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65
Quadratic Stabilization of DiscreteTime Uncertain Nonlinear MultiModel Systems using Piecewise Affine StateFeedback
 International Journal of Control
, 1998
"... In this paper a method for nonlinear robust stabilization based on solving a bilinear matrix inequality (BMI) feasibility problem is developed. Robustness against model uncertainty is handled. In different nonoverlapping regions of the statespace known as clusters the plant is assumed to be an ele ..."
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Cited by 9 (4 self)
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In this paper a method for nonlinear robust stabilization based on solving a bilinear matrix inequality (BMI) feasibility problem is developed. Robustness against model uncertainty is handled. In different nonoverlapping regions of the statespace known as clusters the plant is assumed to be an element in a polytope which vertices (local models) are affine systems. In the clusters containing the origin in their closure, the local models are restricted to being linear systems. The clusters cover the region of interest in the statespace. An affine statefeedback is associated with each cluster. By utilizing the affinity of the local models and the statefeedback, a set of linear matrix inequalities (LMIs) combined with a single nonconvex BMI are obtained which, if feasible, guarantee quadratic stability of the origin of the closedloop. The feasibility problem is attacked by a branchandbound based global approach. If the feasibility check is successful, the Liapunov matrix and the piecewise ...
Feedback minmax Model predictive Control Using a Single Linear Program: Robust Stability and the Explicit Solution
, 2002
"... 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 openloop trajectories. All specific proposals to date have required the solution of nonlinear programs and/or the solution of a larg ..."
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Cited by 9 (5 self)
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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 openloop 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 multiparametric linear program, which implies that the receding horizon control (RHC) law is piecewise affine, and can be explicitly precomputed, so that the linear program does not have to be solved online. 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.
Modelbased Predictive Control for Hammerstein systems
 International Journal of Control
, 2001
"... Hammersteinsy5 ems are a class ofsy] ems represented by a static nonlinearity at the input followed by a linear dy1 mic block. In this paper the static input nonlinearity is transformed into a poly opic description. The remaining uncertain linear model is used in a MPC algorithm of which the optimi ..."
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Cited by 8 (0 self)
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Hammersteinsy5 ems are a class ofsy] ems represented by a static nonlinearity at the input followed by a linear dy1 mic block. In this paper the static input nonlinearity is transformed into a poly opic description. The remaining uncertain linear model is used in a MPC algorithm of which the optimization problem involves minimization of a linear objective function subject to Linear Matrix Inequalities (LMIs), which is a convex problem. A procedure is presented to remove a number of LMIs from the optimization problem, prior to solving it.By means of an iterative procedure the conservatism of the poly13#R description can be reduced. Nominal closed loop stability of this Hammerstein MPC algorithm is guaranteed. A comparison is presented between the proposed algorithm and an algorithm which removes the nonlinearity from the control problem via an inversion. Key words: Predictive control, Hammersteinsynj160 Linear matrix inequalities, Stability , Actuator nonlinearities 1 Introduction In...
Iterative Risk Allocation: A New Approach to Robust Model Predictive Control with a Joint Chance Constraint
"... Abstract — This paper proposes a novel twostage 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 ..."
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Cited by 8 (6 self)
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Abstract — This paper proposes a novel twostage 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 upperstage that optimizes risk allocation, and the lowerstage that optimizes control sequence with tightened constraints. The lowerstage is a regular convex optimization, such as Linear Programming or Quadratic Programming. The
Model Predictive Controllers: A Critical Synthesis of Theory and Industrial Needs
, 1998
"... 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 rigoro ..."
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Cited by 7 (2 self)
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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...
Robust constrained receding horizon control for trajectory planning
 In Proc. AIAA Guidance, Navigation, and Control Conference
, 2005
"... 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 an ..."
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Cited by 5 (4 self)
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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 nofly zones are included in the environment. The proposed algorithm modifies these constraints to ensure that the online 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 online. The full algorithm is demonstrated in several numerical simulations.
Bilinear Matrix Inequalities and Robust Stability of Nonlinear MultiModel MPC
 In Proc. Amer. Contr. Conf
, 1998
"... A BMIbased approach to an online 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 driv ..."
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Cited by 4 (2 self)
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A BMIbased approach to an online 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 continuoustime systems, and [11] on unconstrained discretetime systems. Finally, works on robust synthesis, i.e. an uncertainty model is explicitly used when...
Receding Horizon Output FeedbackControl for Linear Systems with Input Saturation
 39 th IEEE Conference on Decision and Control
, 2000
"... 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 dualmode paradigm which consists of a `feasible invariant set' and `free control moves'. Polyhedral feasible invariant sets o ..."
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Cited by 4 (0 self)
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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 dualmode 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 dualmode paradigm provides an efficient way to guar...
A New Approach to Stability Analysis for Constrained Finite Receding Horizon Control without End Constraints
, 1997
"... 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 c ..."
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Cited by 3 (1 self)
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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 positivedefinite 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 online 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 ...