Improved optimisation approach to the robust H2/H∞ control problem for linear systems (original) (raw)
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This paper presents a strategy for robust H2/H∞ dynamic outputfeedback control synthesis, with regional pole placement, applied to linear continuous-time time-invariant systems with polytope-bounded uncertainty. The proposed synthesis approach is based on a multiobjective optimization algorithm applied directly in the space of controller parameters. The H2 and H∞ norms, computed in all polytope vertices and in possible “worst case” interior points are taken as the optimization objectives. A branch-and-bound algorithm based on LMI guaranteed cost formulation is applied to validate the controller design. Examples are presented to show the effectiveness of the proposed strategy, including examples of full order and low order, centralized and decentralized control systems. Copyright c ©2005 IFAC.
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This paper presents a strategy for robust H 2 /H ∞ dynamic outputfeedback control synthesis, with regional pole placement, applied to linear continuous-time time-invariant systems with polytope-bounded uncertainty. The proposed synthesis approach is based on a multiobjective optimization algorithm applied directly in the space of controller parameters. The H 2 and H ∞ norms, computed in all polytope vertices and in possible "worst case" interior points are taken as the optimization objectives. A branch-and-bound algorithm based on LMI guaranteed cost formulation is applied to validate the controller design. Examples are presented to show the effectiveness of the proposed strategy, including examples of full order and low order, centralized and decentralized control systems.
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This paper presents an algorithm for robust H2/H∞ state-feedback control synthesis, with regional pole placement, based on a multiobjective optimization algorithm with non-smooth problem-solving capability. The problem is formulated with the state-feedback matrix coefficients as optimization parameters. The closed-loop performance obtained by means of the proposed strategy is assessed for the whole uncertainty-set through an LMI-based H2 and H∞ guaranteed cost computation. The proposed strategy is compared with three former LMI approaches, for systems with polytope-bounded uncertainties, and presents better results.
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52nd IEEE Conference on Decision and Control, 2013
In this paper, a new approach to fixed-order H∞ and H2 output feedback control of MIMO discrete-time systems with polytopic uncertainty is proposed. The main idea of this approach is based on the definition of SPR-pair matrices and the use of some instrumental matrices which operates as a tool to overcome the original non-convexity of fixed-order controller design. Then, stability condition as well as H∞ and H2 performance constraints are presented by a set of linear matrix inequalities with linearly parameter dependent Lyapunov matrices. An iterative algorithm for update on the instrumental matrices is developed, that monotonically converges to a suboptimal solution. Simulation results show the effectiveness of the proposed approach.
H/sub 2//H/sub /spl infin// filter design for systems with polytope-bounded uncertainty
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This correspondence presents a strategy for robust H =H filtering design, with regional pole placement, applied to discrete-or continuous-time linear time-invariant (LTI) systems with polytope-bounded uncertainty. To overcome the conservatism of linear matrix inequality (LMI)-based formulations, the proposed design approach is based on a multiobjective optimization algorithm applied directly in the space of the filter parameters. The H and H norms, computed in all polytope vertices and in possible "worst case" interior points, are taken as the optimization objectives. A combination of branch-and-bound algorithm and LMI guaranteed cost formulations is applied to compute the coordinates of the worst case norms and to validate the filter design to the whole polytope. Examples are presented to illustrate the effectiveness of the proposed strategy.
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This paper addresses the problem of dynamic output feedback robust mixed H 2 / H"" norm optimal control with regional pole constraints. The problem can be formulated a optimization problem involving LMI, Linear Matrix Inequalities. The main purpose of the robust optimal control problem is to minimize mixed H 2 / H"" norm of the closed loop transfer function matrix under some constraints. In the other words, the main objectives of the robust optimal control is to minimize mixed H 2 / H"" norm of the closed loop transfer function matrix under the system performance constraints. In this paper, mixed H 2 / H"" performance index is minimized under the constraint of H 2 performance, the constraint of H"" performance and the regional pole placement. Recent years LMI are extensively used in control system synthesis. The synthesis problem is solved via LMI.
H 2 Robust Control with Pole Placement
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Conditions are given for pole assignability in particular regions of the complex plane such as circular region, vertical strip, and circular sector. The conditions are formulated in terms of semi positive definite matrices which constitute a parametrization of the feedback controls. The malO pOint IS that this parametrization is made through convex parameter domains so that the control determination can be carned by solving convex parametric optimization problems. The f{, transfer matriX norm IS used to define the cost function for these optimization problems so that the optimal solutIOn provides a guaranteed bound for the 1-l2 norm. Both certain and uncertain linear time invariant systems are considered. Numerical experiments illustrate the usefulness of the method.
H∞ design with pole placement constraints: An LMI approach
Automatic Control, IEEE Transactions on, 1996
This paper addresses the design of state-or outputfeedback H , controllers that satisfy additional constraints on the closed-loop pole location. Sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane. These conditions are expressed in terms of linear matrix inequalities (LMI's), and our formulation is therefore numerically tractable via LMI optimization. In the state-feedback case, mixed H , / H , synthesis with regional pole placement is also discussed. Finally, the validity and applicability of this approach are illustrated by a benchmark example.