We consider a Bolza type optimal control problem of the form [see formula in PDF] Subject to: where Λ( s , y u ) is locally Lipschitz just Borel ( ), b has at most linear growth and both Lagrangian Λ end-point cost function g may take value +∞. If ≡ 1, 0, P t, x classical Calculus Variations. suppose validity slow condition introduced by Clarke 1993, including Lagrangians superlinear case. show...

This paper considers an LG–Holling type II diseased predator ecosystem with Lévy noise and white noise. In this prey–predator system, assuming that the predator population is infected by disease and divided into two classes: susceptible predator and infected predator, we show that the system has a unique global positive solution. We investigate the persistence in the mean and extinction for the...

The direct adaptive dynamic regulation of unknown nonlinear multi variable systems is investigated in this chapter in order to address the problem of controlling non-Brunovsky and non-square systems with control inputs less than the number of states. The proposed neuro-fuzzy model acts as a universal approximator. While with the careful selection of a Lyapunov-like function, the authors prove t...

Global existence is established for classical solutions to a chemotaxis model with signal-dependent motility general class of functions γ which may in particular decay an arbitrary way at infinity. Assuming further that non-increasing and decays sufficiently slowly infinity, the sense γ(s)∼s−k as s→∞ some k∈(0,N/(N−2)+), it also shown global are uniformly bounded respect time. The admissible in...

Prediction-based Iterative Learning Control (PILC) is proposed in this paper for a class of time varying nonlinear uncertain systems. Convergence of PILC is analyzed and the uniform boundedness of tracking error is obtained in the presence of uncertainty and disturbances. It is shown that the learning algorithm not only guarantees the robustness, but also improves the learning rate despite the ...

This paper considers the controllability and Riesz basis generation property of linear infinite dimensional systems with group generators and one-dimensional admissible input operators. The corresponding results of [Advances in Mathematical Systems Theory, 2000, pp. 221-242] under the assumption of algebraic simplicity for eigenvalues of the generator are generalized to the case in which the ei...