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25
A tutorial on linear and bilinear matrix inequalities
, 2000
"... This is a tutorial on the mathematical theory and process control applications of linear matrix inequalities (LMIs) and bilinear matrix inequalities (BMIs). Many convex inequalities common in process control applications are shown to be LMIs. Proofs are included to familiarize the reader with the ma ..."
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Cited by 44 (0 self)
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This is a tutorial on the mathematical theory and process control applications of linear matrix inequalities (LMIs) and bilinear matrix inequalities (BMIs). Many convex inequalities common in process control applications are shown to be LMIs. Proofs are included to familiarize the reader with the mathematics of LMIs and BMIs. LMIs and BMIs are applied to several important process control applications including control structure selection, robust controller analysis and design, and optimal design of experiments.
Survey of Robust Control for Rigid Robots
 IEEE Control System Magazine
, 1991
"... This survey discusses current approaches to the robust control of the motion of rigid robots and summarizes the available literature on the subject. The five major designs discussed are the "LinearMultivariable " approach, the "Passivity " approach, the "VariableStructur ..."
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Cited by 29 (2 self)
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This survey discusses current approaches to the robust control of the motion of rigid robots and summarizes the available literature on the subject. The five major designs discussed are the "LinearMultivariable " approach, the "Passivity " approach, the "VariableStructure " approach, the "Saturation " approach and the "RobustAdaptive " approach.
OF STRUCTURES
"... In this paper, some recent advances and a few novel concepts are presented for motion control of highrise building and bridge structures under dynamic wind and earthquake loading. Recent research performed by the authors in the areas of smart structures, hybrid control, tuned liquid column damper, a ..."
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Cited by 23 (2 self)
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In this paper, some recent advances and a few novel concepts are presented for motion control of highrise building and bridge structures under dynamic wind and earthquake loading. Recent research performed by the authors in the areas of smart structures, hybrid control, tuned liquid column damper, and wavelets is reviewed.
Global Optimization for the Biaffine Matrix Inequality Problem
, 1995
"... It has recently been shown that an extremely wide array of robust controller design problems may be reduced to the problem of finding a feasible point under a Biaffine Matrix Inequality (BMI) constraint. The BMI feasibility problem is the bilinear version of the Linear (Affine) Matrix Inequality (L ..."
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Cited by 16 (0 self)
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It has recently been shown that an extremely wide array of robust controller design problems may be reduced to the problem of finding a feasible point under a Biaffine Matrix Inequality (BMI) constraint. The BMI feasibility problem is the bilinear version of the Linear (Affine) Matrix Inequality (LMI) feasibility problem, and may also be viewed as a bilinear extension to the Semidefinite Programming (SDP) problem. The BMI problem may be approached as a biconvex global optimization problem of minimizing the maximum eigenvalue of a biaffine combination of symmetric matrices. This paper presents a branch and bound global optimization algorithm for the BMI. A simple numerical example is included. The robust control problem, i.e., the synthesis of a controller for a dynamic physical system which guarantees stability and performance in the face of significant modelling error and worstcase disturbance inputs, is frequently encountered in a variety of complex engineering applications including the design of aircraft, satellites, chemical plants, and other precision positioning and tracking systems.
A reduced basis approach to the design of loworder feedback controllers for nonlinear continuous systems
 J. Vib. Control
, 1998
"... Abstract: In this paper, the authors discuss a reduced basis approach to the development of loworder nonlinear feedback controllers for hybrid distributed parameter systems. This approach involves the use of distributed parameter control theory to design "optimal " infinite dimensional fe ..."
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Cited by 14 (0 self)
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Abstract: In this paper, the authors discuss a reduced basis approach to the development of loworder nonlinear feedback controllers for hybrid distributed parameter systems. This approach involves the use of distributed parameter control theory to design "optimal " infinite dimensional feedback control laws and approximation theory to design and compute loworder finite dimensional compensators. The resulting finite dimensional controller combines a nonlinear observer with a linear feedback law to produce a practical design. The authors concentrate on a weakly nonlinear distributed parameter system to illustrate the ideas. Key Words: Reduced order controller, dynamic compensator, distributed parameter system, structural control problem
Criteria for robust absolute stability of timevarying nonlinear continuoustime systems
 AUTOMATICA
, 2002
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Analysis of Robust Pole Clustering in a Good Ride Quality Region for Uncertain Matrices
"... This paper presents a general analysis of robust pole clustering in a good ride quality region of aircraft, a specific nonWtransformable region, for uncertain matrices. The region is an intersection of a ring and a horizontal strip, located on the left halfplane. From experiments, it is known that ..."
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Cited by 1 (0 self)
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This paper presents a general analysis of robust pole clustering in a good ride quality region of aircraft, a specific nonWtransformable region, for uncertain matrices. The region is an intersection of a ring and a horizontal strip, located on the left halfplane. From experiments, it is known that the control system with poles located in this specific region provides a good ride quality for aircraft. The paper applies Rayleigh principle along the norm theory to analyze robust pole clustering within this good ride quality region since the generalized Lyapunov theory is not valid for nonWtransformable regions. The mainly concerned uncertainties are unstructured uncertainties. A simple extension of the results for structured uncertainties is also provided. Two examples illustrate the results for a perturbed closedloop system matrix of F16 aircraft approximation model. The results are useful for robustness analysis and, especially, analysis of robust good ride quality of aircraft, shu...
Robust Stability Of Linear Continuous And DiscreteTime Systems Under Parametric Uncertainty
 TECHNICAL REPORT OF THE ISIS GROUP AT THE UNIVERSITY OF NOTRE DAME
, 1994
"... Conditions for robust stability in linear continuous systems are derived, when all matrices of the statespace model are perturbed by independent uncertain parameters and static output feedback is applied. Two different approaches are presented. Then, improved conditions for robust stability in line ..."
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Cited by 1 (1 self)
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Conditions for robust stability in linear continuous systems are derived, when all matrices of the statespace model are perturbed by independent uncertain parameters and static output feedback is applied. Two different approaches are presented. Then, improved conditions for robust stability in linear discretetime systems with both unstructured and structured perturbations in the system matrix A are derived. Finally, a sufficient condition for robust stability when again all matrices of the statespace model are perturbed by independent uncertain parameters and static output feedback is applied, is derived. The analysis for all the problems studied above is based on the direct method of Lyapunov. Several examples are used to illustrate the results.
On nonautonomous H ∞ control with infinite horizon. ∗
"... We study the linear H ∞ control problem in the infinitehorizon case when the coefficients are timevarying and bounded. We pass in a standard way from a Riccati equation to a linear Hamiltonian system of ordinary differential equations, which we study using exponential dichotomies and rotation nu ..."
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We study the linear H ∞ control problem in the infinitehorizon case when the coefficients are timevarying and bounded. We pass in a standard way from a Riccati equation to a linear Hamiltonian system of ordinary differential equations, which we study using exponential dichotomies and rotation numbers. In particular we use the dichotomy concept to define the critical attenuation value. 1
A Minimax Stochastic Optimal Control for Bounded uncertain Systems
, 2008
"... Abstract: A minimax stochastic optimal control strategy for boundeduncertain stochastic systems is proposed. The minimax dynamical programming equation for an uncertain stochastic control system is firstly derived based on the optimality principle and Itô differential rule. A new type of bangbang ..."
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Abstract: A minimax stochastic optimal control strategy for boundeduncertain stochastic systems is proposed. The minimax dynamical programming equation for an uncertain stochastic control system is firstly derived based on the optimality principle and Itô differential rule. A new type of bangbang constraint on the bounded uncertain disturbance is proposed to form a class of minimax stochastic optimal control problems. Then the worst disturbance and minimax optimal control are obtained for the bangbangtype uncertain system under stochastic excitations. According to this method, the quasi linear control law is obtained for linear stochastic systems with bounded uncertainty and the statedependent quasi Riccati equation is derived from the minimax dynamical programming equation. Furthermore, a minimax stochastic optimal control strategy for uncertain stochastic quasi Hamiltonian systems is developed based on the stochastic averaging method and minimax dynamical programming equation. The worst disturbance and minimax optimal control for the stochastically averaged system are obtained by the similar procedure. The proposed and developed minimax stochastic optimal control strategies are illustrated with an example of a singledegreeoffreedom uncertain stochastic control system.