Static Output Feedback Design Research Articles

Robust Static Output Feedback $\mathcal {H}_\infty$ Control for Uncertain Takagi–Sugeno Fuzzy Systems

In this work, a robust static output feedback (SOF) design for continuous-time nonlinear systems under norm bounded uncertainties, described as a Takagi–Sugeno (TS) system is proposed. The key features are that a switching control law is used to activate the SOF gains to stabilize the uncertain TS fuzzy system and the SOF design does not require the measurements of all premise variables in real time as in the standard fuzzy parallel distributed compensation design. The main result is given in terms of linear matrix inequalities, which guarantees a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$</tex-math></inline-formula> attenuation level of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gamma$</tex-math></inline-formula> for the SOF control system. The efficiency of the main results is illustrated with examples, including a nonlinear active suspension system under uncertain driver masses, and compared with other published results from the literature.

Stabilization of rational nonlinear discrete-time systems by state feedback and static output feedback

The design of State Feedback (SF) and Static Output Feedback (SOF) controllers for nonlinear discrete-time systems subject to time-varying parameters is discussed in the context of Difference-Algebraic Representations (DAR) and parameter-dependent Lyapunov functions applied to obtain convex conditions in the form of Linear Matrix Inequalities (LMI). The proposed conditions guarantee the system robust stabilization and provide an estimate of the Domain-of-Attraction (DoA). Firstly, a novel strategy for gain-scheduled SF control is proposed incorporating information on the system’s nonlinearities to compute the control action. Secondly, a new gain-scheduled SOF control design solution is derived, without structural constraints imposed on the output matrix and without making use of iterative algorithms, unlike most approaches in the current literature. Finally, numerical examples illustrate the proposed methodology’s potential.

Distributed static output feedback robust model predictive control for process networks

This paper formulates a distributed static output feedback robust model predictive control for process networks to solve problems relating to unmeasured states and interconnected couplings. The initial conditions on the couplings are predicted by previous information and the boundedness of the predicted error is proved. In light of the static output feedback design conditions, the distributed static output feedback robust model predictive control is designed by transforming an infinite time optimization problem into a tractably solved one. The solvability of the optimization problem and the stability are proved to underpin the proposed approach. Simulations and an experimental case study are provided to validate the effectiveness of the proposed approach.

Design of Static Output Feedback and Structured Controllers for Active Suspension with Quarter-Car Model

This paper presents a method to design active suspension controllers for a 7-Degree-of-Freedom (DOF) full-car (FC) model from controllers designed with a 2-DOF quarter-car (QC) one. A linear quadratic regulator (LQR) with 7-DOF FC model has been widely used for active suspension control. However, it is too hard to implement the LQR in real vehicles because it requires so many state variables to be precisely measured and has so many elements to be implemented in the gain matrix of the LQR. To cope with the problem, a 2-DOF QC model describing vertical motions of sprung and unsprung masses is adopted for controller design. LQR designed with the QC model has a simpler structure and much smaller number of gain elements than that designed with the FC one. In this paper, several controllers for the FC model are derived from LQR designed with the QC model. These controllers can give equivalent or better performance than that designed with the FC model in terms of ride comfort. In order to use available sensor signals instead of using full-state feedback for active suspension control, LQ static output feedback (SOF) and linear quadratic Gaussian (LQG) controllers are designed with the QC model. From these controllers, observer-based controllers for the FC model are also derived. To verify the performance of the controllers for the FC model derived from LQR and LQ SOF ones designed with the QC model, frequency domain analysis is undertaken. From the analysis, it is confirmed that the controllers for the FC model derived from LQ and LQ SOF ones designed with the QC model can give equivalent performance to those designed with the FC one in terms of ride comfort.

H∞ and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults

In this paper, the problem of reliable control design with mixed H∞ /passive performance is discussed for a class of Takagi–Sugeno TS fuzzy descriptor systems with time-varying delay, sensor failure, and randomly occurred non-linearity. Based on the Lyapunov theory, firstly, a less conservative admissible criterion is established by combining the delay decomposition and reciprocally convex approaches. Then, the attention is focused on the design of a reliable static output feedback (SOF) controller with mixed H∞ /passive performance requirements. The key merit of the paper is to propose a simple method to design such a controller since the system output is subject to probabilistic missing data and noise. Using the output vector as a state component, an augmented model is introduced, and sufficient conditions are derived to achieve the desired performance of the closed-loop system. In addition, the cone complementarity linearization (CCL) algorithm is provided to calculate the controller gains. At last, three numerical examples, including computer-simulated truck-trailer and ball and beam systems are given to show the efficacy of our proposed approach, compared with existing ones in the literature.

STATIC OUTPUT FEEDBACK DESIGN USING MODEL REDUCTION METHODS FOR SECOND-ORDER SYSTEMS

<abstract> In this paper, the static output feedback design is investigated using model reduction methods for large-scale second-order systems. First, based on the second-order Krylov subspace method, a low dimensional structure-preserving second-order system is derived. Then, applying matrix transformation, the relationship between input variables and output variables is directly established in the low dimensional system. We design output feedback controller for this system. Finally, using the argument principle, a computable stability criterion is presented to check the stability of the closed-loop system. Furthermore, a numerical algorithm is provided to design the output feedback controller for large-scale second-order systems. Numerical examples are given to illustrate the effectiveness of the algorithms. </abstract>

Iterative LMI approach to robust static output feedback control of uncertain polynomial systems with bounded actuators

This paper presents a novel static output feedback stabilization of polynomial systems with bounded actuators. We propose a new sufficient condition for static output feedback design for nominal polynomial systems with constraints on input magnitudes. In the proposed stabilization condition, the system matrices and the Lyapunov matrices are separated, and hence parameterization of the controller is independent of the Lyapunov matrices. The main result is the novel parameter-dependent Lyapunov functions that are readily applied to robust static output feedback design of polynomial systems subject to parametric uncertainty. The proposed design conditions are bilinear in the decision variables. Hence, we provide iterative algorithms to solve the design problems. At each iteration, the design condition is cast as parameter-dependent linear matrix inequalities using the sum-of-squares technique and can be efficiently solved. The proposed approach leads to enhanced static output feedback design with computationally tractable formulation. Effectiveness of the proposed approach is demonstrated by numerical examples.

Eigenvalue Placement by Quantifier Elimination - the Static Output Feedback Problem

This contribution deals with the static output feedback problem of linear time-invariant systems. This is still an area of active research, in contrast to the observer-based state feedback problem, which has been solved decades ago. We consider the formulation and solution of static output feedback design problems using quantifier elimination techniques. Stabilization as well as more specified eigenvalue placement scenarios are the focus of the paper.

New results on restricted static output feedback controller design with regional pole placement

This study addresses the design of static output feedback (SOF) controller for continuous time linear systems. New sufficient conditions are derived for designing SOF controllers. The development involves suitable decomposition of Lyapunov matrices and deriving linear matrix inequality (LMI) criterion that ensures H ∞ performance. LMI criteria for pole placement in the LMI region are also derived. The proposed criteria can be used for restricted SOF controller design effectively. Several numerical examples are presented to demonstrate the effectiveness of the proposed results.

Robust static output feedback design with pole placement constraints for linear systems with polytopic uncertainties

A necessary and sufficient condition for static output feedback (SOF) controller design for linear systems with polytopic uncertainties is derived in the form of the linear matrix inequalities (LMI...

Resilient adaptive and [formula omitted] controls of multi-agent systems under sensor and actuator faults

Resilience of multi-agent systems (MAS) reflects their capability to maintain normal operation, at a prescribed level in the presence of unintended faults. In this paper, we investigate resilient control of MAS under faults on sensors and actuators. We propose four resilient state feedback based leader–follower tracking protocols. For the case of sensor faults, we develop an adaptive compensation protocol and an H∞ control protocol. For the case of simultaneous sensor and actuator faults, we further propose an enhanced adaptive compensation protocol and an enhanced H∞ control protocol. We show the duality between the adaptive compensation protocols and the H∞ control protocols. For adaptive compensation protocols, faults on sensors and actuators are rejected by using local adaptive sensor and actuator compensators, respectively. Moreover, by employing a static output-feedback design technique, we propose H∞ control protocols that guarantee bounded L2 gains of certain errors in terms of the L2 norms of fault signals. This further allows us to prove resilience even if sensor faults are unbounded. Finally, simulation studies validate the effectiveness of the proposed protocols.

Active aeroelastic output feedback control with partial measurements by the method of receptances

The method of receptances allows the design of active aeroelastic control for suppressing the flutter instabilities and for augmenting the flutter boundaries by pole placement. This method is purely based on available receptance transfer functions, which can be available for controller design from the embedded sensors and actuators on the aircraft. In recent years, receptance based single-input and multiple-input full state feedback control has been developed, which requires the displacement and velocity measurements associated with each degree of freedom, which may not be available in practice. The design of a controller using partially available measurements in these scenarios is related to the static output feedback design, which leads to the solution of associated nonlinear problems and/or the design of complimentary state estimators or observers. In order to overcome such restrictions, in this paper a method for feedback control design using the receptance method is presented which can utilize the available partial measurements for control gain computation. This is achieved by introducing redundancy of acceleration measurement and adding associated acceleration feedback in the controller loop. This leads to a linear constrained least-square problem for the design of the controller. The working of this approach is shown with numerical examples associated with various wing models. It is demonstrated that prescribed aeroelastic modes can be controlled to achieve flutter suppression and flutter boundary extension, by designing a feedback controller using partial measurements from the available sensors. Parametric studies are presented to demonstrate that such output feedback control allows the optimal selection of measurements and the corresponding sensor location to minimize the controller norm.

Static output feedback fault tolerant control using control allocation scheme

SummaryThis paper describes two novel schemes for fault tolerant control using robust suboptimal static output feedback design methods. These schemes can also be employed as actuator redundancy management for overactuated uncertain linear systems. In contrast to many existing methods in the literature that assume the control input matrix (i) is not of full‐rank such that it can be factorized into two matrices and (ii) it does not involve uncertainty, these schemes can be applied to systems whose control input matrix cannot be factorized and/or involve uncertainty. The so‐called virtual control, in these schemes, is calculated using suboptimal ‐based static output feedback design schemes constructed to be robust against uncertainties emanating from inherent input matrix uncertainty and visibility of the control allocator to the controller. Then, using two proposed control allocation schemes (fixed and on‐line), the obtained virtual control signal is redistributed among remaining (redundant or nonfaulty) set of actuators. As the proposed schemes are modular‐based, they can be employed as real‐time fault tolerant control schemes with no need to reconfigure the controller in the case of actuator faults or failures. The effectiveness of the proposed schemes is discussed and compared with numerical examples.

Relaxed LMI Conditions for the Design of Robust Static Output Feedback Controllers

Abstract In this paper, we propose new sufficient conditions in terms of linear matrix inequalities (LMIs) for the design of robust static output feedback (SOF) controllers for linear time-invariant systems. With this approach, it is possible to deal with the practical problem of not having all state variables available to be directly measured. Additionally, this strategy considers systems subject to the presence of uncertain parameters in its structure. The proposed LMIs were obtained using the Finsler’s Lemma. We also present the employment of two relaxation strategies to improve the feasibility region in the controller design. Moreover, this paper presents the results of a practical implementation in an active suspension system susceptible to a fault in the actuator control signal to evaluate the technique’s efficiency.

A shifting pole placement approach for the design of performance-varying multivariable PID controllers via BMIs

In this paper, the design of a performance-varying multivariable Proportional-Integral-Derivative (PID) controllers is presented. The main objective is to provide a framework for changing online the closed-loop behavior of the controlled system using the shifting pole placement approach. In order to carry out this target, the PID design problem is transformed into a static output feedback design problem which is analyzed through the linear parameter-varying (LPV) paradigm. An academic example is used to demonstrate the effectiveness of the proposed approach.

Fault-tolerant control of flexible air-breathing hypersonic vehicles via static output feedback

This paper addresses the fault-tolerant control issue of static output feedback design for flexible air-breathing hypersonic vehicles. Firstly, a longitudinal dynamic model with process faults is established, which contains an ordinary differential equation (ODE) for rigid body, an Euler-Bernoulli beam equation for elastic modes, and a new boundary interconnection between them; Secondly, a novel fault-tolerant control scheme via static output feedback control strategy is proposed to accommodate process faults and suppress vibrations, which relies on the direct Lyapunov method and the bilinear matrix inequalities (BMIs) technique; Thirdly, in order to compute the gain matrices of the fault-tolerant control law, a two step algorithm is provided to solve the BMI feasibility problem in terms of linear matrix inequality (LMI) optimization technique. Finally, the simulation results are provided to illustrate the effectiveness of the theoretical results.

Static output feedback design for a class of constrained Takagi–Sugeno fuzzy systems

This paper addresses the static output feedback (SOF) control problem of Takagi–Sugeno fuzzy systems subject to both control input and state constraints. A new parameter-dependent sector condition is proposed to deal with the input saturation in SOF control context. Based on a judicious use of Finsler’s lemma in fuzzy Lyapunov control framework, new design conditions guaranteeing the existence of a stabilizing controller are recast as an LMI-based optimization with additional slack variables. These extra variables offer more flexibility to reduce the design conservatism. In particular, the proposed method requires neither special constraints on the state-space system matrices nor linear matrix equalities, which are hard to be satisfied. Several numerical examples are given to demonstrate the interests of the new control method.

Design of simultaneous static output feedback low‐gain H∞ controllers for a collection of time‐delay system

SummaryThis paper considers the design of simultaneous static output feedback controllers for a finite collection of time‐delay linear systems. By solving a minimization problem, we try to find an output feedback low‐gain controller such that all resultant closed‐loop time‐delay systems are internally stable and satisfy a prespecified H∞‐norm requirement. Based on the barrier method, necessary conditions for local optimum of the minimization problem are derived. An example is given for illustration.

Robust non-fragile finite-frequency H∞ static output-feedback control for active suspension systems

This paper deals with the problem of non-fragile H∞ static output-feedback control of vehicle active suspension systems with finite-frequency constraint. The control objective is to improve ride comfort within the given frequency range and ensure the hard constraints in the time-domain. Moreover, in order to enhance the robustness of the controller, the control gain perturbation is also considered in controller synthesis. Firstly, a new non-fragile H∞ finite-frequency control condition is established by using generalized Kalman-Yakubovich-Popov (GKYP) lemma. Secondly, the static output-feedback control gain is directly derived by using a non-iteration algorithm. Different from the existing iteration LMI results, the static output-feedback design is simple and less conservative. Finally, the proposed control algorithm is applied to a quarter-car active suspension model with actuator dynamics, numerical results are made to show the effectiveness and merits of the proposed method.

Distributed [formula omitted]-gain output-feedback control of homogeneous and heterogeneous systems

The importance of static output feedback (OPFB) design for aircraft control, process control, and elsewhere has been well documented since the 1960s, since full state measurements are not usually available in practical systems. This problem is compounded in the case of multi-agent systems (MAS) where each agent has its own state variable and measured outputs. Therefore, this paper addresses the L2-gain OPFB synchronization of linear MAS subject to external disturbances. Both homogeneous and heterogeneous MAS are considered. For homogeneous MAS, it is shown that the L2-gain static OPFB synchronization problem of MAS can be cast into the L2-gain static OPFB problem for a set of decoupled systems that depend on the graph topology. A modified Riccati equation is introduced which gives the OPFB gain and the coupling gain of the proposed static OPFB control protocol. For heterogeneous MAS, it is shown that the L2-gain synchronization problem can be cast into the L2-gain static OPFB problem of a set of decoupled systems plus a coupling condition on their dynamic compensators that depends on the graph topology. A certain novel gain matrix is introduced in the dynamics of the control protocol to improve the performance.