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

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 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

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

Synthesis of Adaptive Gain Robust Controllers for Polytopic Uncertain Systems

We present a new adaptive gain robust controller for polytopic uncertain systems. The proposed adaptive gain robust controller consists of a state feedback law with a fixed gain and a compensation input with adaptive gains which are tuned by updating laws. In this paper, we show that sufficient conditions for the existence of the proposed adaptive gain robust controller are given in terms of LMIs. Finally, illustrative examples are presented to show the effectiveness of the proposed adaptive gain robust controller

Consensus via Adaptive Gain Controllers Considering Relative Distances for Multi-Agent Systems

In this paper, for multi-agent systems (MASs) with leader-follower structures, we present a linear matrix inequality (LMI)-based design method of an adaptive gain controller considering relative distances between agents. The proposed adaptive gain controller consists of fixed gains and variable ones tuned by time-varying adjustable parameters. The objective of this paper is to derive enough conditions for the existence of the proposed adaptive gain controller which achieves consensus for each agent. The advantages of the proposed adaptive gain controller are as follows; The proposed controller can be obtained by solving LMI, and the proposed control system can achieve consensus and formation control, even if uncertainties are included in the information for relative distances. In this paper, we show that the design problem of the proposed adaptive gain controller can be reduced to the solvability of LMI. Finally, simple numerical examples are included to illustrate the effectiveness of the proposed adaptive gain controller for MASs

Achieving LDL cholesterol target levels <1.81 mmol/L may provide extra cardiovascular protection in patients at high risk: Exploratory analysis of the Standard Versus Intensive Statin Therapy for Patients with Hypercholesterolaemia and Diabetic Retinopathy study

Aims To assess the benefits of intensive statin therapy on reducing cardiovascular (CV) events in patients with type 2 diabetes complicated with hyperlipidaemia and retinopathy in a primary prevention setting in Japan. In the intension-to-treat population, intensive therapy [targeting LDL cholesterol = 2.59 to = 100 to = 2.59 to <3.10 mmol/L in patients with hypercholesterolaemia and diabetic retinopathy

Synthesis of Decentralized Variable Gain Robust Controllers with Guaranteed L2 Gain Performance for a Class of Uncertain Large-Scale Interconnected Systems

We consider a design problem of a decentralized variable gain robust controller with guaranteed L2 gain performance for a class of uncertain large-scale interconnected systems. For the uncertain large-scale interconnected system, the uncertainties and the interactions satisfy the matching condition. In this paper, we show that sufficient conditions for the existence of the proposed decentralized variable gain robust controller with guaranteed L2 gain performance are given in terms of linear matrix inequalities (LMIs). Finally, simple illustrative examples are shown

Synthesis of Decentralized Variable Gain Robust Controllers for Large-Scale Interconnected Systems with Structured Uncertainties

In this paper, we propose a decentralized variable gain robust controller which achieves not only robust stability but also satisfactory transient behavior for a class of uncertain large-scale interconnected systems. For the uncertain large-scale interconnected system, the uncertainties and the interactions satisfy the matching condition. The proposed decentralized robust controller consists of a fixed feedback gain controller and a variable gain one determined by a parameter adjustment law. In this paper, we show that sufficient conditions for the existence of the proposed decentralized variable gain robust controller are given in terms of LMIs. Finally, a simple numerical example is included