systems for constrained systems since the constraints can be satisfied for all time if and only if the initial state is contained inside an invariant set. This thesis is concerned with robust set invariance theory and its application to guaranteeing feasibility in model predictive control. In… (More)

The solution to the problem of optimal control of piecewise affine systems with a bounded disturbance is characterised. Results that allow one to compute the value function, its domain (robustly controllable set) and the optimal control law are presented. The tools that are employed include dynamic programming, polytopic set algebra and parametric… (More)

In order to ensure robust feasibility and stability of model predictive control (MPC) schemes, it is often necessary to optimise over feedback policies rather than open-loop trajectories. All specific proposals to date have required the solution of nonlinear programs and/or the solution of a large number of optimisation problems. In this paper we introduce… (More)

- Raphael Cagienard, Pascal Grieder, Eric C. Kerrigan, Manfred Morari
- 2004

In order to deal with the computational burden of optimal control, it is common practice to reduce the degrees of freedom by fixing the input or its derivatives to be constant over several time-steps. This policy is referred to as “move blocking”. This paper will address two issues. First, a survey of various move blocking strategies is presented and the… (More)

An understanding of invariant set theory is essential in the design of controllers for constrained systems, since state and control constraints can be satisfied if and only if the initial state belongs to a positively invariant set for the closed-loop system. The paper briefly reviews some concepts in invariant set theory and shows that the various sets can… (More)

Finite horizon optimal control of piecewise affine systems with a piecewise affine (1-norm or ∞-norm) stage cost and terminal cost is considered. Provided the respective constraint sets are given as the unions of polyhedra, it is shown that the partial value functions and partial optimal control laws are piecewise affine on a polyhedral cover of the set of… (More)

- Sasa V. Rakovic, Eric C. Kerrigan, David Q. Mayne, John Lygeros
- IEEE Trans. Automat. Contr.
- 2006

This paper presents new results that allow one to compute the set of states that can be robustly steered in a finite number of steps, via state feedback control, to a given target set. The assumptions that are made in this paper are that the system is discrete-time, nonlinear and time-invariant and subject to mixed constraints on the state and input. A… (More)

A number of results are derived for analysing the robust feasibility of a given Model Predictive Control (MPC) scheme which ignores model mismatch and/or disturbances during control input computation. The main contribution of this paper is the development of computationally tractable tests for determining the robust feasibility of an MPC controller for… (More)

One of the strengths of Model Predictive Control (MPC) is its ability to incorporate constraints in the control formulation. Often a disturbance drives the system into a region where the MPC problem is infeasible and hence no control action can be computed. Feasibility can be recovered by softening the constraints using slack variables. This approach does… (More)