Robust Static Output Feedback Research Articles

Discretization and event triggered digital output feedback control of LPV systems

This paper investigates the problem of discretization and digital output feedback control design for continuous-time linear parameter-varying (LPV) systems subject to a time-varying networked-induced delay. The proposed discretization procedure converts a continuous-time LPV system into an equivalent discrete-time LPV system based on an extension of the Taylor series expansion and using an event-based sampling. The scheduling parameters are continuously measured and modeled as piecewise constant. A new transmission of the measured output to the controller is triggered by significant changes in the parameters, yielding time-varying transmission intervals. The obtained discretized model has matrices with polynomial dependence on the time-varying parameters and an additive norm-bounded term representing the discretization residual error. A two step strategy based on linear matrix inequality conditions is then proposed to synthesize a digital static scheduled output feedback control law that stabilizes both the discretized and the LPV model. The conditions can also be used to provide robust (i.e., independent of the scheduling parameter) static output feedback controllers. The viability of the proposed design method is illustrated through numerical examples.

Robust static output feedback [formula omitted] control design for linear systems with polytopic uncertainties

This paper investigates the problem of robust static output feedback H∞ control for linear systems with polytopic uncertainties. A new method is proposed for robust static output feedback H∞ controller design. The proposed design method is applicable for general uncertain systems, without the need to impose any constraints on system matrices. The corresponding design conditions are presented in the form of linear matrix inequalities (LMIs). One of the advantages of the new method lies in its less conservatism. The proposed design method is also applicable to both continuous-time and discrete-time systems. The performance of the method is compared with other methods based on several examples.

Robust control of discrete-time singular Markovian jump systems with partly unknown transition probabilities by static output feedback

This paper considers the robust control of discrete-time uncertain singular Markovian jump systems with partially unknown transition probabilities by static output feedback. Based on a necessary and sufficient condition of the stochastic stability with partially unknown transition probabilities of the unforced systems, some sufficient conditions are obtained to design of a static output feedback controller and a robust static output feedback controller, which guarantee that the closed-loop systems are piecewise regular, causal and stochastically stable by employing the linear matrix inequality technique. Finally, some examples are provided to demonstrate the effectiveness of the proposed approach.

Robust Static Output Feedback Control for Switched Systems with Input Constraints

In the paper, an LMI robust static output feedback (SOF) controller design procedure for switched discrete-time systems with constrained control variables is proposed, based on previous results on SOF controller design and input constraint control. The heuristic iterative procedure is described, using linearization to receive LMI conditions. The proposed SOF controller design is illustrated on a case study of two tank switched system.

Robust static output feedback [formula omitted] control for uncertain fuzzy systems

This paper will focus on robust static output feedback (SOF) H∞ control for discrete-time Takagi–Sugeno (T–S) fuzzy systems with time-varying norm bounded uncertainties. First, a new H∞ performance analysis criterion is proposed for the fuzzy systems. Then, sufficient conditions for designing fuzzy SOF H∞ controllers are given in terms of solutions to a set of linear matrix inequalities (LMIs). In contrast to the existing methods for designing the SOF H∞ controllers, the output matrices of the considered fuzzy system are allowed to be non-common and to have uncertainties. Moreover, theoretical proof is given to show that the proposed design conditions include some existing results as special cases. Simulation examples are provided to show the effectiveness of the proposed design method.

Robust Static Output Feedback Controllers via Robust Stabilizability Functions

This technical note addresses the design of robust static output feedback controllers that minimize a polynomial cost and robustly stabilize a system with polynomial dependence on an uncertain vector constrained in a semialgebraic set. The admissible controllers are those in a given hyper-rectangle for which the system is well-posed. First, the class of robust stabilizability functions is introduced, i.e., the functions of the controller that are positive whenever the controller robustly stabilizes the system. Second, the approximation of a robust stabilizability function with a controller-dependent lower bound is proposed through a sums-of-squares (SOS) program exploiting a technique developed in the estimation of the domain of attraction. Third, the derivation of a robust stabilizing controller from the found controller-dependent lower bound is addressed through a second SOS program that provides an upper bound of the optimal cost. The proposed method is asymptotically non-conservative under mild assumptions.

Robust Static Output-Feedback Control for Uncertain Linear Discrete-Time Systems via the Generalized KYP Lemma

This paper is concerned with robust static output-feedback (SOF) control for linear discrete-time systems subject to polytopic uncertainty and restricted frequency-domain specifications (RFDSs) via the generalized Kalman-Yakubovich-Popov (KYP) lemma. Polytopic uncertainties are assumed to enter all the system matrices, while RFDSs are motivated by the fact that practical design specifications are often described in restricted finite frequency ranges. Dilated multipliers are first introduced to relax the GKYP lemma for SOF controller synthesis and robust performance analysis. Then a two-stage approach to SOF controller synthesis is proposed: at the first stage, a robust full-information (FI) controller is designed, which is used to construct a required SOF controller at the second stage. To improve the solvability of the synthesis method, an iterative algorithm is further formulated for exploring the SOF gain. The effectiveness of the proposed design method is finally demonstrated by a numerical example.

Robust static output feedback control synthesis for linear continuous systems with polytopic uncertainties

This paper studies the static output feedback (SOF) control problem of continuous-time linear systems with polytopic uncertainties. Novel LMI conditions with a line search over a scalar variable for designing robust SOF controllers are proposed, where the uncertain output matrix of the considered system is allowed to be not of full row rank. In particular, it is shown that the new method can give less or at least the same conservative results than those methods by inserting a matrix equality constraint between system output matrix and Lyapunov matrix. Furthermore, the result is extended to the case of H∞ control. Numerical examples are given to illustrate the effectiveness of the proposed method.

Robust non-quadratic static output feedback controller design for Takagi–Sugeno systems using descriptor redundancy

This work concerns robust static output feedback controller (SOFC) design for uncertain and disturbed Takagi–Sugeno (TS) systems using an H-infinity criterion. The main result is based on a descriptor formulation of the closed-loop dynamics. The proposed approach allows avoiding appearance of crossing terms between the controller’s and the TS system’s input matrices leading to easier LMI formulation than existing studies in the literature. Moreover, the proposed SOFC design conditions do not require any restrictions on the output equation and allow dealing with unmeasurable premise variables. Indeed, taking advantage of the uncertain TS modeling, nonlinearities associated to unmeasurable premises variables can be reported from the nominal part to the uncertainties. To provide LMIs of less conservatism, the results are conducted in the non-quadratic framework. Finally, two numerical examples and a benchmark of a crane system are proposed to illustrate the efficiency of the SOFC design methodology.

Robust and optimal control approach for exothermic reactor stabilization

In this paper, the possibility to stabilise open-loop unstable exothermic reactors with temperature measurements is studied. Moreover, the reactors are considered to be multi-input multi-output systems with parametric uncertainties. Robust static output feedback and optimal controllers are designed for stabilization of the exothermic reactors into their open-loop unstable steady states. Stabilization of reactors is simulated using designed controllers. The possibility of using both types of controllers for energy savings is studied and measured by coolant consumption. The approach is tested with a representative example. Obtained simulations results confirm that the robust static output feedback controllers outperform optimal controllers when systems with parametric uncertainties are controlled.

Design of Robust Static Output Feedback Flight Control Law Using Structured Singular Value Optimization

This work proposes solutions for the Robust Static Output Feedback problem using optimization. The application considered is the design of flight control laws, taking into account structured uncertainties and flying qualities criteria, written in the μ robust control framework. An analysis of the resultant cost function is presented, some methods for solution are proposed and the results are discussed.

Robust Static Output Feedback Control and Remote PID Design for Networked Motor Systems

In this paper, we investigate the problem of robust static output feedback (SOF) control for networked control systems (NCSs) subject to network-induced delays and missing data. The uncertain system matrices are assumed to lie in a convex polytope. The network-induced delays are time varying but within a given interval. The random data missing is characterized by the Bernoulli random binary distribution. Delay-dependent conditions for the exponential mean-square stability are first established in terms of matrix inequalities. Then, for the robust stabilization problem, the design of an SOF controller is presented by solving bilinear matrix inequalities (BMIs). In order to efficiently solve a nonconvex BMI, we propose an approach based on the linear matrix inequality technique. Furthermore, the developed approach is employed to design the remote proportional–integral–derivative (PID) controller for NCSs. The design of a digital PID controller is formulated as a synthesis problem of the SOF control via an augmentation method. Simulation examples illustrate the effectiveness of the proposed methods.

Robust static output feedback controller LMI based design via elimination

A linear algebra result, known as Elimination Lemma, has been used to solve a large number of filtering and control problems. In this paper for special case we present a robust version of this result which simplifies, among other problems, the design of a robustly stabilizing static output feedback for linear polytopic systems.

Robust Static and Fixed-order Dynamic Output Feedback Control of Discrete-time Lur'e Systems

AbstractThis paper considers the design of static and fixed-order dynamic output feedback controllers for discrete-time Lur'e systems with sector-bounded nonlinearities and polytopic parametric uncertainty. Controller design equations are derived for systems with multiple states, outputs, and nonlinearities in terms of linear matrix inequalities (LMIs). The design methods are based on parameter-dependent Lyapunov functions (PDLFs) combined with the latest in theoretical and iterative numerical methods for solving certain classes of nonconvex inequalities. The design methods are illustrated in several numerical examples.

Robust ℋ︁2 static output feedback design starting from a parameter-dependent state feedback controller for time-invariant discrete-time polytopic systems

This paper investigates the problem of computing robust ℋ︁2 static output feedback controllers for discrete-time uncertain linear systems with time-invariant parameters lying in polytopic domains. A two stages design procedure based on linear matrix inequalities is proposed as the main contribution. First, a parameter-dependent state feedback controller is synthesized and the resulting gains are used as an input condition for the second stage, which designs the desired robust static output feedback controller with an ℋ︁2 guaranteed cost. The conditions are based on parameter-dependent Lyapunov functions and, differently from most of existing approaches, can also cope with uncertainties in the output control matrix. Numerical examples, including a mass–spring system, illustrate the advantages of the proposed procedure when compared with other methods available in the literature. Copyright © 2009 John Wiley & Sons, Ltd.

LINEAR MATRIX INEQUALITY BASED DESIGN OF FLIGHT CONTROL SYSTEM COMBINED WITH FUZZY TUNING

This paper is dedicated to the synthesis of combined control structure. The architecture of the controller is divided into two loops. The inner loop controller is based on robust static output feedback design under linear matrix inequality approach with H-infinity method in order to attenuate the external disturbances at pre-determined level. The outer loop controller is designed using fuzzy Takagi-Sugeno inference system. The efficiency of the proposed approach is demonstrated on example of lateral channel control of small Unmanned Aerial Vehicle.

Gain-scheduled ℋ2 and ℋ∞ control of discrete-time polytopic time-varying systems

This study presents ℋ2 and ℋ∞ performance analysis and synthesis procedures for the design of both gain-scheduled and robust static output feedback controllers for discrete-time linear systems with time-varying parameters. The obtained controllers guarantee an upper bound on the ℋ2 or ℋ∞ performance of the closed-loop system. As an immediate extension, the mixed ℋ2/ℋ∞ guaranteed cost control problem is also addressed. The scheduling parameters vary inside a polytope and are assumed to be a priori unknown, but measured in real-time. If bounds on the rate of parameter variation are known, they can be taken into account, providing less conservative results. The geometric properties of the polytopic domain are exploited to derive finite sets of linear matrix inequalities (LMIs) based on the existence of a parameter-dependent Lyapunov function. An application of the methodology to a realistic vibroacoustic problem, with experimentally obtained data, illustrates the benefits of the proposed approach and shows that the techniques can be used for real engineering problems.

Robust static output feedback controller synthesis using Kharitonov’s theorem and evolutionary algorithms

This paper presents a simple but effective tuning strategy for robust static output feedback (SOF) controllers with minimal quadratic cost in the context of multiple parametric uncertainties. Finding this type of controller is known to be computationally intractable using conventional techniques. This is mainly due to the non-convexity of the resulting control problem, which has a fixed structure. To solve this kind of control problem easily and directly, without using any complicated mathematical manipulations, we utilize Kharitonov’s theorem and an evolutionary algorithm (EA) for the resolution of the underlying constrained optimization problem. Using Kharitonov’s theorem, a family of bounded, robustly stable static output feedback controllers can be defined and EA is used to select the controller that ensures a minimal quadratic cost within this family. The resulting tuning strategy is applicable to both stable and unstable systems, without any limitations on the order of the process to be controlled. A numerical study was conducted to demonstrate the validity of the proposed tuning procedure.

Robust stabilization of a chemical reactor

AbstractRobust static output feedback control was applied to a continuous stirred tank reactor with parametric uncertainty and multiple steady states in which exothermic reaction takes place. The problem of robust controller design was converted to a solution of linear matrix inequalities and a computationally simple non-iterative algorithm is presented. The possibility of using robust static output feedback for stabilization of reactors with uncertainty and comparison of robust P and PI controllers with an optimal controller is demonstrated by simulation results.

Robust static output feedback control for linear discrete-time systems with time-varying uncertainties

This paper is concerned with the problem of designing robust static output feedback controllers for linear discrete-time systems with time-varying polytopic uncertainties. Sufficient conditions for robust static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities, and the results are extended to H 2 and H ∞ static output feedback controller designs. Numerical examples are given to illustrate the effectiveness of the proposed design methods.