H2 dynamic output feedback control of phase-type semi-Markov jump linear systems

Emerging approaches for nonlinear parameter varying systems

This paper proposes a new scheme for estimating the actuator and sensor fault for Lipschitz nonlinear systems with unstructured uncertainties using the sliding mode observer (SMO) technique. Initially, a coordinate transformation is introduced to transform the original state vector into two parts such that the actuator faults only appear in the dynamics of the second state vector. The concept of equivalent output error injection is then employed to estimate the actuator fault. The effects of system uncertainties on the estimation errors of states and faults are minimized by integrating anuncertainty attenuation level into the observer. The sufficient conditions for the state estimation error to be bounded and satisfy a prescribedperformance are derived and expressed as a linear matrix inequality (LMI) optimization problem. Furthermore, the proposed actuator fault estimation method is extended to sensor fault estimation. Finally, the effectiveness of the proposed scheme in estimating actuator and sensor faults has been illustrated considering an example of a single‐link flexible joint robot system.

The paper presents a linear matrix inequality (LMI)-based approach for the simultaneous optimal design of output feedback control gains and damping parameters in structural systems with collocated actuators and sensors. The proposed integrated design is based on simplified H 2 and H ? norm upper bound calculations for collocated structural systems. Using these upper bound results, the combined design of the damping parameters of the structural system and the output feedback controller to satisfy closed-loop H 2 or H ? performance specifications is formulated as an LMI optimization problem with respect to the unknown damping coefficients and feedback gains. Numerical examples motivated from structural and aerospace engineering applications demonstrate the advantages and computational efficiency of the proposed technique for integrated structural and control design. The effectiveness of the proposed integrated design becomes apparent, especially in very large scale structural systems where the use of classical methods for solving Lyapunov and Riccati equations associated with H 2 and H ? designs are time-consuming or intractable.

The paper presents a linear matrix inequality (LMI)-based approach for the simultaneous optimal design of output feedback control gains and damping parameters in structural systems with collocated actuators and sensors. The proposed integrated design is based on simplified \(\mathcal{H}^2\) and \(\mathcal{H}^{\infty}\) norm upper bound calculations for collocated structural systems. Using these upper bound results, the combined design of the damping parameters of the structural system and the output feedback controller to satisfy closed-loop \(\mathcal{H}^2\) or \(\mathcal{H}^{\infty}\) performance specifications is formulated as an LMI optimization problem with respect to the unknown damping coefficients and feedback gains. Numerical examples motivated from structural and aerospace engineering applications demonstrate the advantages and computational efficiency of the proposed technique for integrated structural and control design. The effectiveness of the proposed integrated design becomes apparent, especially in very large scale structural systems where the use of classical methods for solving Lyapunov and Riccati equations associated with \(\mathcal{H}^2\) and \(\mathcal{H}^{\infty}\) designs are time-consuming or intractable.

Robust sensor fault estimation scheme for satellite attitude control systems

In this chapter, we propose a robust active fault-tolerant control (AFTC) scheme for a class of uncertain nonlinear systems with simultaneous actuator and sensor faults described via Takagi-Sugeno (T-S) multiple models. First, by transforming the sensor fault into pseudoactuator fault, a novel T-S sliding-mode observer (TS-SMO) with two discontinuous terms is developed to provide separate estimates of the actuator and sensor faults for the purpose of fault compensation. The robustness of the proposed observer against uncertainties has been taken into account via H∞ norm minimization. Second, we use obtained on-line fault estimation information to design dynamic output feedback controller (DOFC) for robustly compensating the effects of actuator and sensor faults from the system inputs and outputs and guarantee the stability of the overall closed-loop system. The stability proof with H∞ performances and D-stability constraints is formulated as a linear matrix inequalities (LMI) optimization problem. The effectiveness of the proposed robust AFTC approach to treat simultaneous actuator and sensor faults is illustrated using a nonlinear inverted pendulum with cart system.

This paper addresses the problem of simultaneously estimating actuator and sensor faults of Lipschitz nonlinear systems with non-parametric uncertainties. The proposed fault estimation scheme initially takes sensor faults as auxiliary states and an augmented descriptor system is constructed. By designing a modified proportional and derivative (PD) observer with an adaptive law for this system, the estimation of the original system states, sensor faults and actuator faults can be obtained simultaneously. The sufficient condition for stability of the proposed observer with ℋ ∞ performance has been derived based on Lyapunov theory. The stability condition is expressed as Linear Matrix Inequality (LMI) optimization problem for minimizing the ℋ ∞ norm of transfer matrix between the estimation error and uncertainties, which outlines a constructive design procedure for observer parameters. It is shown from the simulation that the proposed approach is capable of successfully estimating states and faults not only for nonlinear state-space systems, but also for nonlinear descriptor systems.

The present study proposes two schemes for simultaneously estimating actuator and sensor faults for a class of uncertain non‐linear systems. In the first scheme, two sliding mode observers (SMOs) are designed to estimate actuator and sensor faults, respectively, under the assumption that the matching condition holds. In the second scheme, the assumption of matching condition is relaxed and an adaptive observer has been designed to estimate the sensor fault instead of using an SMO. The effects of the system uncertainties on the estimation errors of states and faults are reduced by integrating a prescribed ℋ∞ disturbance attenuation level into the proposed schemes. The sufficient condition for the existence of the proposed observers with ℋ∞ tracking performance is derived and expressed as a linear matrix inequality optimisation problem such that the ℒ2 gain between the estimation errors and system uncertainties is minimised. Finally, a simulation study is presented to illustrate the effectiveness of the proposed schemes.

The theory of K/sub m///spl mu/-synthesis and analysis introduced by Safonov (1983) and Doyle (1983) essentially performs the following D-K iteration steps: 1) design a /spl Hscr//sub /spl infin//-controller K(s) such as to maximize the multivariable stabilty margin K/sub m/; and 2) for discrete frequencies, find a diagonal scaling frequency response matrix D(jw) as to maximize K/sub m/ for a fixed K(s). Step 1 can be cast as a linear matrix inequalities (LMI) optimization problem for full order controller. The K/sub m/ analysis in step 2 has been shown to be a LMI optimization problem. The paper reviews the fixed order optimal multiplier K/sub m/ analysis theory and presents state space parameterization for the set of multipliers subject to mixed dynamic and real parametric uncertainties. A numerical example involving the robustness analysis of the Cassini spacecraft thrust vector control system is also included.

This paper considers linear time-invariant continuous-time systems with control input saturation nonlinearities, and proposes two regional stability synthesis methods of output feedback controllers such as an ellipsoid defined by a level set of a quadratic Lyapunov function to be a domain of attraction for the systems based on the generalized sector approach. One of them is an integrated design of full-order dynamical output feedback and anti-windup controllers with the same plant order, while the other is an integrated design of reduced-order dynamical output feedback and antiwindup controllers to be less than the number of available plant states from the plant order. The two methods assume the output of the nonlinearities to be available for the control. In this case, this paper indicates that the synthesis problems using the two methods can be recast as linear matrix inequality (LMI) optimization problems respectively. Furthermore, it is proved that two subsets of achievable domains of attraction using the two controllers are exactly the same. Thus this paper concludes that the reduced-order controller does not decrease the size of the achievable domain of attraction, within our framework, when compared with that resulting from the full-order controller.

This paper deals with the output feedback stabilization problem for 2-D discrete linear systems without or with parameter uncertainty. The class of systems under investigation is described by the 2-D local state space (LSS ) FornasiniMarchesini second model. We focus on the design of a dynamic output feedback controller to achieve asymptotic stability for the closed-loop system. It is shown that the design of an output feedback controller can be recast to a convex optimization problem characterized by linear matrix inequalities (LMIs). Furthermore, the LMI approach is extended to solve the output feedback stabilization problem for 2-D uncertain systems subject to norm-bounded uncertainty.

Takagi-Sugeno (TS) fuzzy models can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input-output submodels. In this paper, the TS fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation. The TS fuzzy representation of a nonlinear system subject to actuator saturation is presented. In our TS fuzzy representation, the modeling error is also captured by norm-bounded uncertainties. A set invariance condition for the system in the TS fuzzy representation is first established. Based on this set invariance condition, the problem of estimating the domain of attraction of a TS fuzzy system under a constant state feedback law is formulated and solved as a linear matrix inequality (LMI) optimization problem. By viewing the state feedback gain as an extra free parameter in the LMI optimization problem, we arrive at a method for designing state feedback gain that maximizes the domain of attraction. A fuzzy scheduling control design method is also introduced to further enlarge the domain of attraction. An inverted pendulum is used to show the effectiveness of the proposed fuzzy controller.

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 (LMIs) with a line search over some scalar parameters to locate the closed-loop poles in the desired complex plane. The extension of the result to H2 SOF synthesis is studied, which guarantees a minimum bound on the H2 performance level in addition to the pole placement constraints. One of the advantages of the new method is the possibility of applying them to general systems without any constraints on the system matrices. In order to improve the performance and reduce conservatism of the SOF conditions, the Lyapunov matrix is considered parameter dependent. Numerical examples are presented to show the performance and effectiveness of the proposed methods.

To address the issue of inadequate control effect resulting from the challenge of measuring state feedback information comprehensively, this paper proposes an iterative output feedback energy-to-peak control method that solely depends on partial external observation data. This paper presents the computational steps for achieving a suboptimal solution to the output feedback bilinear matrix inequality constrained problem using an iterative linear matrix inequality approach. The proposed method overcomes the challenge of numerically solving the optimization problem. The unknown variables in the output feedback linear matrix inequality optimization problem are transformed equivalently to obtain a new linear matrix inequality optimization problem. The numerical results of the two optimization problems are then used to iterate with each other and obtain a suboptimal solution. A comprehensive analysis was conducted on an 8-story building structure, utilizing state feedback, output feedback, and iterative output feedback energy-to-peak control techniques. The results of the study indicate that the proposed iterative output feedback energy-to-peak control approach efficiently reduces the displacement and acceleration response of the structure, exhibiting superior control effectiveness than both the state feedback and output feedback energy-to-peak control methods. The findings demonstrate the practicality and versatility of the suggested method.

This paper focuses on analyzing a new model transformation of discrete-time Takagi–Sugeno (T–S) fuzzy systems with time-varying delays and applying it to dynamic output feedback (DOF) controller design. A new comparison model is proposed by employing a new approximation for time-varying delay state, and then, a delay partitioning method is used to analyze the scaled small gain of this comparison model. A sufficient condition on discrete-time T–S fuzzy systems with time-varying delays, which guarantees the corresponding closed-loop system to be asymptotically stable and has an induced <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\ell_{2}$</tex></formula> disturbance attenuation performance, is derived by employing the scaled small-gain theorem. Then, the solvability condition for the induced <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\ell_{2}$</tex></formula> DOF control is also established, by which the DOF controller can be solved as linear matrix inequality optimization problems. Finally, examples are provided to illustrate the effectiveness of the proposed approaches.