A new controller design method for nonaffine nonlinear dynamic systems is presented in this paper. An identified neural network model of the nonlinear plant is used in the proposed method. The method is based on a new control law that is developed for any discrete deterministic time-invariant nonlinear dynamic system in a subregion Phi(x) of an asymptotically stable equilibrium point of the plant. The performance of the control law is not necessarily dependent on the distance between the current state of the plant and the equilibrium state if the nonlinear dynamic system satisfies some mild requirements in Phi(x). The control law is simple to implement and is based on a novel linearization of the input-output model of the plant at each instant in time. It can be used to control both minimum phase and nonminimum phase nonaffine nonlinear plants. Extensive empirical studies have confirmed that the control law can be used to control a relatively general class of highly nonlinear multiinput-multioutput (MIMO) plants.

Assuming small input signal magnitudes, ARMA models can approximate the NARMA model of nonaffine plants. Recently, NARMA-L1 and NARMA-L2 approximate models were introduced to relax such input magnitude restrictions. However, some applications require larger input signals than allowed by ARMA, NARMA-L1 and NARMA-L2 models. Under certain assumptions, we recently developed an affine approximate model that eliminates the small input magnitude restriction and replaces it with a requirement of small input changes. Such a model complements existing models. Using this model, we present an adaptive controller for discrete nonaffine plants with unknown system equations, accessible input-output signals, but inaccessible states. Our approximate model is realized by a neural network that learns the unknown input-output map online. A deadzone is used to make the weight update algorithm robust against modeling errors. A control law is developed for asymptotic tracking of slowly varying reference trajectories.

A problem of feedback stabilization of hybrid systems with time-varying delay and Markovian switching is considered. Sufficient conditions for stability based on linear matrix inequalities (LMIs) for stochastic asymptotic stability is obtained. The stability result depended on the mode of the system and of delay-independent. The robustness results of such stability concept against all admissible uncertainties are also investigated. An example is given to demonstrate the obtained results.

Larger and more powerful space based instruments are needed to meet increasingly sophisticated scientific demand. To support this need, concepts for telescopes with apertures of 100 meters are

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