Suboptimal Guaranteed Cost Controller Research Articles

Switching design for suboptimal guaranteed cost control of 2-D nonlinear switched systems in the Roesser model

This paper deals with the problem of switching design for guaranteed cost control of discrete-time two-dimensional (2-D) nonlinear switched systems described by the Roesser model. The switching signal, which determines the active mode of the system, is subject to a state-dependent process whose values belong to a finite index set. By using 2-D common Lyapunov function approach, a sufficient condition expressed in terms of tractable matrix inequalities is first established to design a min-projection switching rule that makes the 2-D switched system asymptotically stable. The obtained result on stability analysis is then utilized to synthesize a suboptimal state feedback controller that minimizes the upper bound of a given infinite-horizon cost function. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.

Guaranteed cost control design for delayed teleoperation systems

A procedure for guaranteed cost control design of delayed linear bilateral teleoperation systems with nonlinear external forces is proposed. The assumption that the external forces are nonlinear functions of velocities and/or positions of local devices, and one part of these forces satisfies a sector condition has been made. A virtual tool system is introduced to ‘observe’ the forces at the remote sides, the position and velocity information of the master, the slave and the virtual tool are feedbacked to the controllers, hence the proposed control scheme actually has a four-channel architecture. A delay-dependent stability criterion is formulated, and then a sub-optimal guaranteed cost controller is obtained by solving a convex optimization problem in the form of linear matrix inequalities (LMIs). The behavior of the resulting teleoperation system is illustrated in simulations.

Guaranteed cost control of linear uncertain discrete-time impulsive systems

The guaranteed cost control problem for a class of linear uncertain discrete-time impulsive systems is considered. The parametric uncertainties are assumed to be time-varying and norm-bounded. The problem is to design a robust state feedback controller such that the resulting closed-loop system is robustly exponentially stable, and the closed-loop value of a specified quadratic cost function is not more than a certain upper bound for all admissible uncertainties and for all admissible impulse time sequences. A sufficient condition for the existence of guaranteed cost state feedback controllers is derived via a time-varying Lyapunov function approach. This condition is expressed in terms of linear matrix inequalities. Furthermore, the problem of selecting a suboptimal guaranteed cost controller is formulated as a convex optimization problem. An example is provided to demonstrate the effectiveness of the proposed results.

Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.

LMI Approach to Suboptimal Guaranteed Cost Control for 2-D Discrete Uncertain Systems

This paper studies the problem of the guaranteed cost control via static-state feedback controllers for a class of two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model with norm bounded uncertainties. A convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the suboptimal guaranteed cost controller which ensures the quadratic stability of the closed-loop system and minimizes the associated closed-loop cost function. Application of the proposed controller design method is illustrated with the help of one example.

Guaranteed cost repetitive control for uncertain discrete-time systems

This paper considers the problem of guaranteed cost repetitive control for uncertain discrete-time systems. The uncertainty in the system is assumed to be norm-bounded and time-varying. The objective is to develop a novel design method for the repetitive control systems by introducing a robust output feedback controller so that the closed-loop system is quadratically stable and a certain bound of performance index is guaranteed for all admissible uncertainties. Necessary and sufficient conditions for the existence of such controllers are derived in terms of linear matrix inequality (LMI). A suboptimal guaranteed cost controller is obtained by solving an optimization problem with LMI constraints. Finally, a simulation example is provided to illustrate the validity of the proposed method.

Suboptimal reliable guaranteed cost control for continuous-time systems with multi-criterion constraints

The suboptimal reliable guaranteed cost control (RGCC) with multi-criterion constraints is investigated for a class of uncertain continuous-time systems with sensor faults. A fault model in sensors, which considers outage or partial degradation of sensors, is adopted. The influence of the disturbance on the quadratic stability of the closed-loop systems is analyzed. The reliable state-feedback controller is developed by a linear matrix inequalities (LMIs) approach, to minimize the upper bound of a quadratic cost function under the conditions that all the closed-loop poles be placed in a specified disk, and that the prescribed level of H∞ disturbance attenuation and the upper bound constraints of control inputs’ magnitudes be guaranteed. Thus, with the above multi-criterion constraints, the resulting closed-loop system can provide satisfactory stability, transient property, a disturbance rejection level and minimized quadratic cost performance despite possible sensor faults.

A Galerkin/Neural-Network-Based Design of Guaranteed Cost Control for Nonlinear Distributed Parameter Systems

This paper presents a Galerkin/neural-network- based guaranteed cost control (GCC) design for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities. A parabolic PDE system typically involves a spatial differential operator with eigenspectrum that can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement. Motivated by this, in the proposed control scheme, Galerkin method is initially applied to the PDE system to derive an ordinary differential equation (ODE) system with unknown nonlinearities, which accurately describes the dynamics of the dominant (slow) modes of the PDE system. The resulting nonlinear ODE system is subsequently parameterized by a multilayer neural network (MNN) with one-hidden layer and zero bias terms. Then, based on the neural model and a Lure-type Lyapunov function, a linear modal feedback controller is developed to stabilize the closed-loop PDE system and provide an upper bound for the quadratic cost function associated with the finite-dimensional slow system for all admissible approximation errors of the network. The outcome of the GCC problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal guaranteed cost controller in the sense of minimizing the cost bound is obtained. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.

Guaranteed cost control with constructing switching law of uncertain discrete-time switched systems

A guaranteed cost control problem for a class of linear discrete-time switched systems with norm-bounded uncertainties is considered in this article. The purpose is to construct a switching rule and design a 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 under the constructed switching rule. A sufficient condition for the existence of guaranteed cost controllers and switching rules is derived based on the Lyapunov theory together with the linear matrix inequality (LMI) approach. Furthermore, a convex optimization problem with LMI constraints is formulated to select the suboptimal guaranteed cost controller. A numerical example demonstrates the validity of the proposed design approach.

Networked, guaranteed cost control for a class of industrial processes with state delay

AbstractThis paper addresses a class of industrial processes with state delay and controlled over communication networks. With consideration of network‐induced delay and data packet dropout, a model is proposed for networked control systems (NCSs). With the introduction of free weighting matrices, a method for suboptimal guaranteed cost controller design is proposed in the form of matrix inequalities. A nonconvex minimization problem is then formulated for finding suboptimal allowable equivalent delay bound (SAEDB) and the feedback gain of a memoryless controller. The proposed method is demonstrated through networked injection velocity control in thermoplastic injection molding. Copyright © 2007 Curtin University of Technology and John Wiley & Sons, Ltd.

Robust guaranteed cost control for descriptor systems with Markov jumping parameters and state delays

AbstractThis paper deals with robust guaranteed cost control for a class of linear uncertain descriptor systems with state delays and jumping parameters. The transition of the jumping parameters in the systems is governed by a finite-state Markov process. Based on stability theory for stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost controllers is derived. In terms of the LMI (linear matrix inequality) approach, a linear state feedback controller is designed to stochastically stabilise the given system with a cost function constraint. A convex optimisation problem with LMI constraints is formulated to design the suboptimal guaranteed cost controller. A numerical example demonstrates the effect of the proposed design approach.

LMI approach to suboptimal guaranteed cost control for uncertain time-delay systems

Results on the design of robust memoryless state feedback controllers for uncertain time-delay systems with norm bounded uncertainty are presented. It is proved that the feasibility of a linear matrix inequality (LMI) problem is necessary and sufficient for the quadratic stabilisation of an uncertain time-delay system. A robust state feedback controller can be constructed using the corresponding feasible solution of the LMI problem. A procedure is given to select a suitable state feedback controller that is also suboptimal in the sense of minimising a bound on a quadratic performance index.