Robust State Feedback Controller Research Articles

Formula omitted]-like control for nonlinear stochastic systems

In this paper we develop a H ∞ -type theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we introduce the notion of stochastic dissipative systems analogously to the familiar notion of dissipation associated with deterministic systems and utilize it as a basis for the development of our theory. Having discussed certain properties of stochastic dissipative systems, we consider time-varying nonlinear systems for which we establish a connection between what is called the L 2 -gain property and the solution to a certain Hamilton–Jacobi inequality (HJI), that may be viewed as a bounded real lemma for stochastic nonlinear systems. The time-invariant case with infinite horizon is also considered, where for this case we synthesize a worst case-based stabilizing controller. Stability in this case is taken to be in the mean-square sense. In the stationary case, the problem of robust state feedback control is considered in the case of norm-bounded uncertainties. A solution is then derived in terms of linear matrix inequalities.

Decentralized Adaptive Robust State Feedback for Uncertain Large-Scale Interconnected Systems with Time Delays

The problem of the decentralized robust control is considered for a class of large-scale time-varying systems withdelayed state perturbations and external disturbances in the interconnections. Here, the upper bounds of the delayed stateperturbations and external disturbances in the interconnections are assumed to be unknown. Adaptation laws areproposed to estimate such unknown bounds; by making use of the updated values of the unknown bounds, decentralized linear and nonlinear memoryless robust state feedback controllers are constructed. Based on Lyapunov stability theoryand Lyapunov–Krasovskii functionals, as well as employing the proposed decentralized nonlinear robust state feedback controllers, it is shown that the solutions of the resulting adaptive closed-loop large-scale time-delay system can be guaranteed to be uniformly bounded and that the states converge uniformly and asymptotically to zero. It is also shown that the proposed decentralized linear robust state feedback controllers can guarantee the uniform ultimate boundedness of the resulting adaptive closed-loop large-scale time-delay system. Finally, a numerical example is given to demonstrate the validity of the results.

H-infinity control for networked control systems (NCS) with time-varying delays

This paper discusses H-infinity state feedback control for a networked control system with time-varying delays. Based on the free-weighing matrix method, a delay-dependent stability criterion satisfying a prescribed H-infinity norm bound is presented for an NCS with unknown, time-varying and bounded delays. And then, the criterion is transformed into sufficient conditions based on linear matrix inequalities for H-infinity control. The conditions thus obtained are also used to design an H-infinity state feedback controller. This design method is further extended to solve the design problem of robust H-infinity state feedback control. A numerical example demonstrates the validity of die method.

On robust stabilization of Markovian jump systems with uncertain switching probabilities

This brief paper is concerned with the robust stabilization problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertain Markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix. First, a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities. Then, a sufficient condition is proposed for the design of robust state-feedback controllers. A globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively. Finally, a numerical simulation is used to illustrate the developed theory.

A ROBUST VERSION OF THE ELIMINATION LEMMA

In this paper we extend the elimination lemma to hold for a set of inequalities. The elimination lemma is a linear algebra result which has been successfully used to solve a large number of filtering and control problems. We show that the obtained extension can be used to provide alternative solutions to robust state feedback control and robust filtering problems when the uncertainty is described by a convex polytope. We also investigate some conjectures which, if true, would be able to solve an open problem in dynamic output feedback robust control. We provide counter-examples to these conjectures.

ROBUST POLE ASSIGNMENT BY STATE FEEDBACK CONTROL USING INTERVAL ANALYSIS

An interval analysis approach for the design of robust state feedback controllers is proposed. It is shown that when regional pole placement specifications are represented as spectral sets of interval polynomials, the robust state feedback design problem can be entirely formulated and solved in the context of the concepts and methods of interval analysis. Explicit convex polyhedral representations of a class of robust state feedback controllers satisfying an interval Ackerman's equation are derived. A design procedure based on nonlinear programming which aims at maximizing the non-fragility of the resulting robust controller is introduced. Numerical examples illustrate the design of robust state feedback controllers through the interval analysis approach proposed.

ROBUST H∞ CONTROL OF MARKOVIAN JUMP LINEAR SYSTEMS WITH UNCERTAIN SWITCHING PROBABILITIES

This paper is concerned with the robust H∞ control of Markovian jump linear systems with uncertain switching probabilities. The uncertain system under consideration involves norm-bounded uncertainties in system matrices and element-wise bounded uncertainties in the mode transition rate matrix. A new criterion is established to test the robust H∞ performance in terms of linear matrix inequalities and a sufficient condition is addressed for constructing a robust state-feedback controller such that the closed-loop system is robustly mean square stable and has the desired H∞ performance level. A globally convergent algorithm involving convex optimization is also proposed to find such controllers effectively. Finally a numerical example illustrates the usefulness of the developed theory.

Nonlinear control for a class of hydraulic servo system

The dynamics of hydraulic systems are highly nonlinear and the system may be subjected to non-smooth and discontinuous nonlinearities due to directional change of valve opening, friction, etc. Aside from the nonlinear nature of hydraulic dynamics, hydraulic servo systems also have large extent of model uncertainties. To address these challenging issues, a robust state-feedback controller is designed by employing backstepping design technique such that the system output tracks a given signal arbitrarily well, and all signals in the closed-loop system remain bounded. Moreover, a relevant disturbance attenuation inequality is satisfied by the closed-loop signals. Compared with previously proposed robust controllers, this paper's robust controller based on backstepping recursive design method is easier to design, and is more suitable for implementation.

Robust model predictive control with guaranteed setpoint tracking

In this paper a novel robust model predictive control (RMPC) algorithm is proposed, which is guaranteed to stabilize any linear time-varying system in a given convex uncertainty region while respecting state and input constraints. Moreover, unlike most existing RMPC algorithms, the proposed algorithm is guaranteed to remove steady-state offset in the controlled variables for setpoints (possibly) different from the origin when the system is unknown linear time-invariant. The controller uses a dual-mode paradigm (linear control law plus free control moves to reach an appropriate invariant region), and the key step is the design of a robust linear state feedback controller with integral action and the construction of an appropriate polyhedral invariant region in which this controller is guaranteed to satisfy the process constraints. The proposed algorithm is efficient since the on-line implementation only requires one to solve a convex quadratic program with a number of decision variables that scale linearly with the control horizon. The main features of the new control algorithm are illustrated through an example of the temperature control of an open-loop unstable continuous stirred tank reactor.

Robust Stabilization of Delayed Singular Systems with Linear Fractional Parametric Uncertainties

This paper deals with the problem of robust stabilization for delayed singular systems with parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form involving all system matrices. Necessary and sufficient conditions for quadratic stability and quadratic stabilization are obtained. Moreover, the results generalize and improve previous works on delayed singular systems with norm-bounded parametric uncertainties. A strict linear matrix inequality (LMI) design approach is developed such that, when the LMI is satisfied, a desired robust state feedback control law can be constructed. A numerical example is provided to demonstrate the application of the proposed method.

Non-fragile H∞ vibration control for uncertain structural systems

The paper deals with the robust non-fragile H ∞ control problem for uncertain structural systems with additive controller gain variations. The parameter uncertainties for the mass, damping and stiffness of the structural systems are unknown but norm bounded. Based on the H ∞ control theory and a linear matrix inequality formulation, a new method for designing a robust state-feedback control law is presented. The objective is to reduce the disturbance on the controlled output to a prescribed level for all admissible parametric uncertainties and controller gain variations. A four-degree-of-freedom building model subject to seismic excitation is used to illustrate the effectiveness of the approach through simulation.

Robust State Feedback Control Through Actuators With Generalized Sector Nonlinearities And Saturation

ABSTRACTIn control systems, actuators often have nonlinear characteristics that can not be neglected. For linear systems driven by actuators satisfying the generalized sector condition, a robust state feedback controller synthesis method is proposed to achieve the ultimate boundedness control. The method is based on the linear matrix inequality approach and is easy to apply. As an important special case of the generalized sector condition, the saturation characteristic of actuators is discussed separately, and non‐conservative results are obtained.

An ellipsoid algorithm for probabilistic robust controller design

In this paper, a new iterative approach to probabilistic robust controller design is presented, which is applicable to any robust controller/filter design problem that can be represented as an LMI feasibility problem. Recently, a probabilistic Subgradient Iteration algorithm was proposed for solving LMIs. It transforms the initial feasibility problem to an equivalent convex optimization problem, which is subsequently solved by means of an iterative algorithm. While this algorithm always converges to a feasible solution in a finite number of iterations, it requires that the radius of a non-empty ball contained into the solution set is known a priori. This rather restrictive assumption is released in this paper, while retaining the convergence property. Given an initial ellipsoid that contains the solution set, the approach proposed here iteratively generates a sequence of ellipsoids with decreasing volumes, all containing the solution set. At each iteration a random uncertainty sample is generated with a specified probability density, which parameterizes an LMI. For this LMI the next minimum-volume ellipsoid that contains the solution set is computed. An upper bound on the maximum number of possible correction steps, that can be performed by the algorithm before finding a feasible solution, is derived. A method for finding an initial ellipsoid containing the solution set, which is necessary for initialization of the optimization, is also given. The proposed approach is illustrated on a real-life diesel actuator benchmark model with real parametric uncertainty, for which a H 2 robust state-feedback controller is designed.

Bounded robust control of constrained multivariable nonlinear processes

This work focuses on control of multi-input multi-output (MIMO) nonlinear processes with uncertain dynamics and actuator constraints. A Lyapunov-based nonlinear controller design approach that accounts explicitly and simultaneously for process nonlinearities, plant-model mismatch, and input constraints, is proposed. Under the assumption that all process states are accessible for measurement, the approach leads to the explicit synthesis of bounded robust multivariable nonlinear state feedback controllers with well-characterized stability and performance properties. The controllers enforce stability and robust asymptotic reference-input tracking in the constrained uncertain closed-loop system and provide, at the same time, an explicit characterization of the region of guaranteed closed-loop stability. When full state measurements are not available, a combination of the state feedback controllers with high-gain state observes and appropriate saturation filters, is employed to synthesize bounded robust multivariable output feedback controllers that require only measurements of the outputs for practical implementation. The resulting output feedback design is shown to inherit the same closed-loop stability and performance properties of the state feedback controllers and, in addition, recover the closed-loop stability region obtained under state feedback, provided that the observer gain is sufficiently large. The developed state and output feedback controllers are applied successfully to non-isothermal chemical reactor examples with uncertainty, input constraints, and incomplete state measurements. Finally, we conclude the paper with a discussion that attempts to put in perspective the proposed Lyapunov-based control approach with respect to the nonlinear model predictive control (MPC) approach and discuss the implications of our results for the practical implementation of MPC, in control of uncertain nonlinear processes with input constraints.

Comments on "Robust stabilization of a class of time-delay nonlinear systems"

The purpose of the above paper by Nguang (ibid. vol.45 (2000)) is to construct a robust memoryless state feedback controller for a class of uncertain time-delay systems with lower triangular structure, namely, strict feedback structure. However, there are some mistakes in the paper. The purpose of this note is to point out the mistakes and propose some suggestions to correct the mistakes. For simplicity, all the symbols in this note are the same as those in original paper.

Robust active control for uncertain structural systems with acceleration sensors

AbstractNatural hazards such as earthquakes and strong wind events place large forces on tall, slender structures and on long‐span bridges that inherit numerous uncertainties due to model errors, stress calculations, material properties, and load environments. Thus, a robust feedback control for structural systems is needed. This paper develops a robust active control approach for uncertain structural systems with acceleration sensors and white noise. The approach is based on a robust state feedback control, with the robust α‐degree relative stability, robust H∞ δ‐degree disturbance rejection and robust H2 optimality, and a modified Kalman filter, with α0‐degree relative' stability. The uncertainties considered include structural ones in the system and control input matrices and multiplicative nonstructural ones in the disturbance input matrices. Special singular value decomposition (SVD) is applied to structured uncertain structures. Numerical simulations excited by the 1940 El Centro, California, earthquake data have been carried out for the proposed different robust controllers and LQG for comparison. The resulting approach to robust control may be applied to analysis and design of practical structural systems. Copyright © 2003 John Wiley & Sons, Ltd.

Robust H ∞ control for descriptor systems with non-linear uncertainties

This paper considers robust performance analysis and robust H X control for a class of descriptor systems with time-varying and non-linear uncertainties. These uncertainties exist not only in the state, the control input and exogenous input, but also in the derivative of the state. A sufficient condition is firstly proposed to analyse the robust H X performance problem of the unforced systems. Feasible design procedures are presented to construct both the robust state feedback and output feedback controllers such that the closed-loop system has a unique, non-impulsive and asymptotically stable solution and satisfies a robust H X performance criterion. A numerical example is provided to show the efficiency of the approach.

Genetic fuzzy control for time-varying delayed uncertain systems with a robust stability safeguard

This paper proposes a new delay-independent stability criterion for uncertain systems with state time-varying delay. Then, a robust state feedback control law based on it is constructed via sequential quadratic programming method to stabilize uncertain systems. Add a proposed FLC with a small number of rules and membership functions to the above-mentioned robust state feedback control law such that not only closed-loop uncertain systems with time-varying delay are robust stable but also output performance approaches desired one. An example given illustrates the availability of the proposed design method.

Robust stability and stabilization for singular systems with state delay and parameter uncertainty

Considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties, while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. Finally, a numerical example is provided to demonstrate the application of the proposed method.

On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters

In this paper, we investigate the stochastic stabilization problem for a class of bilinear continuous time-delay uncertain systems with Markovian jumping parameters. Specifically, the stochastic bilinear jump system under study involves unknown state time-delay, parameter uncertainties, and unknown nonlinear deterministic disturbances. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process. The whole system may be regarded as a stochastic bilinear hybrid system that includes both time-evolving and event-driven mechanisms. Our attention is focused on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are established to guarantee the existence of desired robust controllers, which are given in terms of the solutions to a set of either linear matrix inequalities (LMIs), or coupled quadratic matrix inequalities. The developed theory is illustrated by numerical simulation.