Stabilization of Uncertain Non-Bilinear Descriptor Dynamical System Via Logarithmic Norm Approach

In this paper a feedback controller stabilization of non-bilinear descriptor system have been developed via logarithmic norm approach. The sufficient conditions on parametric uncertainty where the system is regular or impulse free have been given. Some theoretical results supported have been adopted with suitable illustrations example for designing a stabilizing controller for non-bilinear uncertain descriptor systems based on the theoretical result have also been developed.nbsp nbs

Approximate Solutions for Optimal Control of Fixed Boundary Value Problems Using Variational and Minimum Approaches

The optimal control is the process of finding a control strategy that extreme some performance index for a dynamic system (partial differential equation) over the class of admissibility. The present work deals with a problem of fixed boundary with a control manipulated in the structure of the partial differential equation. An attractive computational method for determining the optimal control of unconstrained linear dynamic system with a quadratic performance index is presented. In the proposed method the difference between every state variable and its initial condition is represented by a finite - term polynomial series, this representation leads to a system of linear algebraic equations which represents the necessary condition of optimality. The linear algebraic system is solved by using two approaches namely the variational iteration method and the minimization approach for unconstrained optimization problem with estimation of gradient and Hessian matrix. These approaches are illustrated by two application examples

Results On Strongly Continuous Semigroup

Some results of strongly continuous semigroup (-semigroup) of functional analysis ofnbsp bounded linear operator defining on a separable Banachnbsp spaces like hypercyclic, topologically transitive, chaotic, mixing, weekly mixing and topologically ergrodic have been discussed. The generalization ofnbsp hypercyclic, topologically transitive, chaotic, mixing, weakly mixingnbsp and topologically ergrodic for the direct sum of two and /or hence to n -semigroup strongly continuous dynamicnbsp system of semigroups in infinite dimensional separable Banach space have been developed with proofs and discusses

Output-Feedback Stochastic Nonlinear Stabilization and Inverse Optimality

Output-feedback (observer-based) robust and optimal control law which guarantees global (local) asymptotic stability in probability for nonlinear stochastic dynamic system are stated, developed and proved with the help of stochastic Lyapunov function approach supported by necessary theorems and an illustrative example. The inverse optimal stabilization in probability with suitable performance index has also been stated and developed