ANALYSIS AND DESIGN OF ROBUST CONTROL FOR LINEAR PARAMETER-VARYING SYSTEMS

Gain-scheduling approach is a powerful tool but it only guarantees the local stability and performance for a slow varying system. Linear parameter varying (LPV) systems hence were developed to overcome this drawback. The LPV system is a linear system with parameter-dependent system matrices, which can be formulated from a nonlinear system via either approximation or function substitution. Three major control design methods includes linear fractional transformation, polytopic system design and gridding approach. All methods results in a convex optimization with either parameter-dependent or parameter-independent linear matrix inequalities (LMIs) and some conservatism may be introduced. Gridding based approach is the main focus in this research because it has no further assumptions about the structure and hence admits less conservatism. However, the number of samples for gridding approach grows up exponentially as the dimension of the problem increases. This drawback hence inspires the approach developed in this research. Several stability and performance conditions are introduced in this research and all controller syntheses arrive at optimization problems with parameter-dependent LMIs. Hence the objective of this research is to solve these problems. We present two methodologies to handle with generic LPV control systems. The first approach is to consider the problem in a stochastic framework so that the stability and performance are guaranteed in the stochastic sense. Two algorithms, i.e. polynomial chaos expansion and stochastic collocation, are used to formulate the convex optimization problems. The other method is to directly interpolate the parameter-dependent LMIs by sparse grid with Smolyak algorithm, which extremely reduces the amount of the sample points and successfully solve the infinite-dimensional optimization by the proposed algorithm. Two examples are shown to compare two proposed controllers with existing methods, where the benefits of the method we develop are shown and some limitations of the current methodologies are discussed