In this paper, implicit controls are investigated for different classes of nonlinear systems, nonaffine systems in pure-feedback form and affine systems in strict-feedback form. While control system design for general unknown nonaffine nonlinear systems needs further investigation, elegant control designs are presented for known systems and systems with unknown scalar parametrization. Though fo...

Trajectory tracking of nonlinear dynamical systems with affine open-loop controls is investigated. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible. We introduce exactly realizable desired trajectories as these trajectories which can be tracked exactly by an appropriate control. Exactly realizable trajectories are characterized mat...

the subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called emph{affine subgroups.}~the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}o^{-}_...

In statistical control, the cost function is viewed as a random variable and one optimizes the distribution of the cost function through the cost cumulants. We consider a statistical control problem for a control-affine nonlinear system with a nonquadratic cost function. Using the Dynkin formula, the Hamilton–Jacobi–Bellman equation for the nth cost moment case is derived as a necessary conditi...

This work analyzes the overall computational complexity of the stochastic Galerkin finite element method (SGFEM) for approximating the solution of parameterized elliptic partial differential equations with both affine and non-affine random coefficients. To compute the fully discrete solution, such approaches employ a Galerkin projection in both the deterministic and stochastic domains, produced...

A deterministic optimal control problem is solved for a control-affine nonlin-ear system with a nonquadratic cost function. We algebraically solve the Hamilton-Jacobi equation for the gradient of the value function. This eliminates the need to explicitly solve the solution of a Hamilton-Jacobi partial differential equation. We interpret the value function in terms of the control Lyapunov functi...

This paper mainly investigates fuzzy control with affine T-S delayed models, which can be applied to some nonlinear systems. Motivated from performing the linearization process associated with distinct operating points for nonlinear systems, an affine T-S fuzzy model with delayed state is addressed. The overall control then can be performed by the fuzzy inference mechanism, in which the consequ...