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Robust Constrained Model Predictive Control using Linear Matrix Inequalities
, 1996
"... The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty i ..."
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Cited by 78 (4 self)
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The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a statefeedback control law which minimizes a "worstcase" infinite horizon objective function, subject to constraints on the control input and plant output. Using standard techniques, the problem of minimizing an upper bound on the "worstcase" objective function, subject to input and output constraints, is reduced to a convex optimization involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon statefeedback control design robustly stabilizes the set of uncertain plants under consideration. Several extensions...
Analysis of Implicit Uncertain Systems Part I: Theoretical Framework
 California Institute of Technology
, 1994
"... This paper introduces a general and powerful framework for the analysis of uncertain systems, encompassing linear fractional transformations, the behavioral approach for system theory and the integral quadratic constraint formulation. In this approach, a system is defined by implicit equations, and ..."
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Cited by 1 (1 self)
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This paper introduces a general and powerful framework for the analysis of uncertain systems, encompassing linear fractional transformations, the behavioral approach for system theory and the integral quadratic constraint formulation. In this approach, a system is defined by implicit equations, and the central analysis question is to test for solutions of these equations. In Part I, the general properties of this formulation are developed, and computable necessary and sufficient conditions are derived for a robust performance problem posed in this framework. 1 Introduction In the predominant viewpoint in systems and control theory, a system is an inputoutput (I/O) entity, where the variables are clearly separated in two groups, and a causeeffect relationship is established between them. This approach entails a "signal flow" conception, adequate for systems which are deliberately built to match the I/O philosophy, such as computers and amplifiers. For many other physical systems this...
Suboptimal Control of Rigid Body Motion with a Quadratic Cost
 3rd IFAC Nonlinear Symposium on Nonlinear Control Systems Design, Tahoe City
, 1995
"... . This paper considers the problem of controlling the rotational motion of a rigid body using three independent control torques. Given a quadratic cost we seek stabilizing state feedback controllers which guarantee that all motions starting within a specified bounded set satisfy a specified bound on ..."
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Cited by 1 (1 self)
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. This paper considers the problem of controlling the rotational motion of a rigid body using three independent control torques. Given a quadratic cost we seek stabilizing state feedback controllers which guarantee that all motions starting within a specified bounded set satisfy a specified bound on a quadratic performance index or cost. For a special class of cost functions, we present explicit expressions for the optimal stabilizing controllers. For the general case, we present sufficient conditions which guarantee the existence of linear, suboptimal, stabilizing controllers. Keywords. Attitude control; quadratic cost; linear matrix inequalities. 1 INTRODUCTION In this paper we consider the problem of controlling the rotational motion of a rigid body using three independent control torques. The minimal requirement on the controller is to stabilize the body about a specified orientation. In addition, we require the controller to guarantee that a quadratic performance index or cost b...
Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts
, 1996
"... Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear timeinvariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the timedomain and the frequen ..."
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Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear timeinvariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the timedomain and the frequencydomain, in terms of linear matrix inequalities (LMIs) and algebraic Riccati equations (AREs). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity and sector conditions for stability. Techniques for selecting power funct...