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Parametric robust H2 control design using LMI synthesis
 AIAA Journal Guidance, Control, and Dynamics
, 2000
"... This paper presents a new, iterative algorithm for designing full order LTI controllers for systems with real parameter uncertainty. Robust stability isdetermined for these systems using the Popov analysis criterion and multiplier, and robust performance is investigated using a bound on the output e ..."
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This paper presents a new, iterative algorithm for designing full order LTI controllers for systems with real parameter uncertainty. Robust stability isdetermined for these systems using the Popov analysis criterion and multiplier, and robust performance is investigated using a bound on the output energy. Control design to minimize the robust performance metric naturally leads to Bilinear Matrix Inequalities, which can be decoupled to a large extent. However, coupling remains in the problem since we simultaneously optimize the parameters of both the Popov stabilitymultiplier and the compensator. We present a heuristic, iterative algorithm to solve this design problem, and demonstrate that it works effectively on two numerical examples. In the process, we illustrate that the key advantages of this control design approach are the high reliability of the numerical techniques and the relative simplicity of implementing the algorithm. 1
Improved LMI Conditions For Gain Scheduling And Related Control Problems
, 1998
"... this paper concerns a linear system whose statespace equations depend rationally on real, timevarying parameters, which are measured in real time. A stabilizing, parameterdependent controller is sought, such that a given L ..."
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Cited by 6 (1 self)
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this paper concerns a linear system whose statespace equations depend rationally on real, timevarying parameters, which are measured in real time. A stabilizing, parameterdependent controller is sought, such that a given L
Robust Mixed Control and LPV Control with Full Block Scalings
 In L. El Ghaoui, S. Niculescu (Eds) Recent Advances on LMI Methods in Control, SIAM Studies in Appliced Mathematics, Philadelphia
, 1999
"... For systems affected by timevarying parametric uncertainties, we devise in this chapter a technique that allows to equivalently translate robust performance analysis specifications characterized through a single Lyapunov function into the corresponding analysis test with multipliers. Out of the mul ..."
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Cited by 6 (0 self)
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For systems affected by timevarying parametric uncertainties, we devise in this chapter a technique that allows to equivalently translate robust performance analysis specifications characterized through a single Lyapunov function into the corresponding analysis test with multipliers. Out of the multitude of possible applications of this socalled full block Sprocedure, we will concentrate on a discussion of robust mixed control and of designing linear parametricallyvarying (LPV) controllers. 1 Introduction In the past years mixed control problems have attracted considerable interest, and the LMI approach to controller design has shown beneficial to tackle design specifications that have deemed untractable. For the design of output feedback controllers, it has been revealed quite recently how a suitable nonlinear change of controller parameters allows to proceed in a straightforward fashion from an analysis specification for a controlled system formulated in terms of matrix inequal...
Lower Bounds in MultiObjective ... Problems
"... . In this paper we discuss a multiobjective control problem that involves several H 2 norm and H1 norm constraints. In an accompanying paper we show how to efficiently compute a sequence of upper bounds that converges monotonically from above to the optimal value of such problems. If more than o ..."
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. In this paper we discuss a multiobjective control problem that involves several H 2 norm and H1 norm constraints. In an accompanying paper we show how to efficiently compute a sequence of upper bounds that converges monotonically from above to the optimal value of such problems. If more than one H1 constraint is involved, it is so far unknown and revealed in this paper how to compute as well a sequence of lower bounds that converges to the optimum. This complements the tools available for multiobjective LMI based control by a stopping criterion. Notation. l n\Thetam 2 denotes the space of sequences X 2 C n\Thetam satisfying kXk 2 2 := P 1 =0 trace(X X ) ! 0. The space of all bounded linear operators l m 2 into l n 2 is denoted as L(l m 2 ; l n 2 ) and equipped with the induced norm k:k. H n\Thetam 1 or H n\Thetam 2 denote the normed algebra or inner product space (with the inner product written as h:; :i) of C n\Thetam  valued mappings f which are an...
Robust Multiobjective Lti Control Design For Systems With Structured Perturbations
, 1996
"... . We consider a multiobjective robust controller synthesis problem for an LTI system subject to structured perturbations. Our design specifications include robust stability, robust performance (H 2 norm) bounds and timedomain bounds (output and command input peak). We derive sufficient conditions, ..."
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. We consider a multiobjective robust controller synthesis problem for an LTI system subject to structured perturbations. Our design specifications include robust stability, robust performance (H 2 norm) bounds and timedomain bounds (output and command input peak). We derive sufficient conditions, based on a single quadratic Lyapunov function, for the existence of an LTI controller such that the closedloop system satisfies all specifications simultaneously. These nonconvex conditions can be numerically checked with an efficient LMIbased heuristic. We illustrate our results on a threeparameter mass/spring system. Keywords. Multiobjective robust control, mixed H 2 /H1 , timedomain specification, structured perturbation, quadratic Lyapunov function, linear matrix inequality. 1. INTRODUCTION In a multiobjective robust control problem, one seeks a control law such that the closedloop system satisfies a number of objectives (specifications) despite unkwnonbut bounded perturbations. I...
Output feedback control with input saturations: LMI design approaches
, 1997
"... This paper addresses the control of linear systems with input saturations. We seek a controller that guarantees for the closed loop system: (i) stability for a given polytope of initial conditions, (ii) a prescribed weak L 2 gain attenuation between inputs and outputs of interest. Two approaches are ..."
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This paper addresses the control of linear systems with input saturations. We seek a controller that guarantees for the closed loop system: (i) stability for a given polytope of initial conditions, (ii) a prescribed weak L 2 gain attenuation between inputs and outputs of interest. Two approaches are proposed based on: (i) ensuring that the controller never saturates: the obtained controller is Linear Time Invariant (LTI), (ii) ensuring absolute stability against the saturations: the controller is then Linear Time Varying (LTV). Existence conditions for these two control structures can be cast as (convex) optimization problems over Linear Matrix Inequalities. At last, using numerical experiments, we compare both approaches. In this numerical examples, the LTI controller presents some advantages.
Robust H 2 and
"... In this paper, the robust H 2 and H# filter design problems are considered, where the uncertainties, unstructured or structured, are norm bounded and represented by linear fractional transformation (LFT). The main result is that after upperbounding the objectives, the problems of minimizing the upp ..."
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In this paper, the robust H 2 and H# filter design problems are considered, where the uncertainties, unstructured or structured, are norm bounded and represented by linear fractional transformation (LFT). The main result is that after upperbounding the objectives, the problems of minimizing the upper bounds are converted to finite dimensional convex optimization problems involving linear matrix inequalities (LMIs). These are extensions of the results for systems with polytopic uncertainty. It is also shown that for the unstructured, norm bounded uncertainty case, the results here are less conservative than former results, where Riccati equation approach are used. A numerical example is given to illustrate the results.
PassivityBased Analysis and Control of Nonlinear Systems
, 2000
"... A new set of tools for the stability analysis and robust control design for nonlinear systems is introduced in this dissertation. The tools have a wide range of applicability, covering systems with common types of hysteresis, as well as systems with memoryless forms such as saturation, or sloperest ..."
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A new set of tools for the stability analysis and robust control design for nonlinear systems is introduced in this dissertation. The tools have a wide range of applicability, covering systems with common types of hysteresis, as well as systems with memoryless forms such as saturation, or sloperestricted nonlinearities (e.g., parameter uncertainty or gain variation), and can be used to guarantee stability for systems with both nonlinearities and additional normbounded uncertainty. These robust stability tests are developed using a combination of passivity and dissipation theories, and are presented in both graphical (Nyquist) and numerical form using linear matrix inequalities (LMIs). The LMI formulation yields tests that are efficiently solved with existing software packages, and allows the extension to the case of multiple nonlinearities. In particular, an asymptotic stability test is developed using LMIs for systems with multiple hysteresis nonlinearities. The invariant set for such systems is shown in general to be a polytopic region of the state space. This analysis
Convergence Analysis of A Parametric Robust H 2 Controller Synthesis Algorithm 1
"... This paper presents an iterative algorithm for solving the parametric robust H2 controller synthesis problem and analyzes the convergence properties of the algorithm on several examples. Iterative procedures are normally applied to a large class of robust control design problems in which the formula ..."
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This paper presents an iterative algorithm for solving the parametric robust H2 controller synthesis problem and analyzes the convergence properties of the algorithm on several examples. Iterative procedures are normally applied to a large class of robust control design problems in which the formulation naturally leads to bilinear matrix inequalities (BMIs). It is di cult to make concrete statements about the behavior of these iterative algorithms, except that it is often conjectured that the cost in each step of the solution procedure is reduced, which implies that the algorithms should converge to a local minimum. Similar di culties exist for the new LMIbased iterative algorithm that we haverecently proposed to solve the BMIs that occur in robust H2 control design. The e ectiveness of the new algorithm has already been demonstrated on several numerical examples. This paper adds an important component tothediscussion on the convergence of the new algorithm by verifying that it e ciently converges to the optimal solution. In the process, we provide some new key insights on the proposed design technique which indicate that it exhibits properties similar to the D{K iteration of the complex =Kmsynthesis. 1