Joost Veenman

A synthesis framework for robust gain-scheduling controllers

We present a general framework for the systematic synthesis of robust gain-scheduling controllers by convex optimization techniques and for uncertain dynamical systems described by standard linear fractional representations. We distinguish between linear time-varying parameters, which are assumed to be available online as scheduling parameters for the controller, and genuine uncertainties, not necessarily time-varying, parametric or linear, that are not available online. Under the rough hypothesis that the control channel is not affected by the unmeasurable uncertainties and that the properties of the uncertainties and scheduling variables are captured by suitable families of integral quadratic constraints, this paper reveals how controller synthesis can be turned into a genuine semi-definite program. The design framework is shown to encompass a rich class of concrete scenarios.

On robust LPV controller synthesis: A dynamic Integral Quadratic Constraint based approach

In this paper the design of robust Linear Parameter Varying (LPV) controllers is addressed. A novel controller/scaling algorithm based on dynamic Integral Quadratic Constraints (IQCs) is proposed that completely avoids gridding as well as curve-fitting. Although, in this paper, we restrict our attention to dynamic DG-scalings, the techniques allow for generalization to the use of arbitrary real-rational IQC multipliers with no poles on the extended imaginary axis. While the classical µ-synthesis approach is restricted to the use of real/complex time-invariant or arbitrarily fast time-varying parametric uncertainties, the IQC framework can be employed for a much larger class of uncertainties involving nonlinearities and bounds on rates of time-varying parametric uncertainties. Moreover, the proposed techniques have a great potential for solutions of the nominal dynamic IQC based LPV controller synthesis problem in terms of LMIs.

Application of LPV modeling, design and analysis methods to a re-entry vehicle

In this paper the application of linear parameter varying (LPV) modeling, design and analysis methods to a re-entry vehicle is presented. The selected atmospheric re-entry benchmark includes full nonlinear motion, a detailed aerodynamic database (from hypersonic to subsonic), relevant actuator and sensor models and physically-meaningful aerodynamic and parametric uncertainty profiles. The results show that: (i) LPV controller design methods can solve gain-scheduling problems in a very effective manner, (ii) integral quadratic constraint (IQC) analysis methods can be used very efficiently to accurately interpret the nonlinear time domain simulation results, and, (iii) the use of linear fractional transformation (LFT) and LPV modeling representations are key to a successful analysis.

Analysis of the Controlled NASA HL20 Atmospheric Re-entry Vehicle based on Dynamic IQCs

The analysis of complicated nonlinear systems is mostly considered as very challenging. Moreover, the available methods and tools suggested in the literature are scarce and not well tested on complex applications. This paper proposes a general procedure based on linear fractional representations (LFR), Integral quadratic constraints (IQC) and mu-theory for the analysis of a linear parameter-varying (LPV) controller that was designed for the NASA HL20 vehicle for a re-entry mission. An LFR was obtained through trimming, linearization and polynomial interpolation of the strongly nonlinear dynamical equations and will be used for the analysis, in order to guarantee stability and a high performance certificate over a large operation range. Special attention is being paid to time invariant parametric uncertainties, smoothly time-varying parametric uncertainties with bounded rates-of-variation, odd-monotone and slope restricted uncertainties to analyze the closed-loop system subject to actuator saturation and uncertain time-delay.

Robust stability and performance analysis based on integral quadratic constraints

The integral quadratic constraints (IQC) approach facilitates a systematic and efficient analysis of robust stability and performance for uncertain dynamical systems based on linear matrix inequality (LMI) optimization. With the intention to make the IQC analysis tools more accessible to control scientists and engineers, we present in this paper a tutorial overview in three main parts: i) the general setup and the basic IQC theorem, ii) an extensive survey on the formulation and parametrization of multipliers based on LMI constraints, and iii) a detailed illustration of how the tools can be applied.

IQC-Based LPV Controller Synthesis for the NASA HL20 Atmospheric Re-entry Vehicle

The synthesis of linear parameter-varying (LPV) controllers for complicated nonlinear systems is mostly considered as very challenging. Moreover, the available methods and tools suggested in the literature are scarce and not well tested on complex applications. In this paper, the design of an LPV controller for the NASA HL20 vehicle during re-entry is addressed. The strongly nonlinear longitudinal motion of the dynamical system has to be stabilized and must exhibit high performance over a large operation range. A general design philosophy is provided which serves as a road-map to ensure a successful synthesis, starting from a linear fractional representation (LFR) of the LPV plant, which is obtained by trimming and linearization of the nonlinear dynamical equations. The design is performed based on LPV synthesis theory which involves Linear Matrix Inequalities (LMIs). The design is validated based on standard Bode-magnitude plots, time-domain simulations within a non-linear simulation environment and analysis results based on the Integral Quadratic Constraint (IQC) framework.

Robust gain-scheduled controller synthesis is convex for systems without control channel uncertainties

In this paper we generalize our previous results on robust controller synthesis to robust gain-scheduled controller synthesis. We present novel insights that reveal how the robust gain-scheduled controller synthesis problem can be turned into a semi-definite program, under the hypothesis that (i) the control channel is not affected by uncertainties and (ii) the uncertainties and scheduling variables are described by full-block multipliers. Feasibility of the resulting LMI conditions ensures the existence of gain-scheduled controllers that guarantee robust stability and performance for the corresponding closed-loop uncertain system.

IQC-Synthesis with General Dynamic Multipliers

Abstract In this paper we generalize our previous results on the synthesis of robust controllers. A novel controller/scaling algorithm is proposed that allows for the use of arbitrary real-rational Integral Quadratic Constraint (IQC) multipliers with no poles on the extended imaginary axis. In contrast to the classical μ-synthesis approaches, the techniques completely avoid gridding as well as curve-fitting. Moreover, while the classical approaches are restricted to the use of real/complex time-invariant or arbitrarily fast time-varying parametric uncertainties, the IQC framework can be employed for a much larger class of uncertainties involving nonlinearities and bounds on rates of time-varying parametric uncertainties. The results are illustrated through a numerical example.

An IQC approach to robust estimation against perturbations of smoothly time-varying parameters

In this paper the design of robust H2-estimators for the class of linear systems that depend rationally on rate-bounded uncertain time-varying parameters is addressed. The uncertainties are characterized by dynamic IQCs and new LMI conditions are formulated that allow for a nontrivial extension of the estimation problem with a weighting filter at the output. In order to show the power of the dynamic IQC approach, a numerical example is included in which the result is compared with alternative approaches based on parameter-dependent Lyapunov functions. The effectiveness of the additional weighting filter is illustrated in a second numerical example.

Robust Estimation with Partial Gain-Scheduling Through Convex Optimization

The problem of robust estimation for uncertain dynamical systems with a linear fractional dependence on uncertainties is considered. It is assumed that some of the parametric uncertainties affecting the system are available online and the estimator is scheduled on these parameters. The integral quadratic constraint (IQC) framework is considered for handling the uncertainties. Full-block static multipliers are used for capturing the properties of the measured parameters in the system while no structural or dynamic restrictions are placed on the multipliers used for the nonmeasured uncertainties. Sufficient existence conditions for constructing such robustly stabilizing, partially gain-scheduled estimators with guaranteed \({\mathcal{L}}_{2}\)-gain bounds are given in terms of finite dimensional linear matrix inequalities. A numerical example illustrates the advantages of gain-scheduling in robust estimation whenever possible.