A new representation of Hinfini suboptimal controllers

Projet META2Elementary state-space concepts are used to derive a transparent solution to the stationary H control problem. The main contribution of this solution is a novel representation of suboptimal controllers in terms of a pair of parametric Riccati equations with a coupling constraint. Unlike the classical parametrization in terms of linear fractional transformation, this state-space representation has a homogeneous Riccati formulation which should help to make the most out of the suboptimal controller diversity. Potential applications include the design of reduced-order controllers and more generally the selection of suboptimal controllers to meet or optimize additional constraints

Reliable computation of H infini central controllers near the optimum

Projet META2The state-space formulas for the usual H central controller become singular when approaching the optimum gopt. A new approach is taken to circumvent this difficulty. It consists of extending the notion of central controller to include proper controllers with a feedthrough term. While such controllers are still derived from the usual Riccati solutions X and Y, their feedthrough gain can be selected so as to neutralize the singularities near gopt. This provides numerically stable formulas for the controller parameters and eliminates the discontinuity between the realizations of nearly optimal and of reduced-order optimal central controllers. The advantages of this method are illustrated on a few examples

A convex parametrization of suboptimal hinfini controllers

Projet META2A new parametrization is proposed for suboptimal H controllers of order no larger than the plant order. Here such controllers are generated from pairs of symmetric matrices (X,Y) constrained by two Riccati matrix inequalities and some positivy requirements. Interestingly, the Riccati expressions and the positivity conditions are exactly those arising in the usual state-space solution of suboptimal H problems. When working with the inverses R and S of X and Y, respectively, the constraints can be rewritten as linear matrix inequalities which define a convex parameter set. This sets up a convenient framework to handle design objectives which can be reflected in terms of (R,S). Examples of such objectives include reduced-order H design and the avoidance of pole/zero cancellation between the plant and the controller

On the game Riccati equations arising in Hinfini control problems

Projet META2In the state-space approach to H optimal control, feasibility of some closed-loop attenuation g is characterized in terms of a pair of game Riccati equations depending on g. This paper is concerned with the properties of these equations as g varies. The most general problem is considered (D11 0) and a thorough analysis of the variations of the Riccati solutions provides insight into the behavior near the optimum and into the dependence on g of the suboptimality conditions. In addition, concavity is established for a criterion which synthesizes the three conditions X 0, Y 0, and p(XY) < g 2. As a result, a numerically reliable Newton scheme can be devised to compute the optimal g. Most presented results are extensions of earlier contributions. The main concern here is to provide a complete and synthetic overview as well as results and formulas tailored to the development of numerically-sound algorithms

Additive-Decomposition-Based Output Feedback Tracking Control for Systems with Measurable Nonlinearities and Unknown Disturbances

In this paper, a new control scheme, called as additive-decomposition-based tracking control, is proposed to solve the output feedback tracking problem for a class of systems with measurable nonlinearities and unknown disturbances. By the additive decomposition, the output feedback tracking task for the considered nonlinear system is decomposed into three independent subtasks: a pure tracking subtask for a linear time invariant (LTI) system, a pure rejection subtask for another LTI system and a stabilization subtask for a nonlinear system. By benefiting from the decomposition, the proposed additive-decomposition-based tracking control scheme i) can give a potential way to avoid conflict among tracking performance, rejection performance and robustness, and ii) can mix both design in time domain and frequency domain for one controller design. To demonstrate the effectiveness, the output feedback tracking problem for a single-link robot arm subject to a sinusoidal or a general disturbance is solved respectively, where the transfer function method for tracking and rejection and backstepping method for stabilization are applied together to the design.Comment: 23 pages, 6 figure

A Data-Driven Method for Computing Fixed-Structure Low-Order Controllers With H∞ Performance

Recently, a new data-driven method for robust control with H∞ performance has been proposed. This method is based on convex optimization and converges to the optimal performance when the controller order increases. However, for low-order controllers, the performance depends heavily on the choice of some fixed parameters that are used for convexifying the optimization problem. In this paper, several data-driven optimization algorithms are proposed to improve the solution for low-order controllers. A non-convex problem is solved (in a data-driven sense) where the parameters of a fixed-structure low-order controller are optimized; the solution to the problem guarantees the stability of the closed-loop system whilst ensuring robust performance. It is shown that by optimizing all of the controller parameters, the H∞ performance for low-order controllers can be significantly improved. The simulation examples illustrate how the proposed method can be used to eliminate the sensitivity associated with the fixed parameters and optimize the system performance

On designing observers for time-delay systems with nonlinear disturbances

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2002 Taylor & Francis LtdIn this paper, the observer design problem is studied for a class of time-delay nonlinear systems. The system under consideration is subject to delayed state and non-linear disturbances. The time-delay is allowed to be time-varying, and the non-linearities are assumed to satisfy global Lipschitz conditions. The problem addressed is the design of state observers such that, for the admissible time-delay as well as non-linear disturbances, the dynamics of the observation error is globally exponentially stable. An effective algebraic matrix inequality approach is developed to solve the non-linear observer design problem. Specifically, some conditions for the existence of the desired observers are derived, and an explicit expression of desired observers is given in terms of some free parameters. A simulation example is included to illustrate the practical applicability of the proposed theory.The work of Z. Wang was supported in part by the University of Kaiserslautern of Germany and the Alexander von Humboldt Foundation of Germany