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This paper presents a novel extended modal series method for solving the infinite horizon optimal control problem of nonlinear interconnected largescale dynamic systems. In this method, the infinite horizon nonlinear largescale two-point boundary value problem (TPBVP), derived from Pontryagin's maximum principle, is transformed into a sequence of linear time-invariant TPBVPs. Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of a uniformly convergent series. Moreover, in special cases, the proposed procedure facilitates the application of parallel processing, which improves its computational efficiency. In this study, an iterative algorithm is also presented, which has a low computational complexity and a fast convergence rate. Just a few iterations are required to obtain a suboptimal trajectory-control pair. Finally, effectiveness of the proposed approach is verified by solving the optimal attitude control problem.

In this paper, qualitative and quantitative differences between nonlinear and linear modal simulations in stressed power system are presented. For the first time in the literature, timedomain nonlinear simulation is used to validate the accuracy of the second order modal model, obtained by using modal series. Furthermore three new selective indices are defined and used to explain and predict the differences between nonlinear and linear modal simulations. These indices also explain the under or over damping results being experienced when a linear system theory designed controller is applied to a nonlinear system.

The position control of a class of servomotors is addressed in this paper via a novel adaptive fuzzy PI sliding mode control. The premise and the consequence parts of the fuzzy rules are tuned with adaptive schemes. To attenuate chattering effectively the discontinuous control is approximated by an adaptive PI control structure. Moreover, the bound of the discontinuous control term is assumed unknown and an adaptive mechanism is used to estimate this bound. All adaptive laws are derived via Lyapunov synthesis method, thereby guaranteeing the closed-loop stability. The proposed approach has the added advantage that for external disturbances it only requires a bound to exist, without needing to know the magnitude of this bound. The proposed controller is applied to control a model of uncertain induction servomotor subject to significant disturbances and a model of DC servomotor with unknown parameters and uncertainty in load condition. Analysis of simulations reveals the effectiveness of the proposed method in controlling servomotors in terms of significant reduction in chattering while maintaining asymptotic convergence.

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