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

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

Observer-Based Quadratic Guaranteed Cost Control for Linear Uncertain Systems with Control Gain Variation

This study proposes a method for designing observer-based quadratic guaranteed cost controllers for linear uncertain systems with control gain variations. In the proposed approach, an observer is designed, and then a feedback controller that ensures the upper bound on the given quadratic cost function is derived. This study shows that sufficient conditions for the existence of the observer-based quadratic guaranteed cost controller are given in terms of linear matrix inequalities. A sub-optimal quadratic guaranteed cost control strategy is also discussed. Finally, the effectiveness of the proposed controller is illustrated by a numerical example. The result shows that the proposed controller is more effective than conventional methods even if system uncertainties and control gain variations exist