Dissipativity-based robust output feedback control for finite-time boundedness of polytopic uncertain systems

International audience

In this study, the problem of finite-time stability and boundedness for parabolic singular distributed parameter systems in the sense of [Formula: see text] norm is investigated. First, two new results on [Formula: see text] norm-based finite-time stability and finite-time boundedness for above-mentioned systems, inspired by the light of partial differential equations theory and Lyapunov functional method, are presented. Then, some sufficient conditions of [Formula: see text] norm-based finite-time stability and boundedness are established by virtue of differential inequalities and linear matrix inequalities. Furthermore, the distributed state feedback controllers are constructed to guarantee the [Formula: see text] norm-based finite-time stable and bounded of the closed-loop singular distributed parameter systems. Finally, numerical simulations on a specific numerical example and the building temperature control system equipped with air conditioning are given to demonstrate the validity of the proposed methods.

In this letter, we investigate the finite-time output feedback control problem for continuous-time Markov jump linear systems. In this context, the first result is a sufficient condition for stochastic finite-time stability, requiring the solution of a feasibility problem constrained by differential linear matrix inequalities. Afterward, we consider the stabilization problem via output feedback dynamical controllers. The usual machinery pursued in the deterministic case would lead to stabilization conditions depending on differential bilinear matrix inequalities, that cannot be solved in practice. Therefore, a different methodology, based on the separation approach provided by Amato et al. , is exploited to design an observer-based output feedback controller, which can be computed by solving an optimization problem depending on linear constraints. A non-trivial application example, involving the finite-time stabilization of the longitudinal dynamics of a helicopter, is presented in order to illustrate the effectiveness of the proposed technique.

Differential Linear Matrix Inequalities in Optimal and Robust Sampled-Data Filtering

This paper investigates the sliding mode control (SMC) design for fractional stochastic systems. We study a very general category of stochastic systems that are nonlinear and driven by fractional Brownian motion (fBm). A robust SMC scheme is presented for a fractional stochastic model with external disturbance, state‐ and disturbance‐dependent noise, and uncertainties, which ensures that the closed‐loop system is stochastically stable. We propose a novel sliding surface and then prove its reachability in the state space. Furthermore, the conditions for the stochastic stability of the sliding motion are derived via nonlinear Hamilton–Jacobi (HJ)‐type inequalities. In addition, an SMC method is developed for a special class of fractional stochastic models, and two sets of linear matrix inequality (LMI) conditions are obtained, which are sufficient for stochastic stability. Eventually, the validity of the results is validated via a simulation example.

State and Unknown Inputs Finite Time Estimation for Time-Varying Nonlinear Lipschitz Systems with Uncertain Disturbances

This technical note addresses robust stability of uncertain systems with rational dependence on unknown time-varying parameters constrained in a polytope. First, the technical note proves that a sufficient linear matrix inequality (LMI) condition that we previously proposed, based on homogeneous polynomial Lyapunov functions (HPLFs) and on the introduction of an extended version of Polya's theorem, is also necessary. Second, the technical note proposes a new sufficient and necessary LMI condition by exploiting properties of the simplex and sum-of-squares (SOS) parameter-dependent polynomials. Lastly, the technical note investigates relationships among these conditions and conditions based on the linear fractional representation (LFR). It is worth remarking that sufficient and necessary LMI conditions for this problem have not been proposed yet in the literature.

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality (LMI) conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with γ-disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the paper.

SummaryThis article addresses a novel technique for the simultaneous design of a robust nonlinear controller and static anti‐windup compensator (AWC) for uncertain nonlinear systems under actuator saturation and exogenous bounded input. The system is presumed to have locally Lipschitz nonlinearities, time‐varying uncertainties (appearing both in the linear as well as nonlinear dynamics and both in the state in addition to the output equations), and external norm‐bounded inputs both in the state and the output equations. Several bilinear matrix inequality–based conditions are derived to simultaneously design the robust nonlinear controller and AWC gains for uncertain nonlinear systems by employing the Lyapunov functional, reformulated Lipschitz property, uncertainty bounds, linear parameter‐varying approach, modified local and global sector conditions, iterative linear matrix inequality algorithm, convex optimization procedure, and gain minimization. The proposed multiobjective AWC‐based dynamic robust nonlinear controller guarantees the mitigation of saturation effects, robustness against time‐varying parametric norm‐bounded uncertainties, the asymptotic stability of the closed‐loop nonlinear system under zero external disturbances, and the attenuation of disturbance effects under nonzero external disturbances. The effectiveness of the proposed AWC‐based dynamic robust nonlinear controller synthesis scheme is illustrated by simulation examples.

Sampled-data control of Lur’e systems

This paper presents a funnel synthesis algorithm for computing controlled invariant sets and feedback control gains around a given nominal trajectory for dynamical systems with locally Lipschitz nonlinearities and bounded disturbances. The resulting funnel synthesis problem involves a differential linear matrix inequality (DLMI) whose solution satisfies a Lyapunov condition that implies invariance and attractivity properties. Due to these properties, the proposed method can balance maximization of initial invariant funnel size, i.e., size of the funnel entry, and minimization of the size of the attractive funnel for attenuating the effect of disturbance. To solve the resulting funnel synthesis problem with the DLMI as constraints, we employ a numerical optimal control approach that uses a multiple shooting method to convert the problem into a finite dimensional semidefinite programming problem. This framework does not require piecewise linear system matrices and funnel parameters, which is typically assumed in recent related work. We illustrate the proposed funnel synthesis method with a numerical example.

PI based indirect-type iterative learning control for batch processes with time-varying uncertainties: A 2D FM model based approach

Robust delay-dependent guaranteed cost controller design for uncertain neutral systems

In this article we provide a solution to the mixed H 2 /H ∞ problem with reduced order controllers for time-varying systems in terms of the solvability of differential linear matrix inequalities and rank conditions, including a detailed discussion of how to construct a controller. Immediate specializations lead to a solution of the full order problem and the mixed H 2 /H ∞ problem for linear systems whose description depends on unknown but in real-time measurable time-varying parameters. As done in the literature for the H ∞ problem, we resolve the quadratic mixed H 2 /H ∞ problem by reducing it to the solution of a finite number of algebraic linear matrix inequalities. Moreover, we point out directions how to overcome the conservatism caused by assuming a particular parameter dependence or by using constant solutions of the differential matrix inequalities. For linear time-invariant systems, we reveal how to incorporate robust asymptotic tracking or disturbance rejection as an objective in the mixed H 2 /H ∞ problem. Finally, we address the specializations to the fully general pure H ∞ or generalized H 2 problem, and provide quadratically convergent algorithms to compute optimal values. Our techniques do not only lead to insights into the structure of the solution sets of the corresponding linear matrix inequalities, but they also allow to explicitly describe the influence of various system zeros on the optimal values.

In this paper, the decentralized robust output-feedback tracking control problem is investigated for a class of uncertain nonlinear interconnected systems subject to high order time varying disturbances. Firstly, generalized-proportional-integral observers (GPIOs) are designed for every subsystems such that the disturbances and unmeasured states can be recovered. Then, based on the estimation information of GPIOs and the output-feedback domination approach, a composite decentralized output-feedback controller is constructed. The proposed decentralized control scheme can not only handle the uncertain nonlinear interconnected terms, but also remove the influences the disturbances effectively via feedforward compensation manner. Finally, a practical example is conducted to demonstrate the effectiveness of the proposed control approach.