| We present an approach for constructing optimal feedback control laws for regulation of a rotating rigid spacecraft. We employ the inverse optimal control approach which circumvents the task of solving a Hamilton-Jacobi equation and results in a controller optimal with respect to a meaningful cost functional. The inverse optimality approach requires the knowledge of a control Lyapunov functio...

Nonlinear PI and PID controllers combining time-(sub)optimality with linear control robustness and antiwindup properties are proposed for first-order and second-order integrator systems, without assuming that the control lower-bound and upper-bound are the opposite of each other. A complementary contribution is the introduction of an integral action with anti-windup properties into the control ...

The analysis of heat conduction through a solid with heat generation leads to a linear matrix differential equation with separated boundary conditions. We present a symmetric second order exponential integrator for the numerical integration of this problem using the imbedding formulation. An algorithm to implement this explicit method in an efficient way with respect to the computational cost o...

We use the idea of nonstandard finite difference methods to derive the discrete variational integrators for multisymplectic PDEs. We obtain a nonstandard finite difference variational integrator for linear wave equation with a triangle discretization and two nonstandard finite difference variational integrators for the nonlinear Klein-Gordon equation with a triangle discretization and a square ...

In this paper, a novel nonlinear hierarchical controller for attitude control is proposed. This controller is obtained using Lyapunov methodology. Model uncertainties in the system are estimated on-line based on a time-delay control approach. The robustness of the flight controller is enhanced using an anti-windup integrator technique and semi-global asymptotical stability is proven. The contro...

The problem of tracking control of nonlinear systems whose the zero dynamics are unstable is addressed in this paper. It is shown that, using a novel cascade structure where the backstepping approach is given to stabilise the internal dynamics and the standard input output linearization to stabilise the external dynamics. Assuming high-gain feedback for the external dynamics, a stability analys...

We introduce two new tools that can be useful in nonlinear observer and output feedback design. The first one is a simple extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability and robustness for a homogeneous in the bi-limit vector field. The ...

We investigate the finite-time consensus problem for heterogeneous multi-agent systems composed of first-order and second-order agents. A novel continuous nonlinear distributed consensus protocol is constructed, and finite-time consensus criteria are obtained for the heterogeneous multi-agent systems. Compared with the existing results, the stationary and kinetic consensuses of the heterogeneou...

This paper illustrates the potential of nonlinear model-based control applied for stabilization of unstable flow in oil wells. A simple empirical model is developed that describes the qualitative behavior of the downhole pressure during severe riser slugging. A nonlinear controller is designed by an integrator backstepping approach, and stabilization for open-loop unstable pressure setpoints is...