Robust State Feedback Controller Research Articles

Neural networks-based adaptive robust controllers and its applications to water pollution control systems

The problem of robust stabilisation of uncertain dynamical systems with non-linear state perturbations is considered. In this paper, the neural networks (NNs) is used to approximate the unknown system dynamics to be a special form, and an adaptation law is employed to estimate the norm of the NNs weight and approximation error. By making use of the updated values of the norm of weight and approximation error, an adaptive robust state feedback control scheme is proposed for such a class of uncertain non-linear systems. It is also shown that by employing the proposed adaptive robust controllers, the state trajectories of uncertain non-linear systems can be guaranteed to be uniformly ultimately bounded. Finally, to demonstrate the validity of the result, we apply it to solve a practical problem of water pollution.

Robust Autopilot Design for Bank-to-Turn Missiles using Disturbance Observers

A decoupling control strategy consisting of robust feedback and feedforward compensation based on disturbance-observers is proposed for bank-to-turn (BTT) missile autopilot. For each of the three channels, the lumped disturbances, which consist of nonlinear couplings and external disturbances, are estimated by a disturbance observer and then feedforward compensated. Three distributed robust state feedback controllers are designed to stabilize the rest linear parts of three channels, respectively. Simulation studies demonstrate the effectiveness of the proposed method.

Robust feedback design for combined therapy of cancer

SUMMARYIn this paper, a mathematical model for the scheduling of angiogenic inhibitors with a killing agent is used to derive a robust state feedback control for the combined therapy of cancer. Robustness is considered against parameter uncertainties through the solution of the associated Hamilton–Jacobi–Isaacs (HJI) partial differential equation. Unlike open‐loop optimal control paradigm, solving the HJI equation provides a guaranteed‐cost feedback control and a whole visibility of the achievable performance for any possible initial state within the region of interest and for any predefined level of parameter uncertainties. Numerical investigation is proposed using an existing model that has been partially validated using human data. Copyright © 2012 John Wiley & Sons, Ltd.

Stability and robust stabilisation for a class of non-linear uncertain discrete-time descriptor Markov jump systems

The stability and robust state feedback stabilisation problems for a class of non-linear discrete-time descriptor Markov jump systems with parameter uncertainties are investigated. The non-linear function satisfies a quadratic constraint. First, based on Lyapunov theory and the implicit function theorem, a linear matrix inequality (LMI) sufficient condition is developed, which guarantees that the non-linear discrete-time descriptor Markov jump systems are regular, causal, and have unique solution in a neighbourhood of the origin, and are stochastically stable. With this condition, another LMI condition is developed based on the singular value decomposition approach, which guarantees that the systems are regular, causal, have unique solution in a neighbourhood of the origin, and are stochastically stable. Then, the design method of robust state feedback controllers is given. Last, numerical examples are provided to illustrate the effectiveness of the proposed methods.

Decentralised adaptive robust control of uncertain large-scale interconnected systems with multiple time-varying delays

The problem of decentralised adaptive robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. It is assumed that the upper bounds of the uncertainties, interconnection terms and external disturbances are unknown, and that the time-varying delays are any nonnegative continuous and bounded functions, and do not require that their derivatives have to be less than one. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of continuous memoryless decentralised local adaptive robust state feedback controllers is proposed. It is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. In addition, since the proposed decentralised local adaptive robust state feedback controllers are completely independent of time delays, the results obtained in this article may also be applicable to a class of large-scale interconnected dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results.

Robust ℋ2 control applied to boost converters: design, experimental validation and performance analysis

This study proposes a design procedure and experimental validation for a robust ℋ2 state feedback controller applied to a DC–DC boost converter modelled as a linear system affected by time-varying parameters lying in known intervals. The parameters considered as time-varying are the input voltage, the load resistance and the operating point duty cycle. A polytopic representation of the system is derived and the controller is designed by means of a convex optimisation problem based on linear matrix inequalities. The conventional ℋ2 controller is extended to cope with alpha-stability and robust linear quadratic regulator design, providing different strategies to trade-off the magnitude of the control gains and the response of the closed-loop system. Tight correspondences between numerical simulations and the experimental results prove the viability of the application of this technique for this kind of plant. Finally, a robust performance analysis illustrates the capacity of the closed-loop system to reject energy bounded disturbances, with interpretation for the cases of time-varying and time-invariant parameters.

Non-fragile robust H ∞ control for uncertain spacecraft rendezvous system with pole and input constraints

This article investigates the robust H ∞ control problem for a class of spacecraft rendezvous systems with parameter uncertainties and subject to input constraint, pole constraint and external and controller perturbations. Based on the Lyapunov theory, a sufficient condition for the existence of the non-fragile robust state-feedback controller is given in terms of linear matrix inequalities (LMIs). Then, proper non-fragile controller design can be cast as a convex optimisation problem subject to LMI constraints. With the obtained controller, the spacecraft rendezvous mission can be accomplished. An illustrative example is provided to show the effectiveness of the proposed control design method.

Stochastic stability and robust stabilization of semi‐Markov jump linear systems

SUMMARYThe semi‐Markov jump linear system (S‐MJLS) is more general than the Markov jump linear system (MJLS) in modeling some practical systems. Unlike the constant transition rates in the MJLS, the transition rates of the S‐MJLS are time varying. This paper focuses on the robust stochastic stability condition and the robust control design problem for the S‐MJLS with norm‐bounded uncertainties. The infinitesimal generator for the constructed Lyapunov function is first derived. Numerically solvable sufficient conditions for the stochastic stability of S‐MJLSs are then established in terms of linear matrix inequalities. To reduce the conservativeness of the stability conditions, we propose to incorporate the upper and lower bounds of the transition rate and meanwhile apply a new partition scheme. The robust state feedback controller is accordingly developed. Simulation studies and comparisons demonstrate the effectiveness and advantages of the proposed methods. Copyright © 2012 John Wiley & Sons, Ltd.

Robust sampled-data stabilization of uncertain fuzzy systems via input delay approach

This paper is concerned with robust sampled-data stabilization for uncertain fuzzy systems. The system is modeled as a continuous-time fuzzy system, while the control input is a zero-order sampled-data signal. When a zero-order control input is considered, the closed-loop system can be seen as an input delay system. Hence, an input delay system approach is introduced for sampled-data control design. Sufficient stability conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Under the assumption that sampling interval is not greater than some prescribed number, stability conditions for fuzzy time-delay systems are given by using Jensen’s Inequality, which simplifies conditions with less matrix variables. A design method of robust sampled-data state feedback controller for uncertain fuzzy systems is then proposed. Numerical examples are given to illustrate our robust sampled-data state feedback control design and to show the effectiveness over other existing results.

Robust Stability and Stabilization of Deterministic Networked Control Systems

Feedback control systems wherein the control loops are closed through a real-time network are called networked control systems. Under some special conditions proposed in literature, the networked control systems with stochastic time delay can be transformed a deterministic system with a constant delay. Based on linear time invariant discrete time process, the robust stability of deterministic networked control systems is analyzed and the designing method of robust state feedback controller for deterministic networked control systems is proposed in this paper for the first time. An example is given to verify the theory results of this paper.

Tube based Quasi-min-max Output Feedback MPC for LPV Systems

Output feedback model predictive control of polytopic linear parameter varying (LPV) systems subject to input constraints is considered in this paper. The proposed control scheme incorporates robust observer and robust state feedback control. To handle disturbances and model uncertainty, disturbance invariant tube and quasi-min-max MPC are combined to achieve recursive feasibility and robust stability. Simulation results are provided to verify the effectiveness of the proposed algorithm.

Decentralised adaptive robust control of uncertain large-scale non-linear dynamical systems with time-varying delays

The problem of decentralised adaptive robust stabilisation is considered for a class of uncertain large-scale interconnected non-linear systems with time-varying delays. It is assumed that the upper bounds of the uncertainties and interconnection terms are unknown, and that the time-varying delays are any non-negative continuous and bounded functions, and do not require their derivatives to be less than one. In particular, it is only required that the non-linear interconnection terms, which can also include time-varying delays, are bounded in any non-negative non-linear functions, which are not required to be known for the system designer. For such a class of uncertain large-scale time-delay interconnected non-linear systems, a new method is presented whereby a class of continuous memoryless decentralised local adaptive robust state feedback controllers with a rather simpler structure is proposed. It is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed as uniformly exponentially convergent towards a ball that can be as small as desired. Finally, a numerical example is given to demonstrate the validity of the results.

Robust sampled-data control of structures subject to parameter uncertainties and actuator saturation

This paper presents a robust sampled-data controller design approach for vibration attenuation of civil structures considering parameter uncertainties and actuator saturation. The parameter uncertainties belong to polytopic form and are assumed to be the variations of the structural stiffness and damping. Regarding the uncertain sampling problem encountered in real world applications, the sampling period designed for the controller is allowed to be variable within a given bound. In order to obtain reduced peak response quantities, the energy-to-peak performance used to describe the peak values of the control output under all possible energy-bounded disturbances is optimised. The robust sampled-data state feedback controller is obtained in terms of the solvability of certain linear matrix inequalities (LMIs). The applicability of the proposed approach is demonstrated by a numerical example on vibration control of a building structure subject to seismic excitation. It is validated by the simulation results confirming that the designed controllers can effectively attenuate the structural vibration and keep the system stability while there are parameter uncertainties and actuator saturation constraints.

Non-fragile guaranteed cost control for robust spacecraft orbit transfer with small thrust

This paper studies the robust orbit transfer problem for low earth orbit spacecraft rendezvous with parameter uncertainties and subject to input constraint and guaranteed cost control. The spacecraft rendezvous process can be divided into in-plane motion and out-of-plane motion because the Clohessy–Wiltshire equations can be decoupled. On this basis, the relative motion models with parameter uncertainties are established. By considering the null controllability with vanishing energy, the problem of orbital transfer control with small thrust and bounded control cost is proposed. Based on Lyapunov theory, a sufficient condition for the existence of the non-fragile robust state feedback controller is given in terms of linear matrix inequalities (LMIs). Then, proper non-fragile controller design can be cast as a convex optimization problem subject to LMI constraints. With the obtained controller, the orbit transfer process can be accomplished with small thrust, where the control cost has an upper bound. An illustrative example is provided to show the effectiveness of the proposed control design method.

LPV Modeling of Buck Converter and Gain Scheduling Control

A kind of gain scheduling control is designed for Buck converter. The small signal model of the Buck converter is translated into the Linear Parameter-Varying (LPV) dynamic equation with the load and the line voltage as the scheduled parameters. Based on it, the closed-loop system poles assignment is taken to the specific area with gain scheduled state feedback via linear matrix inequalities (LMIs) technique, the gain scheduled state feedback is designed to regulate the duty cycle of the switch conduction. Compared with robust state feedback control, it has better disturbance rejection performance.

Dilated LMI conditions for time-varying polytopic descriptor systems: the discrete-time case

This article addresses the admissibility analysis and state-feedback control synthesis problems of discrete-time polytopic descriptor systems with possibly time-varying parameters. First, we present a new necessary and sufficient strict linear matrix inequality (LMI) condition for the admissibility analysis of linear time-invariant (LTI) descriptor systems. Then, based on the concept of poly-quadratic admissibility, introduced in this article, we extend this result to the admissibility analysis of possibly time-varying parameter-dependent descriptor systems. This extension, which applies to both uncertain and measurable parameters, uses parameter-dependent Lyapunov functions and employs two slack variables. The extended conditions are also expressed as strict LMI conditions which are easily tractable numerically compared to the non-strict ones often encountered when dealing with descriptor systems. Note that we have proposed two separate admissibility analysis conditions: one directly exploitable for state estimation and the other for state-feedback control. The need for different admissibility analysis conditions for each synthesis problem is motivated by the fact that the duality between state estimation and state-feedback control, which hold in the case of measurable parameters, does not hold when dealing with uncertain ones. In our approach, we overcome the absence of such duality by considering a dilation only on the dynamical part of the descriptor system. The application of our analysis result to both robust state-feedback control and polytopic state-feedback control are also presented in this article. Our analysis results extend to descriptor systems, some existing results developed for regular systems.

Persistent bounded disturbance rejection for discrete-time delay systems

In this article, we provide a novel solution to the problem of persistent bounded disturbance rejection in linear discrete-time systems with time-varying delays. The solution is developed based on the tools of invariant set analysis and Lyapunov-function method. As an integral part of the solution, we derive less conservative sufficient conditions on robust attractor for discrete-time systems with delays in terms of strict linear matrix inequalities to guarantee the desired ℓ1-performance. A robust state-feedback controller is designed and the associated gain is determined using strict LMIs. The developed results are tested on a representative example.

State Feedback Guaranteed Cost Control of Parameter Uncertain Nonlinear System

In an actual system, the effects of nonlinear factors are inevitable. So in real practice, when a model for complex system is being built, all the features in it will be linearized. Though simplifying the designing and analyzing process, the model being built in this way is thought to be incapable of revealing the true characteristics of the system. In order to solve this problem, the paper analyzes a model combining both linear and nonlinear features while taking the parameter perturbation of the linear part into consideration, which enables the model to retain as many characteristics of the actual system as possible. Provided that the nonlinear function satisfies the Lipschitz constraint conditions, the robust guaranteed cost state feedback control law of nonlinear system is deduced using the Lyapunov function and then converted into the feasible solutions of linear matrix inequality (LMI). The proposed method optimizes the design of controller by modifying the previous oversimplified models that fail to reveal the real characteristics of the actual system, and the effectiveness of the proposed method is being verified through an algorithm simulation example.

Minimização do custo H∞ de sistemas incertos discretos no tempo com atraso nos estados

Neste trabalho são investigados sistemas lineares incertos e discretos no tempo com atraso variante no tempo afetando o vetor de estados. É considerado que as incertezas são representadas em um domínio politópico e que elas podem estar presentes em todas as matrizes do modelo do sistema. Condições expressas como Desigualdades Matriciais Lineares (LMIs, do inglês Linear Matrix Inequalities) são propostas para o cômputo do custo garantido H∞ e para a síntese de ganhos robustos de realimentação de estados que minimizam a norma H∞ entre a entrada de pertubação e a saída do sistema. Essas condições são estabelecidas com a utilização de funções de Lyapunov-Krasovskii (L-K) dependentes de parâmetro. Variáveis matriciais de folga - via Lema de Finsler - são empregadas para desacoplar as matrizes do sistema das matrizes da função de L-K. A "desigualdade de Jensen" é usada para manipular os termos cruzados que aparecem no desenvolvimento das condições, fornecendo uma majoração menos conservadora que outras encontradas na literatura. As condições propostas são dependentes do atraso. Exemplos numéricos são apresentados para ilustrar a eficácia da proposta e para estabelecer comparações com outras encontradas na literatura.

Robust stabilization for nonholonomic systems with state delay and nonlinear drifts

This paper presents a control strategy for stabilization of the nonholonomic control systems with strongly nonlinear drifts and state delay. Applying a novel Lyapunov functional and backstepping recursive method, the design of robust nonlinear state feedback controllers is proposed, which can guarantee the stability of the closed-loop systems. Finally, a numerical example is provided to show the effectiveness of the method.