Hakan Köroğlu

Robust Performance Analysis for Structured Linear Time-Varying Perturbations With Bounded Rates-of-Variation

The robust performance analysis problem is considered for linear time-invariant (LTI) systems subject to block-diagonal structured and bounded linear time-varying (LTV) perturbations with specified maximal rates-of-variation. Analysis methods are developed in terms of semidefinite programming for the computation of upper and lower bounds for the optimum robust performance level. The upper bound computation is based on an integral quadratic constraint (IQC) test developed using a generalized version of the so-called swapping lemma. The lower bound computation method employs an extended version of the power distribution theorem together with a generalized version of the Kalman-Yakubovich-Popov (KYP) lemma and serves as a means to assess the conservatism of the computed upper bounds in the case of dynamic LTV perturbations. As corollaries of the underlying result for lower bound computation, it is shown for general block-diagonal uncertainty structures that thefrequency-dependent/constant D-scaling tests are exact for robust performance analysis against arbitrarily slow/fast dynamic LTV perturbations, respectively

An LMI approach to H∞ synthesis subject to almost asymptotic regulation constraints

A multi-objective controller synthesis problem is considered in which an output is to be regulated approximately by assuring a bound on the steady-state peak amplification in response to an infinite-energy disturbance, while also guaranteeing a desired level of performance measured in terms of the worst-case energy gain from a finite-energy input to a performance output. Relying on a characterization of the controllers with which almost asymptotic regulation is accomplished, the problem of guaranteeing the desired level of performance is reduced to solving a system of linear matrix inequalities subject to a set of linear equality constraints. Based on the solution of this system, a procedure is outlined for the construction of a suitable controller whose order is equal to the order of the plant plus the order of the exogenous system.

Robust Stability Analysis against Perturbations of Smoothly Time-Varying Parameters

Robust stability analysis problem is considered for linear time-invariant systems subject to perturbations of parameters that vary smoothly in time. The problem is formulated by describing the uncertainty in the form of a region-of-variation that covers all possible trajectories obtained by plotting the variation of the parameter at a certain time versus the parameter itself at that same instant of time. In this fashion, the possible and very probable correlation between the parameter and its variation is taken into account. The problem is elaborated on via an integral quadratic constraints approach and, based on a main result relying on the swapping lemma, robust stability analysis tests are derived for polytopic regions of variation as well as for regions with generic descriptions expressed in terms of matrix inequalities. The tests for polytopic regions-of-variation are based on the convex hull and Polya relaxation approaches, whereas the test for general regions relies on the sum-of-squares relaxation approach. The new tests offer significant reduction in conservatism at the cost of extra computational complexity

Brief paper: Generalized asymptotic regulation with guaranteed H2 performance: An LMI solution

A multi-objective controller synthesis problem is considered in which a set of generalized asymptotic regulation constraints are to be satisfied while also guaranteeing a desired level of performance measured in terms of the asymptotic variance of a performance output in response to a white noise random process with zero mean and identity covariance matrix. The generalized regulation constraints are expressed as bounds on the state-steady peak in response to disturbances generated by an anti-stable autonomous exogenous system with nonzero initial states. The controllers that guarantee these constraints can be realized by replicating the dynamics of the exogenous system within a certain structure formed by gain matrices, which are subject to convex constraints, and an accompanying controller with which the feedback loop is to be stabilized. Formulating the design of the accompanying controller in a way to guarantee the additional performance objective, the overall design is rendered tractable over a set of free variables, in terms of which the synthesis of a suitable controller is also outlined. The order of the controller is equal to the order of the plant plus the order of the exogenous system. By an adaptation of the developed techniques, a solution is also provided for the problem of generalized asymptotic regulation with suboptimal transient response.

LPV Control for Robust Attenuation of Non-stationary Sinusoidal Disturbances with Measurable Frequencies

Abstract Attenuation of sinusoidal disturbances with uncertain and arbitrarily time-varying, yet online measurable frequencies is considered. The disturbances are modeled as the outputs of an autonomous exogenous system, whose system matrix depends on some uncertain parameters and is skew-symmetric for all admissible parameter values. A procedure is then developed for the synthesis of an observer-based controller that uses the online measurements of the uncertain parameters to guarantee a desired level of attenuation at steady-state in the face of all admissible parameter variations. The controller is scheduled by the measurements of the uncertain parameters as well as the matrix-valued outputs of a unit that is also scheduled on the uncertain parameters. The synthesis procedure is based on solving a convex optimization problem in which the variables are subject to a set of parameter-dependent matrix inequality constraints, which can be relaxed into finitely many linear matrix inequalities. The procedure also provides options for improving the transient response.

Robust generalized asymptotic regulation via an LPV controller without parameter derivative dependence

Attenuation of sinusoidal disturbances with uncertain and arbitrarily time-varying frequencies is considered for a plant that depends on online measurable parameters. The disturbances are modeled as the outputs of a neutrally stable exogenous system that depends on measurable as well as unmeasurable parameters. Solvability conditions are then derived in the form of parameter-dependent matrix inequalities, based on which a linear parameter-varying controller synthesis procedure is outlined. Alternative conditions are provided for the synthesis of a controller that has no dependence on the derivatives of the parameters. It is also clarified how the transient behavior of the controller can be improved.

Scheduled control for robust attenuation of non-stationary sinusoidal disturbances with measurable frequencies

Attenuation of sinusoidal disturbances with uncertain yet online measurable frequencies is considered. The disturbances are modeled as the outputs of an undisturbed parameter-dependent exogenous system with a skew-symmetric system matrix, obtained in response to nonzero initial conditions. The problem is formulated for a parameter-dependent plant as the synthesis of a parameter-dependent controller in a way to ensure internal stability as well as a desired level of steady-state disturbance attenuation in the face of all admissible parameter variations. The solvability of this problem is first related to the existence of bounded solutions to a matrix differential regulator equation subject to an asymptotic norm constraint. Reformulating this as a parameter-dependent state-feedback like synthesis, based on which suitable solutions to the differential regulator equation can be obtained online, tractable solvability conditions are then provided in the form of parameter-dependent matrix inequalities. Controllers that solve the generalized asymptotic regulation problem are also parameterized in terms of the suitable solutions of the differential regulator equation and some free parameter-dependent matrices that are to be designed off-line to ensure stability. A procedure is then developed to design the free parameters in a way to achieve desirable transient behavior. The use of the developed synthesis procedure is illustrated on a simplified version of the course control problem in ship steering.

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.

New LMI conditions for static output feedback synthesis with multiple performance objectives

The static output feedback synthesis problem is considered with ℋ∞ and generalized ℋ2 performance objectives. New sufficient LMI conditions are derived for guaranteeing the required performance objectives. These conditions also depend on scalar parameters that need to be fixed beforehand. The output feedback gain matrix is computed from the involved matrix variables without the use of system matrices. Hence the conditions can directly be used to solve the multi-objective synthesis problem also for parameter-dependent systems with constant or parameter-dependent gain matrices. The method is illustrated in the adaptive cruise control problem.