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 a new stage cost and show that the use of this cost allows one to formulate a robustly stable MPC problem that can be solved using a single linear program. Furthermore, this is a multi-parametric linear program, which implies that the receding horizon control (RHC) law is piecewise affine, and can be explicitly pre-computed, so that the linear program does not have to be solved on-line. Two numerical examples are presented; one of these is taken from the literature, so that a direct comparison of solutions and computational complexity with earlier proposals is possible.

odel This paper presents a receding horizon controller (RHC) that can be used to design trajectories for an aerial vehicle operating in an environment with disturbances. Various constraints are imposed in the problem, such as turning rate limits and bounds on the vehicle speed, and target regions and no-fly zones are included in the environment. The proposed algorithm modifies these constraints to ensure that the on-line RHC optimization remains feasible even when the vehicle is acted upon by unknown, but bounded, disturbances. The approach uses a robust control invariant admissible set as a terminal set that does not need to be a target set of the overall guidance problem. This result extends previous work in two ways: the vehicle is guaranteed to remain safe under the influence of disturbances; and much longer robust trajectories can be constructed on-line. The full algorithm is demonstrated in several numerical simulations.

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A BMI-based approach to an on-line computationally efficient robust nonlinear MPC is proposed. Theoretical results and a simple example accompany the proposed method. 1 Introduction Model predictive control (MPC) has been an active research area for close to two decades. The research has been driven by numerous successful applications of the technology [1], and during the last years a sound theoretical foundation has been established; [2], [3], and [4]. The issue of robust stability of MPC based control systems, however, is largely unsolved, at least for nonlinear MPC. Some results are available though. Works on robust MPC for linear systems include: [5] on constrained stable systems; [6] on unconstrained systems; [7] and [8] on constrained systems. Works on robust analysis of nonlinear MPC include: [9] and [10] on constrained continuous-time systems, and [11] on unconstrained discrete-time systems. Finally, works on robust synthesis, i.e. an uncertainty model is explicitly used when...

Abstract — This paper proposes a novel two-stage optimization method for robust Model Predictive Control (RMPC) with Gaussian disturbance and state estimation error. Since the disturbance is unbounded, it is impossible to achieve zero probability of violating constraints. Our goal is to optimize the expected value of an objective function while limiting the probability of violating any constraints over the planning horizon (joint chance constraint). Prior arts include ellipsoidal relaxation approach [1] and Particle Control [2], but the former yields very conservative result and the latter is computationally intensive. Our approach divide the optimization problem into two stages; the upper-stage that optimizes risk allocation, and the lower-stage that optimizes control sequence with tightened constraints. The lower-stage is a regular convex optimization, such as Linear Programming or Quadratic Programming. The

After several years of efforts, constrained model predictive control (MPC), the de facto standard algorithm for advanced control in process industries, has finally succumbed to rigorous analysis. Yet successful practical implementations of MPC were already in place almost two decades before a rigorous stability proof for constrained MPC was published. What is then the importance of recent theoretical results for practical MPC applications? In this publication we present a pedagogical overview of some of the most important recent developments in MPC theory, and discuss their implications for the future of MPC theory and practice. 1 (713) 743 4309, fax: (713) 743 4323, email: nikolaou@uh.edu. -- 2 -- TABLE OF CONTENTS 1 INTRODUCTION 3 2 WHAT IS MPC? 3 2.1 A TRADITIONAL MPC FORMULATION 6 2.2 EXPANDING THE TRADITIONAL MPC FORMULATION 7 2.3 MPC WITHOUT INEQUALITY CONSTRAINTS 8 3 STABILITY 10 3.1 WHAT IS STABILITY? 10 3.1.1 Stability with respect to initial conditions 11 3.1.2 Input...

We present a new approach to the stability analysis of finite receding horizon control applied to constrained linear systems. By relating the final predicted state to the current state through a bound on the terminal cost, it is shown that knowledge of upper and lower bounds for the finite horizon costs are sufficient to determine the stability of a receding horizon controller. This analysis is valid for receding horizon schemes with arbitrary positive-definite terminal weights, and does not rely on the use of stabilizing constraints. The result is a computable test for stability, and two simple examples are used to illustrate its application. Keywords: predictive control, constrained systems, linear systems, discrete time. 1 Introduction Receding horizon control (RHC), also known as model predictive control (MPC) [8], is an on-line technique in which a new control action is computed at each time step by solving a finite horizon optimization problem that extends from the current time ...

In this paper, a constrained receding horizon output feedback control method which is based on a state observer is suggested. The proposed method adopts the receding horizon dual-mode paradigm which consists of a `feasible invariant set' and `free control moves'. Polyhedral feasible invariant sets of estimated state are derived along with guaranteed bounds on state estimation errors. The guaranteed bounds on the state estimation error are developed by considering invariantsets of state estimation errors which include possible initial estimation errors. Predictions of future states are made based on estimated current state and bounds on current estimation error. The free control moves are determined so that the predicted future state belongs to the polyhedral feasible invariant set, despite input constraints and measurement noise. Keywords: Output feedback, Input saturation, Feasible and invariants sets, Observer 1Introduction The dual-mode paradigm provides an efficient way to guar...

Modelbased Predictive Control (MPC) is a control technique that is widely used in chemical process industry. In the past decade, stability of MPC has been an intensive research area, resulting in the general acceptance of a theoretical MPC stability framework introducing a terminal cost and terminal constraint to the classic MPC formulation. Although guaranteeing stability, issues regarding optimality and feasibility remain. In this paper, an LMI-based constrained MPC scheme for linear systems is introduced which guarantees stability by use of a time-varying terminal cost and terminal constraint. The online calculation of the terminal cost results in improved performance and feasibility compared to MPC schemes with fixed terminal cost. Finally, the technique is illustrated on a copolymerization reactor.

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