A Design Method of Robust Non - Fragile Guaranteed Cost Controllers for Linear Systems with Structured Uncertainties

This paper deals with a design problem of robust non-fragile stabilizing controllers with guaranteed cost for linearsystems with structured uncertainties. In this paper, we consider two classes of control gain perturbations and show thatsufficient conditions for the existence of the robust non-fragile guaranteed cost controller are given in terms of linearmatrix inequalities (LMIs). Additionally, a design method of optimal robust non-fragile guaranteed cost controllers whichminimize an upper bound on a given quadratic cost function is discussed. Finally, numerical examples are presented todemonstrate the effectiveness of the proposed robust non-fragile controller.This paper deals with a design problem of robust non-fragile stabilizing controllers with guaranteed cost for linearsystems with structured uncertainties. In this paper, we consider two classes of control gain perturbations and show thatsufficient conditions for the existence of the robust non-fragile guaranteed cost controller are given in terms of linearmatrix inequalities (LMIs). Additionally, a design method of optimal robust non-fragile guaranteed cost controllers whichminimize an upper bound on a given quadratic cost function is discussed. Finally, numerical examples are presented todemonstrate the effectiveness of the proposed robust non-fragile controller

Synthesis of Adaptive Robust Controllers for a Class of Nonlinear Systems with Input Saturations

This paper deals with a design problem of an adaptive robust controller for a class of nonlinear systems with specified input saturations. For the nonlinear system under consideration, the nonlinearity means unknown perturbations and satisfies the matching condition. In this paper, we show that sufficient conditions for the existence of the proposed adaptive robust controller giving consideration to input saturations are given in terms of linearmatrix inequalities (LMIs). Finally, simple illustrative examples are shown

Adaptive Gain Robust Control Strategies for Uncertain Dynamical Systems

In this chapter, adaptive gain robust control strategies for uncertain dynamical systems are presented. Firstly, synthesis of centralized adaptive gain robust controllers for a class of uncertain linear systems is shown. The design problem of the centralized controller is reduced to the constrained convex optimization problem, and allowable perturbation regions of unknown parameters are discussed. Next, the result for the centralized robust controller is extended to uncertain large-scale interconnected systems, that is, an LMI-based design approach for decentralized adaptive gain robust controllers is suggested

ℒ

We consider a design problem of a variable gain robust output feedback controller with guaranteed ℒ2 gain performance for a class of Lipschitz uncertain nonlinear systems. The proposed variable gain robust output feedback controller achieves not only robust stability but also a specified ℒ2 gain performance. In this paper, we show that sufficient conditions for the existence of the proposed variable gain robust output feedback controller with guaranteed ℒ2 gain performance are given in terms of linear matrix inequalities (LMIs). Finally, a simple numerical example is included

Synthesis of Adaptive Gain Robust Output Feedback Controllers for a Class of Lipschitz Nonlinear Systems with Unknown Upper Bound of Uncertainty

We propose a new adaptive gain robust output feedback controller for a class of the Lipschitz nonlinear systems with unknown upper bound of uncertainty. The proposed adaptive gain robust output feedback controller is designed so as to reduce the effect of uncertainties and Lipschitz nonlinearities. In this paper, we show that sufficient conditions for the existence of the proposed adaptive gain robust output feedback controller are reduced to LMI conditions. Finally, the effectiveness of the proposed robust output feedback controller is demonstrated by numerical simulations

A Robust Formation Control Strategy for Multi-Agent Systems with Uncertainties via Adaptive Gain Robust Controllers

This paper deals with a design problem of an adaptive gain robust controller which achieves consensus for multi-agent system (MAS) with uncertainties. In the proposed controller design approach, the relative position between the leader and followers are considered explicitly, and the proposed adaptive gain robust controller consisting of fixed gains and variable ones tuned by time-varying adjustable parameters can reduce the effect of uncertainties. In this paper, we show that sufficient conditions for the existence of the proposed adaptive gain robust controller are reduced to solvability of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed robust formation control system is verified by simple numerical simulations. A main result of this study is that the proposed adaptive gain robust controller can achieve consensus and formation control giving consideration to relative distance in spite of uncertainties

Synthesis of Formation Control Systems for Multi-Agent Systems under Control Gain Perturbations

This paper proposed a linear matrix inequality (LMI)-based design method of non-fragile guaranteed cost controllers for multi-agent systems (MASs) with leader-follower structures. In the guaranteed cost control approach, the resultant controller guarantees an upper bound on the given cost function together with asymptotical stability for the closed-loop system. The proposed non-fragile guaranteed cost control system can achieve consensus for MASs despite control gain perturbations. The goal is to develop an LMI-based sufficient condition for the existence of the proposed non-fragile guaranteed cost controller.  Moreover, a design problem of an optimal non-fragile guaranteed cost controller showe that minimizing an upper bound on the given quadratic cost function can be reduced to constrain a convex optimization problem. Finally, numerical examples were given to illustrate the effectiveness of the proposed non-fragile controller for MASs

A Point Memory State Observer with Adjustable Parameters for a Class of Uncertain Linear Systems with State Delays

In this paper, we present a point memory robust state observer with time-varying adjustable parameters for a class of uncertain linear systems with state delays. The point memory robust state observer proposed in this paper consists of fixed observer gain matrices and time-varying adjustable parameters, which are determined by updating rules. Sufficient conditions for the existence of the proposed point memory robust state observer can be reduced to solvability of LMIs. Finally, simple numerical examples are included to illustrate the effectiveness of the proposed robust state observer

Decreasing the Value of Specified Cost Function by Adaptive Controller Based on Modified ACLF for a Class of Nonlinear Systems

A new nonlinear adaptive control law for a class of uncertain nonlinear systems is proposed. The proposed control law is designed by a modified adaptive control Lyapunov function (ACLF) which satisfies a Hamilton-Jacobi-Bellman (HJB) equation. The modified ACLF is derived from transformation of an ACLF. The proposed control law is different from the inverse optimal one in decreasing the value of a cost function specified by a designer. In this paper, we show a transformation coefficient for an ACLF and a design method of a nonlinear adaptive controller. Finally, it is shown by a numerical simulation that the proposed control law decreases the value of a given cost function and achieves the desirable trajectory