Decentralized Stabilization of Interconnected Systems
In this chapter, we propose adaptive backstepping scheme to design decentralized output feedback adaptive controllers. For each subsystem, a general transfer function with arbitrary relative degree is considered. The interactions between subsystems are al
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In this chapter, we propose adaptive backstepping scheme to design decentralized output feedback adaptive controllers. For each subsystem, a general transfer function with arbitrary relative degree is considered. The interactions between subsystems are allowed to satisfy a nonlinear bound with certain structural conditions. The effects due to interactions are taken into consideration in devising local control laws. It is shown that perfect stabilization is ensured and the L2 norm of the system outputs is also shown to be bounded by a function of design parameters.
5.1 Introduction In practice, decentralized control, designed independently for local subsystems and using local available signals for feedback, is usually preferred for interconnected systems. In particular, decentralized adaptive control is employed as such systems usually face poor knowledge on the plant parameters and interactions between subsystems. However, only limited number of results are available due to the complexity of the problem, especially difficulties encountered in handling the effects of interconnections, see for examples [20, 22, 24, 25, 31, 32, 33, 96, 97, 98, 99]. In [22], the first result on decentralized adaptive control was reported, but only for subsystems with relative degrees less than or equal to two. In [20], the requirement on subsystem relative degrees was relaxed and unmodelled dynamics were considered at the expense of requiring information exchanging between subsystems. In [96], a structure condition was required and subsystem relative degrees still cannot exceed two. In [99, 100, 101], all conditions related to subsystem degrees, structure conditions and information exchanging between subsystems were relaxed. The relative degree condition was also relaxed by using the concept of high-order tuners in [102] and [103]. In [104], the subsystem relative degree condition with the control scheme in [22] was also relaxed. Research on decentralized adaptive control using backstpping approach has also received great attentions, due to a number of its advantages such as improving transient performance [1]. In [105], the first decentralized control result J. Zhou & C. Wen: Adapt. Backstepping Ctrl. of Uncertain Systems, LNCIS 372, pp. 65–79, 2008. c Springer-Verlag Berlin Heidelberg 2008 springerlink.com
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Decentralized Stabilization of Interconnected Systems
using such a technique was reported without requirement on subsystem relative degrees. More general class of systems with the consideration of unmodelled dynamics was studied in [32] and [33]. In this chapter, we address decentralized adaptive stabilization for a class of interconnected systems. The interactions between subsystems are unknown and allowed to satisfy a high order nonlinear bound. Due to output feedback, local filters are designed to estimate system states. We use the standard backstepping design approach without any modification to design decentralized adaptive controllers. It is shown that the designed controllers can globally stabilize the overall interconnect
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