Abstract
Recently, the nonlinear H-infinity control schemes have beenintroduced to deal with the robust performance design problem ofnonlinear systems. However, the designer has to solve aHamilton-Jacobi equation, which is a nonlinear partialdifferential equation. Only some very special nonlinearsystems have a closed form solution. In general, conventional nonlinearH-infinity control schemes are not suitable for practicalcontrol system design. Based on the Takagi and Sugeno (TS) fuzzymodel, both state feedback and output feedback decentralizedfuzzy tracking control designs with a guaranteed H-infinitytracking performance will be addressed in this dissertation for amulti-arm system. A fuzzy observer-based control design will beemployed to deal with the output feedback control problem. By theproposed method, the outcome of the fuzzy tracking control designproblem can be parameterized in terms of a linear matrixinequality problem (LMIP) or an eigenvalue problem (EVP). TheLMIP or EVP can be solved very efficiently using the convexoptimization techniques. Systematical design procedure using LMItechniques is proposed to implement the H-infinity fuzzytracking control problems. The results of the proposedH-infinity decentralized fuzzy tracking controller are appliedto a multi-arm system. The main results are summarized asfollows: First, this dissertation introduces a fuzzy controldesign method for nonlinear systems with a guaranteedH-infinity model reference tracking performance. First, theTakagi and Sugeno (TS) fuzzy model is employed to approximate anonlinear system. Next, based on the fuzzy model, a fuzzycontroller is developed to reduce the tracking error as small aspossible for all bounded reference inputs. If the state variablesare unavailable, a fuzzy observer-based tracking control designis also developed. The advantage of proposed tracking controldesign is that only a simple linear fuzzy controller is used inour approach without complicated feedback linearization techniqueand adaptive scheme. By the proposed method, the fuzzy trackingcontrol design problem is parameterized in terms of a linearmatrix inequality problem (LMIP). The LMIP can be solved veryefficiently using the convex optimization techniques. Simulationexamples are given to illustrate the design procedures andtracking performance of the proposed method. Second, it is noteasy to design an H-infinity decentralized controller fornonlinear interconnected systems in general. In thisdissertation, the tracking control problem of nonlinearinterconnected systems is studied via H-infinity decentralizedfuzzy control method. Similarly, the nonlinear interconnectedsystem is represented by an equivalent Takagi-Sugeno type fuzzymodel. A state feedback decentralized fuzzy control scheme isdeveloped to achieve the H-infinity tracking performance.Furthermore, the stability of the nonlinear interconnectedsystems is also guaranteed. This design problem is equivalent tosolving an eigenvalue problem (EVP). Third, due to the physicalconfiguration and high dimensionality of the constrainedmultibody systems, a centralized fuzzy control is neitherefficient nor even necessary. Therefore, a decentralized fuzzycontrol scheme is more suitable for the constrained multibodysystems. In this dissertation, an H-infinity decentralized fuzzytracking control scheme is proposed for a constrained multibodysystem. Finally, in order to illustrate the design effectivenessof the proposed H-infinity decentralized fuzzy tracking controlscheme, an experimental multi-arm system with fully digitalcontroller is setup to confirm the tracking performance.