Sliding mode control approaches are developed to stabilize a class of linear uncertain fractional-order dynamics. After making\ud
a suitable transformation that simplifies the sliding manifold design, two sliding mode control schemes are presented. The\ud
first one is based on the conventional discontinuous first-order sliding mode control technique. The second scheme is based\ud
on the chattering-free second-order sliding mode approach that leads to the same robust performance but using a continuous\ud
control action. Simple controller tuning formulas are constructively developed along the paper by Lyapunov analysis. The\ud
simulation results confirm the expected performance
In this paper, a solution procedure for a class of optimal control problems involving distributed parameter systems described by a generalized, fractional-order heat equation is presented. The first step in the proposed procedure is to represent the original fractional distributed parameter model as an equivalent system of fractional-order ordinary differential equations. In the second step, the necessity for solving fractional Euler-Lagrange equations is avoided completely by suitable transformation of the obtained model to a classical, although infinite-dimensional, state-space form. It is shown, however, that relatively small number of state variables are sufficient for accurate computations. The main feature of the proposed approach is that results of the classical optimal control theory can be used directly. In particular, the well-known "linear-quadratic" (LQR) and "BangBang" regulators can be designed. The proposed procedure is illustrated by a numerical example.
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