Delay-dependent Guaranteed Cost Research Articles

Multiple Delay-Dependent Guaranteed Cost Control for Distributed Engine Control Systems with Aging and Deterioration

Distributed control architecture can bring many benefits to the engine control system, but the delay and packet dropout introduced by network communication will bring negative effects to the control system. The aging and deterioration of the engine are also obstacles in the design of the engine control system. This paper is concerned with the problem of guaranteed cost control for a distributed engine control system (DECS) with these negative constraints. Firstly, a model of DECS with multiple delays, packet dropouts and uncertainties is built. Secondly, a multiple delay-dependent guaranteed cost controller design method is proposed in the form of a set of linear matrix inequalities (LMIs). The non-convex optimal controller design problem is transformed into a convex optimization problem through the cone complementarity linearization (CCL) method, and the suboptimal controller is designed iteratively. Thirdly, turboshaft engine aging and deterioration are treated as sources of uncertainties, and the norm-bounded uncertain model of the turboshaft engine is modeled. Finally, the numerical simulations demonstrate the effectiveness and applicability of the guaranteed cost controller designed for DECS with multiple delays, packet dropouts, engine aging and deteriorations.

A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach

This paper deals with the new formulated problem of designing a robust delay-dependent guaranteed optimal cost proportional-integral-derivative (PID) multivariable output feedback controller for linear uncertain time delay systems with nonlinear parameter perturbations using a linear matrix inequalities (LMI) approach. Several less conservative delay-dependent stability conditions are formulated for the time-delay system under consideration in terms of LMIs. Based on an augmented form of Lyapunov-Krasovskii functionals, the free weighting matrices and Wirtinger inequality techniques are employed to obtain improved performance. An optimal guaranteed cost PID controller which minimizes the upper bound of cost function is provided. The main advantage of the proposed approach is to decouple the input and the output gain matrices allowing to synthesize the controller gain matrices through a strict LMI technique. The synthesis conditions are thus formulated in LMI form which avoids the use of any iterative approach to resolve the feasibility problem. Two numerical examples selected from the literature are presented to illustrate the effectiveness of the developed methodology. The numerical results indicate that the proposed method performs efficiently in comparison to the approaches from the existing literature.

Multiple delay-dependent guaranteed cost control for uncertain switched random nonlinear systems against intermittent sensor and actuator faults

In this paper, guaranteed cost control is investigated for switched random nonlinear systems against multiple state delays, model uncertainties, intermittent sensor and actuator faults. Other factors containing nonlinear dynamics, external disturbances as well as measurement noise are also considered. This is the first try to realize guaranteed cost control for uncertain switched random nonlinear systems against multiple time delays. In practice, color noise is more common than white noise in some specific situations. Thus, this paper considers random systems with color noise. In contrast to the previous study works, the suggested system can be applied to a wider range. First, a dynamic full-order output feedback controller is established to make the system stable. And an entire closed-loop system is got to achieve guaranteed cost control. Then, the multiple delay-dependent sufficient conditions are acquired through the piecewise Lyapunov function in the framework of linear matrix inequalities (LMIs). In the meantime, controller gain matrices are obtained. At last, two simulation examples are presented to verify the availability of the suggested approach.

Multiple delay-dependent H ∞ guaranteed cost control for uncertain semi-Markovian jump random nonlinear systems with intermittent actuator and sensor faults and input constraint

In this study, multiple delay-dependent guaranteed cost control is first investigated for uncertain semi-Markovian jump random nonlinear systems with intermittent actuator and sensor faults and input constraint. First, a semi-Markovian jump dynamic output feedback controller is first designed for this model. Multiple delay-dependent noise-to-state stochastic stability conditions are acquired by involving slack matrices by means of bounded real lemma (BRL) as well as linear matrix inequalities (LMIs), leading to the less conservatism. control and guaranteed cost control are achieved simultaneously. Finally, the effectiveness and novelty of the approach are demonstrated through three examples.

Delay-Dependent Non-Fragile Robust Guaranteed Cost Control for Switched Systems with Multiple Time Delays

The non-fragile guaranteed cost control is discussed for the polytopically uncertain switched discrete time systems with multi-delays in states and inputs. Based on the piecewise quadratic Lyapunov functions, the synthesis approach of the delay-dependent non-fragile guaranteed cost controllers is proposed. By the obtained control law, the perturbed switched discrete time systems can be asymptotically stabilized and the close loop cost is not greater than a specified upper limit for all admissible uncertainties. The numerical example is given to illustrate the validity of the presented controller design method.

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

In this paper, a novel robust delay-dependent guaranteed cost controller is introduced for a class of uncertain nonlinear neutral systems with both norm-bounded uncertainties and nonlinear parameter perturbations. A neutral memory state-feedback control law is chosen such that a quadratic cost function is minimized. On the basis of a descriptor type model transformation, an augmented descriptor form Lyapunov–Krasovskii functional is proposed in order to derive a linear matrix inequality (LMI) condition of the synthesis of a robust stabilizing guaranteed cost controller for uncertain nonlinear neutral systems. The descriptor approach is applied for both the delay-differential equation and the neutral difference operator allowing to introduce several additional free weighting matrices in order to obtain further relaxation in the synthesis process. The proposed method of introducing some relaxation into design problem also leads to develop LMI conditions which can be easily solved using interior point algorithms. Two numerical examples have been introduced to show the application of the theoretical results which indicate that the proposed approach improves the guaranteed cost performance.

Delay-dependent guaranteed cost control for state-delayed system with disturbance and its application to engine idle speed control

This paper proposes a delay-dependent guaranteed cost control scheme for engine idle speed control (ISC) with induction-to-torque delay and external load disturbance. An augmented linearization model of engine at idle speed operating mode was developed based on physical principle and experiment data. To provide a compromise between disturbance rejection and other performance requirements of ISC, a multi-objective cost function upper bound was given, which can help us to take into account the fuel economy and disturbance rejection performance together in ISC. Poles constraint was added to the closed-loop system to guarantee convergence rates of state. The whole optimization solution to ISC can be solved under the framework of LMI. A commercial engine model was utilized to assess the performance of the controller. Simulation results on this model show us that designed controller can achieve desired performance.

Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays

This paper considers the design problems of a delay-dependent robust and non-fragile guaranteed cost controller for singular systems with parameter uncertainties and time-varying delays in state and control input. The designed controller, under the possibility of feedback gain variations, can guarantee that a closed-loop system is regular, impulse-free, stable, an upper bound of guaranteed cost function, and non-fragility in spite of parameter uncertainties, time-varying delays, and controller fragility. The existence condition of the controller, the controller’s design method, the upper bound of guaranteed cost function, and the measure of non-fragility in the controller are proposed using the linear matrix inequality (LMI) technique. Finally, numerical examples are given to illustrate the effectiveness and less conservatism of the proposed design method.

Robust delay‐dependent guaranteed cost controller design for uncertain nonlinear neutral systems with time‐varying state delays

AbstractIn this paper, the problem of robust delay‐dependent guaranteed cost control for uncertain nonlinear neutral systems with time‐varying state delay is investigated. The control law is chosen to be a memoryless type one. Neither any model transformation nor bounding of any cross terms are utilized. The system under consideration may be subjected to both norm‐bounded uncertainties and nonlinear parameter perturbations. A delay‐dependent sufficient condition is obtained in terms of a matrix inequality for which a cone complementarity problem is introduced to provide a feasible solution set. Two numerical examples have been demonstrated to show the effective application of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.

Delay-Dependent Guaranteed Cost Control of an Interval System with Interval Time-Varying Delay

This paper concerns the problem of the delay-dependent robust stability and guaranteed cost control for an interval system with time-varying delay. The interval system with matrix factorization is provided and leads to less conservative conclusions than solving a square root. The time-varying delay is assumed to belong to an interval and the derivative of the interval time-varying delay is not a restriction, which allows a fast time-varying delay; also its applicability is broad. Based on the Lyapunov-Ktasovskii approach, a delay-dependent criterion for the existence of a state feedback controller, which guarantees the closed-loop system stability, the upper bound of cost function, and disturbance attenuation lever for all admissible uncertainties as well as out perturbation, is proposed in terms of linear matrix inequalities (LMIs). The criterion is derived by free weighting matrices that can reduce the conservatism. The effectiveness has been verified in a number example and the compute results are presented to validate the proposed design method.

Delay-dependent guaranteed cost control for uncertain 2-D discrete systems with state delay in the FM second model

This paper is concerned with the problem of delay-dependent guaranteed cost control for uncertain two-dimensional (2-D) state delay systems described by the Fornasini and Marchesini (FM) second state-space model. Given a scalar α∈(0,1), a sufficient condition for the existence of delay-dependent guaranteed cost controllers is given in terms of a linear matrix inequality (LMI) based on a summation inequality for 2-D discrete systems. A convex optimization problem is proposed to design a state feedback controller stabilizing the 2-D state delay system as well as achieving the least guaranteed cost for the resulting closed-loop system. Finally, the simulation example of thermal processes is given to illustrate the effectiveness of the proposed result.

Delay-Dependent Guaranteed Cost Control for Uncertain Stochastic Fuzzy Systems With Multiple Time Delays

This paper studies the guaranteed cost control problem for a class of uncertain stochastic nonlinear systems with multiple time delays represented by the Takagi-Sugeno fuzzy model with uncertain parameters. By constructing a new stochastic Lyapunov-Krasovskii functional, sufficient conditions for delay-dependent guaranteed cost control are obtained which do not require system transformation or relaxation matrices. Conditions for the existence of an optimal guaranteed cost controller are presented in the linear matrix inequality format. Simulation examples are provided to demonstrate the effectiveness of the proposed approach in this paper.

DESIGN OF ROBUST DELAY-DEPENDENT GUARANTEED COST CONTROLLER FOR UNCERTAIN NONLINEAR NEUTRAL SYSTEMS: AN LMI DESCRIPTOR APPROACH

Abstract In this paper, a novel robust delay-dependent guaranteed cost controller is introduced for a class of uncertain nonlinear neutral systems with both norm-bounded uncertainties and nonlinear parameter perturbations. A neutral memory state-feedback control law is chosen such that a quadratic cost function is minimized. On the basis of a descriptor type model transformation, an augmented descriptor form Lyapunov-Krasovskii functional is proposed. A linear matrix inequality (LMI) of synthesis condition is derived. Two numerical examples have been introduced to show the application of the theoretical results.

Delay-dependent guaranteed cost control for uncertain neutral systems with nonlinear parameter perturbations

The delay-dependent guaranteed cost control problem for uncertain neutral systems with nonlinear time-varying parameter perturbations is studied. By using a newly established integral inequality, the delay-dependent conditions for the existence of memoryless and memory state feedback guaranteed cost controllers are derived in terms of nonlinear matrix inequalities without involving model transformation and bounding technique for cross terms. An iterative algorithm involving convex optimisation is presented to solve these nonlinear matrix inequalities. A numerical example is given to demonstrate the effectiveness and superiority of the proposed results.

Guaranteed cost control for uncertain stochastic fuzzy systems with time delay

This paper studies a delay-dependent guaranteed cost control problem for a class of uncertain nonlinear stochastic systems with time delay represented by the Takagi-Sugeno (T-S) fuzzy model with uncertain parameters. The descriptor system method and Gu's inequality are employed to obtain delay-dependent sufficient conditions such that the closed-loop system is asymptotically stable with a certain guaranteed cost control performance. The effectiveness of the proposed method is shown by a simulation example.

Delay-dependent conditions for guaranteed cost observer-based control of uncertain neutral systems with time-varying delays

In this paper, delay-dependent guaranteed cost observer-based control for neutral systems with time-varying delays is considered. Control and observer gains will be given from the linear matrix inequality feasible solutions. Optimal guaranteed cost observer-based control which will minimize the guaranteed cost of the system is provided.

Delay-dependent guaranteed cost control for uncertain systems with state and input delays

The authors deal with the problem of delay-dependent guaranteed cost control for uncertain linear systems with time-varying delays in both the state and the input. The purpose of this is to design state-feedback controllers such that the resulting closed-loop system is robustly stable, and a specified linear integral-quadratic cost function has an upper bound for all delays in the given intervals. Two types of the time-varying delays are considered. Delay-dependent sufficient conditions for the solvability of the problem are developed in terms of matrix inequalities. By the cone complementary linearisation method, desired state-feedback controllers can be constructed. A numerical example is provided to demonstrate the applicability of the proposed method.

Delay-dependent and delay-independent guaranteed cost control for uncertain neutral systems with time-varying delays via LMI approach

This paper investigates the robust guaranteed cost control for a class of uncertain neutral system with time-varying delays. Based on Lyapunov–Krasovskii functional theory, some stabilization criteria are derived and guaranteed costs are given. Delay-dependent and delay-independent criteria are proposed for the stabilization of our considered systems. State feedback control is considered to stabilize the uncertain neutral system and upper bounds on the closed-loop cost function are given. Linear matrix inequality (LMI) approach and genetic algorithm (GA) are used to solve the stabilization problems. The optimal guaranteed cost control which will minimize the guaranteed cost for the system is provided. A procedure for the controller design is provided. Finally, two numerical examples are illustrated to show the use of our obtained results.

Delay-dependent nonfragile guaranteed cost control for nonlinear time-delay systems

This paper concerns the nonfragile guaranteed cost control problem for a class of nonlinear dynamic systems with multiple time delays and controller gain perturbations. Guaranteed cost control law is designed under two classes of perturbations, namely, additive form and multiplicative form. The problem is to design a memoryless state feedback control law such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Based on the linear matrix inequality (LMI) approach, some delay-dependent conditions for the existence of such controller are derived. A numerical example is given to illustrate the proposed method.

Delay-dependent robust guaranteed cost control of an uncertain linear system with state and input delay

This paper is concerned with the problems of robust stabilization and robust guaranteed cost control for linear systems with delays in both state and input subject to norm bounded parameter uncertainties. A delay-dependent design method (referred to delay-dependent design) is developed with guaranteed close-loop stability and cost for any delay no larger than a given bound and for all admissible uncertainties. A systematic approach via linear matrix inequalities (LMI) is proposed, and the control law can be computed using the standard LMI techniques.