Cost Control Of Linear Systems Research Articles

Static-feedback guaranteed cost control for linear systems with outage and loss of effectiveness actuator faults

This paper investigates the static-feedback guaranteed cost control problem for linear systems with actuator faults including outage and loss of effectiveness. Under the actuator redundancy condition, theoretical analysis shows that a static-feedback guaranteed cost controller can always be well designed to ensure that the resulting closed-loop system is stable with desirable quadratic performance. In particular, the feedback gain can be determined through the solution of a modified algebraic Riccati equation. Furthermore, extension to the system with uncertainties is further studied. Compared with the dynamic feedback controller, the static-feedback controller consists only of logical gates/modules and it does not require any memory element, and hence it is simplest in a design perspective. Different from the existing results, the severe and time-varying actuator outage faults can be handled very well by the proposed control strategy. Finally, simulation on a linearised reduced-order aircraft system is provided for verifying the theoretical results.

Dynamic output feedback guaranteed cost control for linear systems with interval time-varying delays in states and outputs

This paper addresses the dynamic output feedback guaranteed cost control problem of a class of time-delay systems where the state and output contain interval non-differentiable time-varying delays. The proposed controller uses only the delayed output measurement to stabilize the closed-loop system and guarantee an adequate level of system performance. By constructing a set of multiple Lyapunov–Krasovskii functionals which include triple-integral terms, a new criterion for the existence of dynamic output feedback guaranteed cost controllers is established and expressed in terms of linear matrix inequality (LMI). A numerical example is given to illustrate the obtained results.

Optimal Guaranteed Cost Control of Linear Systems with Mixed Interval Time-Varying Delayed State and Control

This paper deals with the problem of optimal guaranteed cost control for linear systems with interval time-varying delayed state and control. The time delay is assumed to be a continuous function belonging to a given interval, but not necessary to be differentiable. A linear–quadratic cost function is considered as a performance measure for the closed-loop system. By constructing a set of augmented Lyapunov–Krasovskii functional combined with Newton–Leibniz formula, a guaranteed cost controller design is presented and sufficient conditions for the existence of a guaranteed cost state-feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

Guaranteed cost control of linear systems with distributed delays: A complete type functionals approach

The design of a control law guaranteeing an upper bound on the performance index of linear systems with point wise and distributed delay is addressed. The control law is computed through an iterative procedure: at each step, it is the solution that minimizes the Bellman type equation obtained from plugging in the functional of complete type associated to the closed loop system of the previous step. It is shown that at each step, the closed loop system remains into the class of systems with distributed delays, the stability of the closed loop is maintained, and the guaranteed cost does not increase. The allowed continuous time varying norm bounded uncertainties guaranteeing the cost are also characterized. An illustrative example validates the approach.

Dynamic output-feedback guaranteed cost control for linear systems with uniform input quantization

There have existed the researches on guaranteed cost control for systems with the dynamic or logarithmic quantizer; however, intensive studies not only on continuous-time output-feedback linear systems with uniform input quantization but also on guaranteed cost control for such systems have not been carried out thus far. This paper first solves the problem of guaranteeing the linear quadratic (LQ) cost for continuous-time output-feedback linear systems with uniform input quantization. The proposed output-feedback controller comprises the main and the additional control parts. The former part is designed as a linear dynamic output-feedback controller for determining the fundamental characteristics of the system associated with the LQ cost, and the latter part is constructed as an integer multiple of the quantization level for eliminating the effect of uniform input quantization. The additional control part adopts the state estimate instead of the state itself, which causes the state estimation errors. By computing their quantity added to the upper bound of the LQ cost, this paper shows that the proposed controller still guarantees the LQ cost despite the state estimation errors.

Guaranteed cost control of linear systems over networks with state and input quantisations

The guaranteed cost control design for linear systems connected over a common digital communication network is addressed. A new model is proposed that takes into consideration the effect of both the quantisation levels and the network conditions. A control design criterion is derived on the basis of the Lyapunov functional method and the idea of the cone complementary linearisation algorithm. A numerical example is given to show the application of the method proposed.

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.

Minimax Guaranteed Cost Control for Linear Systems with Large Uncertain Parameters - Riccati Equation Approach

Given a linear system with large but bounded time-varying uncertainty and a quadratic cost criterion, the Minimax Guaranteed Cost Control (MGCC) robust design method proposed in this paper results in a simple linear feedback control law to guarantee both the asymptotic stability of the closed-loop system and the minimized maximal performance bound over all possible parameter perturbations. A comparative study of two illustrative examples show the improvements and advantages of the proposed method over previous ones.

Inverse Problem for Linear Systems Containing Uncertain Parameters

The concept of fuzzy dynamic programming and of guaranteed cost control initiated by Chang is applied to the inverse problem of guaranteed cost control for linear systems containing uncertain parameters. Obtained, for a class of linear systems with uncertain parameters, is a frequency-domain criterion which, analogous to that for the deterministic system, is sufficient for the control law to be of guaranteed cost type. The author presents an iterative method which, if convergent, enables one to solve the inverse problem for the general linear systems.